I’ve officially counted to infinity! [on hold]Mysterious Murder Mystery 3Man’s Best FriendThe Infinite CreekLet's help Sherlock, shall we?The Djinni, the Marid and the Oracle (working title) :PHow was the math test?A death at a restaurantEveryone knows bullets are magnetically pulled to anyone who's about to retireThe shrink and his patient (Part 1)A locked room puzzle
How long would it take for people to notice a mass disappearance?
Can I use a fetch land to shuffle my deck while the opponent has Ashiok, Dream Render in play?
Should I dumb down my writing in a foreign country?
Something that can be activated/enabled
Find the cheapest shipping option based on item weight
Should I mention being denied entry to UK due to a confusion in my Visa and Ticket bookings?
Does it make sense for a function to return an rvalue reference?
Shutter speed -vs- effective image stabilisation
Python 3 - simple temperature program
How can internet speed be 10 times slower without a router than when using a router?
Why do people keep telling me that I am a bad photographer?
ZSPL language, anyone heard of it?
How to write a 12-bar blues melody
How to adjust tikz picture so it fits to current size of a table cell?
What does this wavy downward arrow preceding a piano chord mean?
What is the solution to this metapuzzle from a university puzzling column?
Proving n+1 th differential as zero given lower differentials are 0
I'm in your subnets, golfing your code
Can my 2 children 10 and 12 Travel to the USA on expired American Passports? They are US citizens
Word meaning as function of the composition of its phonemes
Upside-Down Pyramid Addition...REVERSED!
Flatness of submodules of free modules
Understanding trademark infringements in a world where many dictionary words are trademarks?
Do I add modifiers to the Charisma check roll of 15 granted by the Glibness spell?
I’ve officially counted to infinity! [on hold]
Mysterious Murder Mystery 3Man’s Best FriendThe Infinite CreekLet's help Sherlock, shall we?The Djinni, the Marid and the Oracle (working title) :PHow was the math test?A death at a restaurantEveryone knows bullets are magnetically pulled to anyone who's about to retireThe shrink and his patient (Part 1)A locked room puzzle
$begingroup$
Sarah called me today and explained that she had counted to infinity. I shrugged and said it was impossible. She said that since I didn’t believe her, she would do it again, and this time in only ten minutes. I thought it was impossible but she did it right before my eyes!
How did Sarah count to infinity in only ten minutes?
Hints
Sarah started slow, but as time went on she got incredibly fast!
Clarifications
Sarah indeed counted all the way to infinity. She provided mathematical proof that she could count any infinite set, to include $א_0$, in any finite time span.
mathematics knowledge story situation
asked Apr 29 at 23:25
PerpetualJPerpetualJ
4,248648
$endgroup$
put on hold as off-topic by Rand al'Thor, w l, athin, Glorfindel, noedne 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question may invite speculative answers, as the question is not fully defined. The validity of some answers may be based upon opinion. Good questions for this site have a limited number of objectively correct answers. See also: Why are questions off-topic if they invite answers which are not demonstrably correct, or are otherwise speculative?" – Rand al'Thor, w l, athin, Glorfindel, noedne
|
show 14 more comments
$begingroup$
Sarah called me today and explained that she had counted to infinity. I shrugged and said it was impossible. She said that since I didn’t believe her, she would do it again, and this time in only ten minutes. I thought it was impossible but she did it right before my eyes!
How did Sarah count to infinity in only ten minutes?
Hints
Sarah started slow, but as time went on she got incredibly fast!
Clarifications
Sarah indeed counted all the way to infinity. She provided mathematical proof that she could count any infinite set, to include $א_0$, in any finite time span.
mathematics knowledge story situation
asked Apr 29 at 23:25
PerpetualJPerpetualJ
4,248648
$endgroup$
put on hold as off-topic by Rand al'Thor, w l, athin, Glorfindel, noedne 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question may invite speculative answers, as the question is not fully defined. The validity of some answers may be based upon opinion. Good questions for this site have a limited number of objectively correct answers. See also: Why are questions off-topic if they invite answers which are not demonstrably correct, or are otherwise speculative?" – Rand al'Thor, w l, athin, Glorfindel, noedne
1
$begingroup$
@MrPie All the way to infinity!
$endgroup$
– PerpetualJ
Apr 29 at 23:40
9
$begingroup$
This question feels a bit too broad. Are you sure there's one demonstrably correct answer to this one?
$endgroup$
– PiIsNot3
Apr 30 at 0:29
4
$begingroup$
An appropriate question for your username, @PerpetualJ.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 0:59
13
$begingroup$
My concern is that there may be more than one valid answer, and without specifying further restrictions, the “correct” one becomes an arbitrary choice. There’s already many good answers that could potentially be correct, which feeds into my concern
$endgroup$
– PiIsNot3
Apr 30 at 4:06
5
$begingroup$
@PerpetualJ Several different answers already do so. As it stands, this seems to be too broad.
$endgroup$
– Deusovi♦
2 days ago
|
show 14 more comments
$begingroup$
Sarah called me today and explained that she had counted to infinity. I shrugged and said it was impossible. She said that since I didn’t believe her, she would do it again, and this time in only ten minutes. I thought it was impossible but she did it right before my eyes!
How did Sarah count to infinity in only ten minutes?
Hints
Sarah started slow, but as time went on she got incredibly fast!
Clarifications
Sarah indeed counted all the way to infinity. She provided mathematical proof that she could count any infinite set, to include $א_0$, in any finite time span.
mathematics knowledge story situation
asked Apr 29 at 23:25
PerpetualJPerpetualJ
4,248648
$endgroup$
Sarah called me today and explained that she had counted to infinity. I shrugged and said it was impossible. She said that since I didn’t believe her, she would do it again, and this time in only ten minutes. I thought it was impossible but she did it right before my eyes!
How did Sarah count to infinity in only ten minutes?
Hints
Sarah started slow, but as time went on she got incredibly fast!
Clarifications
Sarah indeed counted all the way to infinity. She provided mathematical proof that she could count any infinite set, to include $א_0$, in any finite time span.
mathematics knowledge story situation
mathematics knowledge story situation
asked Apr 29 at 23:25
PerpetualJPerpetualJ
4,248648
asked Apr 29 at 23:25
PerpetualJPerpetualJ
4,248648
edited 2 days ago
PerpetualJ
asked Apr 29 at 23:25
PerpetualJPerpetualJ
4,248648
asked Apr 29 at 23:25
PerpetualJPerpetualJ
4,248648
asked Apr 29 at 23:25
PerpetualJPerpetualJ
4,248648
4,248648
put on hold as off-topic by Rand al'Thor, w l, athin, Glorfindel, noedne 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question may invite speculative answers, as the question is not fully defined. The validity of some answers may be based upon opinion. Good questions for this site have a limited number of objectively correct answers. See also: Why are questions off-topic if they invite answers which are not demonstrably correct, or are otherwise speculative?" – Rand al'Thor, w l, athin, Glorfindel, noedne
put on hold as off-topic by Rand al'Thor, w l, athin, Glorfindel, noedne 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question may invite speculative answers, as the question is not fully defined. The validity of some answers may be based upon opinion. Good questions for this site have a limited number of objectively correct answers. See also: Why are questions off-topic if they invite answers which are not demonstrably correct, or are otherwise speculative?" – Rand al'Thor, w l, athin, Glorfindel, noedne
1
$begingroup$
@MrPie All the way to infinity!
$endgroup$
– PerpetualJ
Apr 29 at 23:40
9
$begingroup$
This question feels a bit too broad. Are you sure there's one demonstrably correct answer to this one?
$endgroup$
– PiIsNot3
Apr 30 at 0:29
4
$begingroup$
An appropriate question for your username, @PerpetualJ.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 0:59
13
$begingroup$
My concern is that there may be more than one valid answer, and without specifying further restrictions, the “correct” one becomes an arbitrary choice. There’s already many good answers that could potentially be correct, which feeds into my concern
$endgroup$
– PiIsNot3
Apr 30 at 4:06
5
$begingroup$
@PerpetualJ Several different answers already do so. As it stands, this seems to be too broad.
$endgroup$
– Deusovi♦
2 days ago
|
show 14 more comments
1
$begingroup$
@MrPie All the way to infinity!
$endgroup$
– PerpetualJ
Apr 29 at 23:40
9
$begingroup$
This question feels a bit too broad. Are you sure there's one demonstrably correct answer to this one?
$endgroup$
– PiIsNot3
Apr 30 at 0:29
4
$begingroup$
An appropriate question for your username, @PerpetualJ.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 0:59
13
$begingroup$
My concern is that there may be more than one valid answer, and without specifying further restrictions, the “correct” one becomes an arbitrary choice. There’s already many good answers that could potentially be correct, which feeds into my concern
$endgroup$
– PiIsNot3
Apr 30 at 4:06
5
$begingroup$
@PerpetualJ Several different answers already do so. As it stands, this seems to be too broad.
$endgroup$
– Deusovi♦
2 days ago
1
1
$begingroup$
@MrPie All the way to infinity!
$endgroup$
– PerpetualJ
Apr 29 at 23:40
$begingroup$
@MrPie All the way to infinity!
$endgroup$
– PerpetualJ
Apr 29 at 23:40
9
9
$begingroup$
This question feels a bit too broad. Are you sure there's one demonstrably correct answer to this one?
$endgroup$
– PiIsNot3
Apr 30 at 0:29
$begingroup$
This question feels a bit too broad. Are you sure there's one demonstrably correct answer to this one?
$endgroup$
– PiIsNot3
Apr 30 at 0:29
4
4
$begingroup$
An appropriate question for your username, @PerpetualJ.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 0:59
$begingroup$
An appropriate question for your username, @PerpetualJ.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 0:59
13
13
$begingroup$
My concern is that there may be more than one valid answer, and without specifying further restrictions, the “correct” one becomes an arbitrary choice. There’s already many good answers that could potentially be correct, which feeds into my concern
$endgroup$
– PiIsNot3
Apr 30 at 4:06
$begingroup$
My concern is that there may be more than one valid answer, and without specifying further restrictions, the “correct” one becomes an arbitrary choice. There’s already many good answers that could potentially be correct, which feeds into my concern
$endgroup$
– PiIsNot3
Apr 30 at 4:06
5
5
$begingroup$
@PerpetualJ Several different answers already do so. As it stands, this seems to be too broad.
$endgroup$
– Deusovi♦
2 days ago
$begingroup$
@PerpetualJ Several different answers already do so. As it stands, this seems to be too broad.
$endgroup$
– Deusovi♦
2 days ago
|
show 14 more comments
17 Answers
17
active
oldest
votes
$begingroup$
This feels underspecified:
clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.
Here are a few possibilities. One:
She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.
Two:
She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)
Three:
She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)
Four:
She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.
Five:
Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".
Apparently that last one is what the OP had in mind. Here are some more details.
Suppose it takes her two seconds to say "one", and then each new number is said 0.5% faster than the previous one -- so the next number takes 1.99 seconds, the next just over 1.98 seconds, etc. Then counting all the positive integers takes $2left(1+frac199200+left(frac199200right)^2+left(frac199200right)^3+cdotsright)$ seconds, which equals $frac21-frac199200$ or 400 seconds. This gives Sarah plenty of time to take a big breath and add "infinity", all within ten minutes.
answered Apr 29 at 23:51
Gareth McCaughan♦Gareth McCaughan
69.6k3176272
$endgroup$
5
$begingroup$
I think you're missing an option: she counted to five -- she counted "All" "the" "way" "to" "infinity" as five words, which is a valid interpretation of what she said
$endgroup$
– postmortes
Apr 30 at 6:31
$begingroup$
@postmortes must be a very slow counter then if it takes her ten minutes ;)
$endgroup$
– Mark
2 days ago
$begingroup$
@Mark I agree :)
$endgroup$
– postmortes
2 days ago
1
$begingroup$
Gareth, your last one is the closest explanation! We all know there is no final number, but you can count an infinite set in a finite time span for sure!
$endgroup$
– PerpetualJ
2 days ago
1
$begingroup$
OK, done. I decided to make her speed up more slowly. 10 minutes is plenty of time :-).
$endgroup$
– Gareth McCaughan♦
2 days ago
|
show 3 more comments
$begingroup$
I find it hard to believe she managed this in only 10 minutes, but all she needs to do is count to 1,461,559,270,678...
she just needs to do it in base 36, in which case the digits of the number are
INFINITY.
answered Apr 30 at 3:06
jasonharperjasonharper
670613
$endgroup$
6
$begingroup$
She could count 200+ billion digits less if she used base 35
$endgroup$
– b a
2 days ago
4
$begingroup$
Arguably this is the only answer yet that actually describes a finite process that could in any way be described correctly as "counting to infinity". (Arguably.)
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
maybe she rot13(pbhagrq ol 7OW2OG (442628489 onfr gra) yrnivat bayl 3302 vgrengvbaf, rnfvyl qbar va 10 zvahgrf!). on a side note, who knew rot13(gur cevzr snpgbef bs VASVAVGL jrer (onfr 10) 2, 13, 127, 149, 18923, naq 2970661?)
$endgroup$
– SteveV
2 days ago
add a comment |
$begingroup$
There goes one Infiniti G35! And there goes another!
There. I've counted two Infiniti. ;)
answered Apr 30 at 1:39
ikegamiikegami
30126
New contributor
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
7
$begingroup$
Hahaha this was awesome lol
$endgroup$
– PerpetualJ
Apr 30 at 2:19
$begingroup$
Ah, the punch buggy no punch back answer :)
$endgroup$
– Captain Man
2 days ago
add a comment |
$begingroup$
Perhaps
clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"
answered Apr 30 at 0:17
SteveVSteveV
7,0732635
$endgroup$
8
$begingroup$
If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 1:00
$begingroup$
I don't see how this fits with the "Sarah started slow, but as time went on she got incredibly fast!" hint.
$endgroup$
– Simon Baars
2 days ago
$begingroup$
It was posted before that hint was added. (As were almost all the answers, including one of mine that already does the slow-then-faster thing. I suppose the hint was added more to make the question less too-broad than because it was needed as a hint :-).)
$endgroup$
– Gareth McCaughan♦
2 days ago
1
$begingroup$
But that's only to "infinity" - far too low. If you instead listed Disney catch-phrases, then you could count "To Infinity, and Beyond"
$endgroup$
– Chronocidal
2 days ago
add a comment |
$begingroup$
Did Sarah count
All of the avengers movies up to and including infinity war?
answered Apr 30 at 4:31
DunhamDunham
2714
New contributor
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
She counted "to infinity", 10 letters, 1 space.
answered Apr 30 at 5:26
TatranskymedvedTatranskymedved
2464
New contributor
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Ah, that explains the timing as well, unlike some of the other answers! (+1) Good first post! :P
$endgroup$
– Mr Pie
Apr 30 at 5:34
$begingroup$
That explains ten minutes?
$endgroup$
– Peregrine Rook
2 days ago
add a comment |
$begingroup$
How about counting:
$frac11000, frac1999, frac1998, cdots, frac12, frac11, frac10$
answered Apr 30 at 4:40
athinathin
9,37723284
$endgroup$
2
$begingroup$
Your final term is not defined... but.... meh ;)
$endgroup$
– Mr Pie
Apr 30 at 4:48
add a comment |
$begingroup$
I can do it in 15 minutes. Duh.
answered 2 days ago
GOTO 0GOTO 0
9,94554089
$endgroup$
$begingroup$
Do you actually mean 40 minutes?
$endgroup$
– Arnaud Mortier
2 days ago
3
$begingroup$
@ArnaudMortier 15 minutes because he rotated it 90 degrees (desperately trying not to spoil)
$endgroup$
– Steve-O
2 days ago
$begingroup$
@Steve-O Thanks, I see it now.
$endgroup$
– Arnaud Mortier
2 days ago
add a comment |
$begingroup$
Possible mathematical answer
I think this is linked to
Zeno's paradoxes
Possible approach
Sarah defines for you a new number system. The number $1$ is represent by saying the letter "a" for a duration of $10$ seconds, the number $2$ is represented by saying the letter "a" for $5$ seconds, the number $3$ is represented by saying the letter "a" for a duration of $2.5$ seconds and, in general, the number $n$ is represented by saying the letter "a" for a duration of $frac102^n-1$ seconds.
She then says "a" for a duration of $20$ seconds to count to infinity.
answered 2 days ago
hexominohexomino
48.4k4143228
$endgroup$
$begingroup$
There’s a name for this phenomenon!
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
@PerpetualJ I've added an extra line. Is this the phenomenon you're talking about?
$endgroup$
– hexomino
2 days ago
$begingroup$
Surely that is counting to 0, not to ∞? (sincen = 1+ln(10/t)/ln(2))
$endgroup$
– Chronocidal
2 days ago
$begingroup$
The 20 seconds, is counting 1,2,3,4,5,... consecutively. I understand there is ambiguity here (1 is the same as 2 2s etc) but I decided it was not important to address in the context of the problem.
$endgroup$
– hexomino
2 days ago
add a comment |
$begingroup$
The definition of infinity in some circles is
the highest conceivable number.
Therefore, all Sarah needs to do is count to
the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".
answered Apr 30 at 0:00
BewildererBewilderer
3245
$endgroup$
1
$begingroup$
Finitism much (it seems that Sarah is accepting the highest number she can count to as infinity)?
$endgroup$
– MilkyWay90
Apr 30 at 1:17
add a comment |
$begingroup$
Sarah is also known as
Chuck Norris
Indeed:
"Chuck Norris counted to infinity. Twice."
And since
"Chuck Norris has his own Gender.", Sarah is a suitable second name for them.
answered 2 days ago
user60001user60001
411
New contributor
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Sarah isn't great at counting but she is great at improving anything she does while she is doing it.
Therefore, every time she counts a number she can count it faster than the previous one. The improvement it's not that spectacular, and to count one number still takes her 99.8% of the time it took to count the previous one.
This way, if counting to 1 took Sarah 1 second, the time it will take Sarah to count to n is: $1+1cdot 0.998 + 1cdot 0.998^2 + .... + 1cdot 0.998^n$
Since that's just a geometric series, it's sum to infinite is $frac11-0.998=500$ seconds.
That is, just thanks to keeping improving continuously, Sarah can count to infinite in 8 minutes and 20 seconds.
answered 2 days ago
PerePere
27316
$endgroup$
1
$begingroup$
I like this one! I actually didn’t expect another answer to come in with good mathematical arguments! +1
$endgroup$
– PerpetualJ
2 days ago
add a comment |
$begingroup$
The answer is:
She starts counting and for each number she takes half the time to count to the next number, through this method you can count to infinity in a finite time.
edited 2 days ago
Tahel
72011
answered 2 days ago
JamesttukJamesttuk
211
New contributor
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Could this be the right approach (even if it is not the correct answer)?
Time is finite, yes, but continuous, so it contains an infinite number of individual positions. If we apply, for example, the function f: x -> 1/(10-x) to the interval of minutes [0,10] belonging to the Real Numbers, just before the 10 minutes we will have reached infinity.
answered 2 days ago
HermesHermes
5359
$endgroup$
add a comment |
$begingroup$
Did Sarah perhaps say once:
$limlimits_xtoinfty x = infty$
edited 2 days ago
trolley813
1,500411
answered 2 days ago
HamstirlyHamstirly
111
New contributor
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Sarah would have to say this very slowly to reach ten minutes, which would be impractical if @PerpetualJ was paying for every minute during the phone call!
$endgroup$
– Mr Pie
2 days ago
add a comment |
$begingroup$
Despite the puzzle being already solved, I have another take on this.
All she needs to do is
use a diverging function.
For instance, she could say
-log(3), -log(2), -log(1), -log(0)
Which is in agreement with the hint that she goes incredibly fast in the end.
answered 2 days ago
legrojanlegrojan
1814
$endgroup$
add a comment |
$begingroup$
My answer is:
As Sarah got really fast, time stopped...according to Einstein's relativity..hence she did it....I know this sounds absurd but ...meh!
edited 2 days ago
Glorfindel
15k45788
answered 2 days ago
user669545user669545
1
New contributor
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
17 Answers
17
active
oldest
votes
17 Answers
17
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This feels underspecified:
clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.
Here are a few possibilities. One:
She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.
Two:
She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)
Three:
She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)
Four:
She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.
Five:
Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".
Apparently that last one is what the OP had in mind. Here are some more details.
Suppose it takes her two seconds to say "one", and then each new number is said 0.5% faster than the previous one -- so the next number takes 1.99 seconds, the next just over 1.98 seconds, etc. Then counting all the positive integers takes $2left(1+frac199200+left(frac199200right)^2+left(frac199200right)^3+cdotsright)$ seconds, which equals $frac21-frac199200$ or 400 seconds. This gives Sarah plenty of time to take a big breath and add "infinity", all within ten minutes.
answered Apr 29 at 23:51
Gareth McCaughan♦Gareth McCaughan
69.6k3176272
$endgroup$
5
$begingroup$
I think you're missing an option: she counted to five -- she counted "All" "the" "way" "to" "infinity" as five words, which is a valid interpretation of what she said
$endgroup$
– postmortes
Apr 30 at 6:31
$begingroup$
@postmortes must be a very slow counter then if it takes her ten minutes ;)
$endgroup$
– Mark
2 days ago
$begingroup$
@Mark I agree :)
$endgroup$
– postmortes
2 days ago
1
$begingroup$
Gareth, your last one is the closest explanation! We all know there is no final number, but you can count an infinite set in a finite time span for sure!
$endgroup$
– PerpetualJ
2 days ago
1
$begingroup$
OK, done. I decided to make her speed up more slowly. 10 minutes is plenty of time :-).
$endgroup$
– Gareth McCaughan♦
2 days ago
|
show 3 more comments
$begingroup$
This feels underspecified:
clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.
Here are a few possibilities. One:
She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.
Two:
She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)
Three:
She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)
Four:
She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.
Five:
Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".
Apparently that last one is what the OP had in mind. Here are some more details.
Suppose it takes her two seconds to say "one", and then each new number is said 0.5% faster than the previous one -- so the next number takes 1.99 seconds, the next just over 1.98 seconds, etc. Then counting all the positive integers takes $2left(1+frac199200+left(frac199200right)^2+left(frac199200right)^3+cdotsright)$ seconds, which equals $frac21-frac199200$ or 400 seconds. This gives Sarah plenty of time to take a big breath and add "infinity", all within ten minutes.
answered Apr 29 at 23:51
Gareth McCaughan♦Gareth McCaughan
69.6k3176272
$endgroup$
5
$begingroup$
I think you're missing an option: she counted to five -- she counted "All" "the" "way" "to" "infinity" as five words, which is a valid interpretation of what she said
$endgroup$
– postmortes
Apr 30 at 6:31
$begingroup$
@postmortes must be a very slow counter then if it takes her ten minutes ;)
$endgroup$
– Mark
2 days ago
$begingroup$
@Mark I agree :)
$endgroup$
– postmortes
2 days ago
1
$begingroup$
Gareth, your last one is the closest explanation! We all know there is no final number, but you can count an infinite set in a finite time span for sure!
$endgroup$
– PerpetualJ
2 days ago
1
$begingroup$
OK, done. I decided to make her speed up more slowly. 10 minutes is plenty of time :-).
$endgroup$
– Gareth McCaughan♦
2 days ago
|
show 3 more comments
$begingroup$
This feels underspecified:
clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.
Here are a few possibilities. One:
She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.
Two:
She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)
Three:
She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)
Four:
She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.
Five:
Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".
Apparently that last one is what the OP had in mind. Here are some more details.
Suppose it takes her two seconds to say "one", and then each new number is said 0.5% faster than the previous one -- so the next number takes 1.99 seconds, the next just over 1.98 seconds, etc. Then counting all the positive integers takes $2left(1+frac199200+left(frac199200right)^2+left(frac199200right)^3+cdotsright)$ seconds, which equals $frac21-frac199200$ or 400 seconds. This gives Sarah plenty of time to take a big breath and add "infinity", all within ten minutes.
answered Apr 29 at 23:51
Gareth McCaughan♦Gareth McCaughan
69.6k3176272
$endgroup$
This feels underspecified:
clearly Sarah is not counting 1, 2, 3, ... (infinitely many numbers go here), infinity; so she's doing something else; but there are quite a lot of something-elses that she could do, and all of them are kinda cheaty, and the question here is what specific kinda-cheaty thing she did.
Here are a few possibilities. One:
She wrote numbers down on their sides, starting at 1 and proceeding as far as 8. An 8 on its side looks very much like the usual mathematical symbol for infinity.
Two:
She started from, let's say, "infinity minus 100" and counted up. (There are in fact number systems in which something a bit like "infinity minus 100" is an actual number.)
Three:
She counted down from, let's say, "infinity plus 100". (You can do something like that in the surreal numbers, mentioned above, but also in other simpler systems such as the ordinal numbers.)
Four:
She started counting normally, and at some point went "... and so on; infinity." I personally wouldn't (ahahaha) count that as counting to infinity, but then I don't think I'd count anything as counting to infinity other than the thing she obviously didn't do.
Five:
Sarah is able to count arbitrarily fast (maybe she's an archangel or something, not a human) and she said each number twice as quickly as its predecessor; after twice the time it took her to say "one", she had named all the positive integers and then said "infinity".
Apparently that last one is what the OP had in mind. Here are some more details.
Suppose it takes her two seconds to say "one", and then each new number is said 0.5% faster than the previous one -- so the next number takes 1.99 seconds, the next just over 1.98 seconds, etc. Then counting all the positive integers takes $2left(1+frac199200+left(frac199200right)^2+left(frac199200right)^3+cdotsright)$ seconds, which equals $frac21-frac199200$ or 400 seconds. This gives Sarah plenty of time to take a big breath and add "infinity", all within ten minutes.
answered Apr 29 at 23:51
Gareth McCaughan♦Gareth McCaughan
69.6k3176272
edited 2 days ago
answered Apr 29 at 23:51
Gareth McCaughan♦Gareth McCaughan
69.6k3176272
answered Apr 29 at 23:51
Gareth McCaughan♦Gareth McCaughan
69.6k3176272
answered Apr 29 at 23:51
Gareth McCaughan♦Gareth McCaughan
69.6k3176272
69.6k3176272
5
$begingroup$
I think you're missing an option: she counted to five -- she counted "All" "the" "way" "to" "infinity" as five words, which is a valid interpretation of what she said
$endgroup$
– postmortes
Apr 30 at 6:31
$begingroup$
@postmortes must be a very slow counter then if it takes her ten minutes ;)
$endgroup$
– Mark
2 days ago
$begingroup$
@Mark I agree :)
$endgroup$
– postmortes
2 days ago
1
$begingroup$
Gareth, your last one is the closest explanation! We all know there is no final number, but you can count an infinite set in a finite time span for sure!
$endgroup$
– PerpetualJ
2 days ago
1
$begingroup$
OK, done. I decided to make her speed up more slowly. 10 minutes is plenty of time :-).
$endgroup$
– Gareth McCaughan♦
2 days ago
|
show 3 more comments
5
$begingroup$
I think you're missing an option: she counted to five -- she counted "All" "the" "way" "to" "infinity" as five words, which is a valid interpretation of what she said
$endgroup$
– postmortes
Apr 30 at 6:31
$begingroup$
@postmortes must be a very slow counter then if it takes her ten minutes ;)
$endgroup$
– Mark
2 days ago
$begingroup$
@Mark I agree :)
$endgroup$
– postmortes
2 days ago
1
$begingroup$
Gareth, your last one is the closest explanation! We all know there is no final number, but you can count an infinite set in a finite time span for sure!
$endgroup$
– PerpetualJ
2 days ago
1
$begingroup$
OK, done. I decided to make her speed up more slowly. 10 minutes is plenty of time :-).
$endgroup$
– Gareth McCaughan♦
2 days ago
5
5
$begingroup$
I think you're missing an option: she counted to five -- she counted "All" "the" "way" "to" "infinity" as five words, which is a valid interpretation of what she said
$endgroup$
– postmortes
Apr 30 at 6:31
$begingroup$
I think you're missing an option: she counted to five -- she counted "All" "the" "way" "to" "infinity" as five words, which is a valid interpretation of what she said
$endgroup$
– postmortes
Apr 30 at 6:31
$begingroup$
@postmortes must be a very slow counter then if it takes her ten minutes ;)
$endgroup$
– Mark
2 days ago
$begingroup$
@postmortes must be a very slow counter then if it takes her ten minutes ;)
$endgroup$
– Mark
2 days ago
$begingroup$
@Mark I agree :)
$endgroup$
– postmortes
2 days ago
$begingroup$
@Mark I agree :)
$endgroup$
– postmortes
2 days ago
1
1
$begingroup$
Gareth, your last one is the closest explanation! We all know there is no final number, but you can count an infinite set in a finite time span for sure!
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
Gareth, your last one is the closest explanation! We all know there is no final number, but you can count an infinite set in a finite time span for sure!
$endgroup$
– PerpetualJ
2 days ago
1
1
$begingroup$
OK, done. I decided to make her speed up more slowly. 10 minutes is plenty of time :-).
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
OK, done. I decided to make her speed up more slowly. 10 minutes is plenty of time :-).
$endgroup$
– Gareth McCaughan♦
2 days ago
|
show 3 more comments
$begingroup$
I find it hard to believe she managed this in only 10 minutes, but all she needs to do is count to 1,461,559,270,678...
she just needs to do it in base 36, in which case the digits of the number are
INFINITY.
answered Apr 30 at 3:06
jasonharperjasonharper
670613
$endgroup$
6
$begingroup$
She could count 200+ billion digits less if she used base 35
$endgroup$
– b a
2 days ago
4
$begingroup$
Arguably this is the only answer yet that actually describes a finite process that could in any way be described correctly as "counting to infinity". (Arguably.)
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
maybe she rot13(pbhagrq ol 7OW2OG (442628489 onfr gra) yrnivat bayl 3302 vgrengvbaf, rnfvyl qbar va 10 zvahgrf!). on a side note, who knew rot13(gur cevzr snpgbef bs VASVAVGL jrer (onfr 10) 2, 13, 127, 149, 18923, naq 2970661?)
$endgroup$
– SteveV
2 days ago
add a comment |
$begingroup$
I find it hard to believe she managed this in only 10 minutes, but all she needs to do is count to 1,461,559,270,678...
she just needs to do it in base 36, in which case the digits of the number are
INFINITY.
answered Apr 30 at 3:06
jasonharperjasonharper
670613
$endgroup$
6
$begingroup$
She could count 200+ billion digits less if she used base 35
$endgroup$
– b a
2 days ago
4
$begingroup$
Arguably this is the only answer yet that actually describes a finite process that could in any way be described correctly as "counting to infinity". (Arguably.)
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
maybe she rot13(pbhagrq ol 7OW2OG (442628489 onfr gra) yrnivat bayl 3302 vgrengvbaf, rnfvyl qbar va 10 zvahgrf!). on a side note, who knew rot13(gur cevzr snpgbef bs VASVAVGL jrer (onfr 10) 2, 13, 127, 149, 18923, naq 2970661?)
$endgroup$
– SteveV
2 days ago
add a comment |
$begingroup$
I find it hard to believe she managed this in only 10 minutes, but all she needs to do is count to 1,461,559,270,678...
she just needs to do it in base 36, in which case the digits of the number are
INFINITY.
answered Apr 30 at 3:06
jasonharperjasonharper
670613
$endgroup$
I find it hard to believe she managed this in only 10 minutes, but all she needs to do is count to 1,461,559,270,678...
she just needs to do it in base 36, in which case the digits of the number are
INFINITY.
answered Apr 30 at 3:06
jasonharperjasonharper
670613
answered Apr 30 at 3:06
jasonharperjasonharper
670613
answered Apr 30 at 3:06
jasonharperjasonharper
670613
answered Apr 30 at 3:06
jasonharperjasonharper
670613
670613
6
$begingroup$
She could count 200+ billion digits less if she used base 35
$endgroup$
– b a
2 days ago
4
$begingroup$
Arguably this is the only answer yet that actually describes a finite process that could in any way be described correctly as "counting to infinity". (Arguably.)
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
maybe she rot13(pbhagrq ol 7OW2OG (442628489 onfr gra) yrnivat bayl 3302 vgrengvbaf, rnfvyl qbar va 10 zvahgrf!). on a side note, who knew rot13(gur cevzr snpgbef bs VASVAVGL jrer (onfr 10) 2, 13, 127, 149, 18923, naq 2970661?)
$endgroup$
– SteveV
2 days ago
add a comment |
6
$begingroup$
She could count 200+ billion digits less if she used base 35
$endgroup$
– b a
2 days ago
4
$begingroup$
Arguably this is the only answer yet that actually describes a finite process that could in any way be described correctly as "counting to infinity". (Arguably.)
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
maybe she rot13(pbhagrq ol 7OW2OG (442628489 onfr gra) yrnivat bayl 3302 vgrengvbaf, rnfvyl qbar va 10 zvahgrf!). on a side note, who knew rot13(gur cevzr snpgbef bs VASVAVGL jrer (onfr 10) 2, 13, 127, 149, 18923, naq 2970661?)
$endgroup$
– SteveV
2 days ago
6
6
$begingroup$
She could count 200+ billion digits less if she used base 35
$endgroup$
– b a
2 days ago
$begingroup$
She could count 200+ billion digits less if she used base 35
$endgroup$
– b a
2 days ago
4
4
$begingroup$
Arguably this is the only answer yet that actually describes a finite process that could in any way be described correctly as "counting to infinity". (Arguably.)
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
Arguably this is the only answer yet that actually describes a finite process that could in any way be described correctly as "counting to infinity". (Arguably.)
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
maybe she rot13(pbhagrq ol 7OW2OG (442628489 onfr gra) yrnivat bayl 3302 vgrengvbaf, rnfvyl qbar va 10 zvahgrf!). on a side note, who knew rot13(gur cevzr snpgbef bs VASVAVGL jrer (onfr 10) 2, 13, 127, 149, 18923, naq 2970661?)
$endgroup$
– SteveV
2 days ago
$begingroup$
maybe she rot13(pbhagrq ol 7OW2OG (442628489 onfr gra) yrnivat bayl 3302 vgrengvbaf, rnfvyl qbar va 10 zvahgrf!). on a side note, who knew rot13(gur cevzr snpgbef bs VASVAVGL jrer (onfr 10) 2, 13, 127, 149, 18923, naq 2970661?)
$endgroup$
– SteveV
2 days ago
add a comment |
$begingroup$
There goes one Infiniti G35! And there goes another!
There. I've counted two Infiniti. ;)
answered Apr 30 at 1:39
ikegamiikegami
30126
New contributor
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
7
$begingroup$
Hahaha this was awesome lol
$endgroup$
– PerpetualJ
Apr 30 at 2:19
$begingroup$
Ah, the punch buggy no punch back answer :)
$endgroup$
– Captain Man
2 days ago
add a comment |
$begingroup$
There goes one Infiniti G35! And there goes another!
There. I've counted two Infiniti. ;)
answered Apr 30 at 1:39
ikegamiikegami
30126
New contributor
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
7
$begingroup$
Hahaha this was awesome lol
$endgroup$
– PerpetualJ
Apr 30 at 2:19
$begingroup$
Ah, the punch buggy no punch back answer :)
$endgroup$
– Captain Man
2 days ago
add a comment |
$begingroup$
There goes one Infiniti G35! And there goes another!
There. I've counted two Infiniti. ;)
answered Apr 30 at 1:39
ikegamiikegami
30126
New contributor
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
There goes one Infiniti G35! And there goes another!
There. I've counted two Infiniti. ;)
answered Apr 30 at 1:39
ikegamiikegami
30126
New contributor
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 30 at 1:44
answered Apr 30 at 1:39
ikegamiikegami
30126
New contributor
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Apr 30 at 1:39
ikegamiikegami
30126
answered Apr 30 at 1:39
ikegamiikegami
30126
30126
New contributor
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
ikegami is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
7
$begingroup$
Hahaha this was awesome lol
$endgroup$
– PerpetualJ
Apr 30 at 2:19
$begingroup$
Ah, the punch buggy no punch back answer :)
$endgroup$
– Captain Man
2 days ago
add a comment |
7
$begingroup$
Hahaha this was awesome lol
$endgroup$
– PerpetualJ
Apr 30 at 2:19
$begingroup$
Ah, the punch buggy no punch back answer :)
$endgroup$
– Captain Man
2 days ago
7
7
$begingroup$
Hahaha this was awesome lol
$endgroup$
– PerpetualJ
Apr 30 at 2:19
$begingroup$
Hahaha this was awesome lol
$endgroup$
– PerpetualJ
Apr 30 at 2:19
$begingroup$
Ah, the punch buggy no punch back answer :)
$endgroup$
– Captain Man
2 days ago
$begingroup$
Ah, the punch buggy no punch back answer :)
$endgroup$
– Captain Man
2 days ago
add a comment |
$begingroup$
Perhaps
clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"
answered Apr 30 at 0:17
SteveVSteveV
7,0732635
$endgroup$
8
$begingroup$
If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 1:00
$begingroup$
I don't see how this fits with the "Sarah started slow, but as time went on she got incredibly fast!" hint.
$endgroup$
– Simon Baars
2 days ago
$begingroup$
It was posted before that hint was added. (As were almost all the answers, including one of mine that already does the slow-then-faster thing. I suppose the hint was added more to make the question less too-broad than because it was needed as a hint :-).)
$endgroup$
– Gareth McCaughan♦
2 days ago
1
$begingroup$
But that's only to "infinity" - far too low. If you instead listed Disney catch-phrases, then you could count "To Infinity, and Beyond"
$endgroup$
– Chronocidal
2 days ago
add a comment |
$begingroup$
Perhaps
clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"
answered Apr 30 at 0:17
SteveVSteveV
7,0732635
$endgroup$
8
$begingroup$
If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 1:00
$begingroup$
I don't see how this fits with the "Sarah started slow, but as time went on she got incredibly fast!" hint.
$endgroup$
– Simon Baars
2 days ago
$begingroup$
It was posted before that hint was added. (As were almost all the answers, including one of mine that already does the slow-then-faster thing. I suppose the hint was added more to make the question less too-broad than because it was needed as a hint :-).)
$endgroup$
– Gareth McCaughan♦
2 days ago
1
$begingroup$
But that's only to "infinity" - far too low. If you instead listed Disney catch-phrases, then you could count "To Infinity, and Beyond"
$endgroup$
– Chronocidal
2 days ago
add a comment |
$begingroup$
Perhaps
clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"
answered Apr 30 at 0:17
SteveVSteveV
7,0732635
$endgroup$
Perhaps
clever Sarah went the appropriate "I" page in the dictionary and counted word entries until she reached "infinity"
answered Apr 30 at 0:17
SteveVSteveV
7,0732635
answered Apr 30 at 0:17
SteveVSteveV
7,0732635
answered Apr 30 at 0:17
SteveVSteveV
7,0732635
answered Apr 30 at 0:17
SteveVSteveV
7,0732635
7,0732635
8
$begingroup$
If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 1:00
$begingroup$
I don't see how this fits with the "Sarah started slow, but as time went on she got incredibly fast!" hint.
$endgroup$
– Simon Baars
2 days ago
$begingroup$
It was posted before that hint was added. (As were almost all the answers, including one of mine that already does the slow-then-faster thing. I suppose the hint was added more to make the question less too-broad than because it was needed as a hint :-).)
$endgroup$
– Gareth McCaughan♦
2 days ago
1
$begingroup$
But that's only to "infinity" - far too low. If you instead listed Disney catch-phrases, then you could count "To Infinity, and Beyond"
$endgroup$
– Chronocidal
2 days ago
add a comment |
8
$begingroup$
If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 1:00
$begingroup$
I don't see how this fits with the "Sarah started slow, but as time went on she got incredibly fast!" hint.
$endgroup$
– Simon Baars
2 days ago
$begingroup$
It was posted before that hint was added. (As were almost all the answers, including one of mine that already does the slow-then-faster thing. I suppose the hint was added more to make the question less too-broad than because it was needed as a hint :-).)
$endgroup$
– Gareth McCaughan♦
2 days ago
1
$begingroup$
But that's only to "infinity" - far too low. If you instead listed Disney catch-phrases, then you could count "To Infinity, and Beyond"
$endgroup$
– Chronocidal
2 days ago
8
8
$begingroup$
If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 1:00
$begingroup$
If so, she didn't count to infinity, she (at best) counted to "infinity". (Personally I don't think even that is a correct description of what she did.) But I don't expect whatever answer OP has in mind to be much more convincing than this.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 1:00
$begingroup$
I don't see how this fits with the "Sarah started slow, but as time went on she got incredibly fast!" hint.
$endgroup$
– Simon Baars
2 days ago
$begingroup$
I don't see how this fits with the "Sarah started slow, but as time went on she got incredibly fast!" hint.
$endgroup$
– Simon Baars
2 days ago
$begingroup$
It was posted before that hint was added. (As were almost all the answers, including one of mine that already does the slow-then-faster thing. I suppose the hint was added more to make the question less too-broad than because it was needed as a hint :-).)
$endgroup$
– Gareth McCaughan♦
2 days ago
$begingroup$
It was posted before that hint was added. (As were almost all the answers, including one of mine that already does the slow-then-faster thing. I suppose the hint was added more to make the question less too-broad than because it was needed as a hint :-).)
$endgroup$
– Gareth McCaughan♦
2 days ago
1
1
$begingroup$
But that's only to "infinity" - far too low. If you instead listed Disney catch-phrases, then you could count "To Infinity, and Beyond"
$endgroup$
– Chronocidal
2 days ago
$begingroup$
But that's only to "infinity" - far too low. If you instead listed Disney catch-phrases, then you could count "To Infinity, and Beyond"
$endgroup$
– Chronocidal
2 days ago
add a comment |
$begingroup$
Did Sarah count
All of the avengers movies up to and including infinity war?
answered Apr 30 at 4:31
DunhamDunham
2714
New contributor
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Did Sarah count
All of the avengers movies up to and including infinity war?
answered Apr 30 at 4:31
DunhamDunham
2714
New contributor
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Did Sarah count
All of the avengers movies up to and including infinity war?
answered Apr 30 at 4:31
DunhamDunham
2714
New contributor
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Did Sarah count
All of the avengers movies up to and including infinity war?
answered Apr 30 at 4:31
DunhamDunham
2714
New contributor
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Apr 30 at 4:31
DunhamDunham
2714
New contributor
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Apr 30 at 4:31
DunhamDunham
2714
answered Apr 30 at 4:31
DunhamDunham
2714
2714
New contributor
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Dunham is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
$begingroup$
She counted "to infinity", 10 letters, 1 space.
answered Apr 30 at 5:26
TatranskymedvedTatranskymedved
2464
New contributor
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Ah, that explains the timing as well, unlike some of the other answers! (+1) Good first post! :P
$endgroup$
– Mr Pie
Apr 30 at 5:34
$begingroup$
That explains ten minutes?
$endgroup$
– Peregrine Rook
2 days ago
add a comment |
$begingroup$
She counted "to infinity", 10 letters, 1 space.
answered Apr 30 at 5:26
TatranskymedvedTatranskymedved
2464
New contributor
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Ah, that explains the timing as well, unlike some of the other answers! (+1) Good first post! :P
$endgroup$
– Mr Pie
Apr 30 at 5:34
$begingroup$
That explains ten minutes?
$endgroup$
– Peregrine Rook
2 days ago
add a comment |
$begingroup$
She counted "to infinity", 10 letters, 1 space.
answered Apr 30 at 5:26
TatranskymedvedTatranskymedved
2464
New contributor
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
She counted "to infinity", 10 letters, 1 space.
answered Apr 30 at 5:26
TatranskymedvedTatranskymedved
2464
New contributor
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Apr 30 at 5:26
TatranskymedvedTatranskymedved
2464
New contributor
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Apr 30 at 5:26
TatranskymedvedTatranskymedved
2464
answered Apr 30 at 5:26
TatranskymedvedTatranskymedved
2464
2464
New contributor
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Tatranskymedved is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Ah, that explains the timing as well, unlike some of the other answers! (+1) Good first post! :P
$endgroup$
– Mr Pie
Apr 30 at 5:34
$begingroup$
That explains ten minutes?
$endgroup$
– Peregrine Rook
2 days ago
add a comment |
1
$begingroup$
Ah, that explains the timing as well, unlike some of the other answers! (+1) Good first post! :P
$endgroup$
– Mr Pie
Apr 30 at 5:34
$begingroup$
That explains ten minutes?
$endgroup$
– Peregrine Rook
2 days ago
1
1
$begingroup$
Ah, that explains the timing as well, unlike some of the other answers! (+1) Good first post! :P
$endgroup$
– Mr Pie
Apr 30 at 5:34
$begingroup$
Ah, that explains the timing as well, unlike some of the other answers! (+1) Good first post! :P
$endgroup$
– Mr Pie
Apr 30 at 5:34
$begingroup$
That explains ten minutes?
$endgroup$
– Peregrine Rook
2 days ago
$begingroup$
That explains ten minutes?
$endgroup$
– Peregrine Rook
2 days ago
add a comment |
$begingroup$
How about counting:
$frac11000, frac1999, frac1998, cdots, frac12, frac11, frac10$
answered Apr 30 at 4:40
athinathin
9,37723284
$endgroup$
2
$begingroup$
Your final term is not defined... but.... meh ;)
$endgroup$
– Mr Pie
Apr 30 at 4:48
add a comment |
$begingroup$
How about counting:
$frac11000, frac1999, frac1998, cdots, frac12, frac11, frac10$
answered Apr 30 at 4:40
athinathin
9,37723284
$endgroup$
2
$begingroup$
Your final term is not defined... but.... meh ;)
$endgroup$
– Mr Pie
Apr 30 at 4:48
add a comment |
$begingroup$
How about counting:
$frac11000, frac1999, frac1998, cdots, frac12, frac11, frac10$
answered Apr 30 at 4:40
athinathin
9,37723284
$endgroup$
How about counting:
$frac11000, frac1999, frac1998, cdots, frac12, frac11, frac10$
answered Apr 30 at 4:40
athinathin
9,37723284
answered Apr 30 at 4:40
athinathin
9,37723284
answered Apr 30 at 4:40
athinathin
9,37723284
answered Apr 30 at 4:40
athinathin
9,37723284
9,37723284
2
$begingroup$
Your final term is not defined... but.... meh ;)
$endgroup$
– Mr Pie
Apr 30 at 4:48
add a comment |
2
$begingroup$
Your final term is not defined... but.... meh ;)
$endgroup$
– Mr Pie
Apr 30 at 4:48
2
2
$begingroup$
Your final term is not defined... but.... meh ;)
$endgroup$
– Mr Pie
Apr 30 at 4:48
$begingroup$
Your final term is not defined... but.... meh ;)
$endgroup$
– Mr Pie
Apr 30 at 4:48
add a comment |
$begingroup$
I can do it in 15 minutes. Duh.
answered 2 days ago
GOTO 0GOTO 0
9,94554089
$endgroup$
$begingroup$
Do you actually mean 40 minutes?
$endgroup$
– Arnaud Mortier
2 days ago
3
$begingroup$
@ArnaudMortier 15 minutes because he rotated it 90 degrees (desperately trying not to spoil)
$endgroup$
– Steve-O
2 days ago
$begingroup$
@Steve-O Thanks, I see it now.
$endgroup$
– Arnaud Mortier
2 days ago
add a comment |
$begingroup$
I can do it in 15 minutes. Duh.
answered 2 days ago
GOTO 0GOTO 0
9,94554089
$endgroup$
$begingroup$
Do you actually mean 40 minutes?
$endgroup$
– Arnaud Mortier
2 days ago
3
$begingroup$
@ArnaudMortier 15 minutes because he rotated it 90 degrees (desperately trying not to spoil)
$endgroup$
– Steve-O
2 days ago
$begingroup$
@Steve-O Thanks, I see it now.
$endgroup$
– Arnaud Mortier
2 days ago
add a comment |
$begingroup$
I can do it in 15 minutes. Duh.
answered 2 days ago
GOTO 0GOTO 0
9,94554089
$endgroup$
I can do it in 15 minutes. Duh.
answered 2 days ago
GOTO 0GOTO 0
9,94554089
answered 2 days ago
GOTO 0GOTO 0
9,94554089
answered 2 days ago
GOTO 0GOTO 0
9,94554089
answered 2 days ago
GOTO 0GOTO 0
9,94554089
9,94554089
$begingroup$
Do you actually mean 40 minutes?
$endgroup$
– Arnaud Mortier
2 days ago
3
$begingroup$
@ArnaudMortier 15 minutes because he rotated it 90 degrees (desperately trying not to spoil)
$endgroup$
– Steve-O
2 days ago
$begingroup$
@Steve-O Thanks, I see it now.
$endgroup$
– Arnaud Mortier
2 days ago
add a comment |
$begingroup$
Do you actually mean 40 minutes?
$endgroup$
– Arnaud Mortier
2 days ago
3
$begingroup$
@ArnaudMortier 15 minutes because he rotated it 90 degrees (desperately trying not to spoil)
$endgroup$
– Steve-O
2 days ago
$begingroup$
@Steve-O Thanks, I see it now.
$endgroup$
– Arnaud Mortier
2 days ago
$begingroup$
Do you actually mean 40 minutes?
$endgroup$
– Arnaud Mortier
2 days ago
$begingroup$
Do you actually mean 40 minutes?
$endgroup$
– Arnaud Mortier
2 days ago
3
3
$begingroup$
@ArnaudMortier 15 minutes because he rotated it 90 degrees (desperately trying not to spoil)
$endgroup$
– Steve-O
2 days ago
$begingroup$
@ArnaudMortier 15 minutes because he rotated it 90 degrees (desperately trying not to spoil)
$endgroup$
– Steve-O
2 days ago
$begingroup$
@Steve-O Thanks, I see it now.
$endgroup$
– Arnaud Mortier
2 days ago
$begingroup$
@Steve-O Thanks, I see it now.
$endgroup$
– Arnaud Mortier
2 days ago
add a comment |
$begingroup$
Possible mathematical answer
I think this is linked to
Zeno's paradoxes
Possible approach
Sarah defines for you a new number system. The number $1$ is represent by saying the letter "a" for a duration of $10$ seconds, the number $2$ is represented by saying the letter "a" for $5$ seconds, the number $3$ is represented by saying the letter "a" for a duration of $2.5$ seconds and, in general, the number $n$ is represented by saying the letter "a" for a duration of $frac102^n-1$ seconds.
She then says "a" for a duration of $20$ seconds to count to infinity.
answered 2 days ago
hexominohexomino
48.4k4143228
$endgroup$
$begingroup$
There’s a name for this phenomenon!
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
@PerpetualJ I've added an extra line. Is this the phenomenon you're talking about?
$endgroup$
– hexomino
2 days ago
$begingroup$
Surely that is counting to 0, not to ∞? (sincen = 1+ln(10/t)/ln(2))
$endgroup$
– Chronocidal
2 days ago
$begingroup$
The 20 seconds, is counting 1,2,3,4,5,... consecutively. I understand there is ambiguity here (1 is the same as 2 2s etc) but I decided it was not important to address in the context of the problem.
$endgroup$
– hexomino
2 days ago
add a comment |
$begingroup$
Possible mathematical answer
I think this is linked to
Zeno's paradoxes
Possible approach
Sarah defines for you a new number system. The number $1$ is represent by saying the letter "a" for a duration of $10$ seconds, the number $2$ is represented by saying the letter "a" for $5$ seconds, the number $3$ is represented by saying the letter "a" for a duration of $2.5$ seconds and, in general, the number $n$ is represented by saying the letter "a" for a duration of $frac102^n-1$ seconds.
She then says "a" for a duration of $20$ seconds to count to infinity.
answered 2 days ago
hexominohexomino
48.4k4143228
$endgroup$
$begingroup$
There’s a name for this phenomenon!
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
@PerpetualJ I've added an extra line. Is this the phenomenon you're talking about?
$endgroup$
– hexomino
2 days ago
$begingroup$
Surely that is counting to 0, not to ∞? (sincen = 1+ln(10/t)/ln(2))
$endgroup$
– Chronocidal
2 days ago
$begingroup$
The 20 seconds, is counting 1,2,3,4,5,... consecutively. I understand there is ambiguity here (1 is the same as 2 2s etc) but I decided it was not important to address in the context of the problem.
$endgroup$
– hexomino
2 days ago
add a comment |
$begingroup$
Possible mathematical answer
I think this is linked to
Zeno's paradoxes
Possible approach
Sarah defines for you a new number system. The number $1$ is represent by saying the letter "a" for a duration of $10$ seconds, the number $2$ is represented by saying the letter "a" for $5$ seconds, the number $3$ is represented by saying the letter "a" for a duration of $2.5$ seconds and, in general, the number $n$ is represented by saying the letter "a" for a duration of $frac102^n-1$ seconds.
She then says "a" for a duration of $20$ seconds to count to infinity.
answered 2 days ago
hexominohexomino
48.4k4143228
$endgroup$
Possible mathematical answer
I think this is linked to
Zeno's paradoxes
Possible approach
Sarah defines for you a new number system. The number $1$ is represent by saying the letter "a" for a duration of $10$ seconds, the number $2$ is represented by saying the letter "a" for $5$ seconds, the number $3$ is represented by saying the letter "a" for a duration of $2.5$ seconds and, in general, the number $n$ is represented by saying the letter "a" for a duration of $frac102^n-1$ seconds.
She then says "a" for a duration of $20$ seconds to count to infinity.
answered 2 days ago
hexominohexomino
48.4k4143228
edited 2 days ago
answered 2 days ago
hexominohexomino
48.4k4143228
answered 2 days ago
hexominohexomino
48.4k4143228
answered 2 days ago
hexominohexomino
48.4k4143228
48.4k4143228
$begingroup$
There’s a name for this phenomenon!
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
@PerpetualJ I've added an extra line. Is this the phenomenon you're talking about?
$endgroup$
– hexomino
2 days ago
$begingroup$
Surely that is counting to 0, not to ∞? (sincen = 1+ln(10/t)/ln(2))
$endgroup$
– Chronocidal
2 days ago
$begingroup$
The 20 seconds, is counting 1,2,3,4,5,... consecutively. I understand there is ambiguity here (1 is the same as 2 2s etc) but I decided it was not important to address in the context of the problem.
$endgroup$
– hexomino
2 days ago
add a comment |
$begingroup$
There’s a name for this phenomenon!
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
@PerpetualJ I've added an extra line. Is this the phenomenon you're talking about?
$endgroup$
– hexomino
2 days ago
$begingroup$
Surely that is counting to 0, not to ∞? (sincen = 1+ln(10/t)/ln(2))
$endgroup$
– Chronocidal
2 days ago
$begingroup$
The 20 seconds, is counting 1,2,3,4,5,... consecutively. I understand there is ambiguity here (1 is the same as 2 2s etc) but I decided it was not important to address in the context of the problem.
$endgroup$
– hexomino
2 days ago
$begingroup$
There’s a name for this phenomenon!
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
There’s a name for this phenomenon!
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
@PerpetualJ I've added an extra line. Is this the phenomenon you're talking about?
$endgroup$
– hexomino
2 days ago
$begingroup$
@PerpetualJ I've added an extra line. Is this the phenomenon you're talking about?
$endgroup$
– hexomino
2 days ago
$begingroup$
Surely that is counting to 0, not to ∞? (since
n = 1+ln(10/t)/ln(2))$endgroup$
– Chronocidal
2 days ago
$begingroup$
Surely that is counting to 0, not to ∞? (since
n = 1+ln(10/t)/ln(2))$endgroup$
– Chronocidal
2 days ago
$begingroup$
The 20 seconds, is counting 1,2,3,4,5,... consecutively. I understand there is ambiguity here (1 is the same as 2 2s etc) but I decided it was not important to address in the context of the problem.
$endgroup$
– hexomino
2 days ago
$begingroup$
The 20 seconds, is counting 1,2,3,4,5,... consecutively. I understand there is ambiguity here (1 is the same as 2 2s etc) but I decided it was not important to address in the context of the problem.
$endgroup$
– hexomino
2 days ago
add a comment |
$begingroup$
The definition of infinity in some circles is
the highest conceivable number.
Therefore, all Sarah needs to do is count to
the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".
answered Apr 30 at 0:00
BewildererBewilderer
3245
$endgroup$
1
$begingroup$
Finitism much (it seems that Sarah is accepting the highest number she can count to as infinity)?
$endgroup$
– MilkyWay90
Apr 30 at 1:17
add a comment |
$begingroup$
The definition of infinity in some circles is
the highest conceivable number.
Therefore, all Sarah needs to do is count to
the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".
answered Apr 30 at 0:00
BewildererBewilderer
3245
$endgroup$
1
$begingroup$
Finitism much (it seems that Sarah is accepting the highest number she can count to as infinity)?
$endgroup$
– MilkyWay90
Apr 30 at 1:17
add a comment |
$begingroup$
The definition of infinity in some circles is
the highest conceivable number.
Therefore, all Sarah needs to do is count to
the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".
answered Apr 30 at 0:00
BewildererBewilderer
3245
$endgroup$
The definition of infinity in some circles is
the highest conceivable number.
Therefore, all Sarah needs to do is count to
the highest number she knows of, be that a hundred, a thousand, whatever. Because she cannot think of any number higher than that, that is her "infinity".
answered Apr 30 at 0:00
BewildererBewilderer
3245
answered Apr 30 at 0:00
BewildererBewilderer
3245
answered Apr 30 at 0:00
BewildererBewilderer
3245
answered Apr 30 at 0:00
BewildererBewilderer
3245
3245
1
$begingroup$
Finitism much (it seems that Sarah is accepting the highest number she can count to as infinity)?
$endgroup$
– MilkyWay90
Apr 30 at 1:17
add a comment |
1
$begingroup$
Finitism much (it seems that Sarah is accepting the highest number she can count to as infinity)?
$endgroup$
– MilkyWay90
Apr 30 at 1:17
1
1
$begingroup$
Finitism much (it seems that Sarah is accepting the highest number she can count to as infinity)?
$endgroup$
– MilkyWay90
Apr 30 at 1:17
$begingroup$
Finitism much (it seems that Sarah is accepting the highest number she can count to as infinity)?
$endgroup$
– MilkyWay90
Apr 30 at 1:17
add a comment |
$begingroup$
Sarah is also known as
Chuck Norris
Indeed:
"Chuck Norris counted to infinity. Twice."
And since
"Chuck Norris has his own Gender.", Sarah is a suitable second name for them.
answered 2 days ago
user60001user60001
411
New contributor
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Sarah is also known as
Chuck Norris
Indeed:
"Chuck Norris counted to infinity. Twice."
And since
"Chuck Norris has his own Gender.", Sarah is a suitable second name for them.
answered 2 days ago
user60001user60001
411
New contributor
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Sarah is also known as
Chuck Norris
Indeed:
"Chuck Norris counted to infinity. Twice."
And since
"Chuck Norris has his own Gender.", Sarah is a suitable second name for them.
answered 2 days ago
user60001user60001
411
New contributor
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Sarah is also known as
Chuck Norris
Indeed:
"Chuck Norris counted to infinity. Twice."
And since
"Chuck Norris has his own Gender.", Sarah is a suitable second name for them.
answered 2 days ago
user60001user60001
411
New contributor
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 days ago
user60001user60001
411
New contributor
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 days ago
user60001user60001
411
answered 2 days ago
user60001user60001
411
411
New contributor
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user60001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
$begingroup$
Sarah isn't great at counting but she is great at improving anything she does while she is doing it.
Therefore, every time she counts a number she can count it faster than the previous one. The improvement it's not that spectacular, and to count one number still takes her 99.8% of the time it took to count the previous one.
This way, if counting to 1 took Sarah 1 second, the time it will take Sarah to count to n is: $1+1cdot 0.998 + 1cdot 0.998^2 + .... + 1cdot 0.998^n$
Since that's just a geometric series, it's sum to infinite is $frac11-0.998=500$ seconds.
That is, just thanks to keeping improving continuously, Sarah can count to infinite in 8 minutes and 20 seconds.
answered 2 days ago
PerePere
27316
$endgroup$
1
$begingroup$
I like this one! I actually didn’t expect another answer to come in with good mathematical arguments! +1
$endgroup$
– PerpetualJ
2 days ago
add a comment |
$begingroup$
Sarah isn't great at counting but she is great at improving anything she does while she is doing it.
Therefore, every time she counts a number she can count it faster than the previous one. The improvement it's not that spectacular, and to count one number still takes her 99.8% of the time it took to count the previous one.
This way, if counting to 1 took Sarah 1 second, the time it will take Sarah to count to n is: $1+1cdot 0.998 + 1cdot 0.998^2 + .... + 1cdot 0.998^n$
Since that's just a geometric series, it's sum to infinite is $frac11-0.998=500$ seconds.
That is, just thanks to keeping improving continuously, Sarah can count to infinite in 8 minutes and 20 seconds.
answered 2 days ago
PerePere
27316
$endgroup$
1
$begingroup$
I like this one! I actually didn’t expect another answer to come in with good mathematical arguments! +1
$endgroup$
– PerpetualJ
2 days ago
add a comment |
$begingroup$
Sarah isn't great at counting but she is great at improving anything she does while she is doing it.
Therefore, every time she counts a number she can count it faster than the previous one. The improvement it's not that spectacular, and to count one number still takes her 99.8% of the time it took to count the previous one.
This way, if counting to 1 took Sarah 1 second, the time it will take Sarah to count to n is: $1+1cdot 0.998 + 1cdot 0.998^2 + .... + 1cdot 0.998^n$
Since that's just a geometric series, it's sum to infinite is $frac11-0.998=500$ seconds.
That is, just thanks to keeping improving continuously, Sarah can count to infinite in 8 minutes and 20 seconds.
answered 2 days ago
PerePere
27316
$endgroup$
Sarah isn't great at counting but she is great at improving anything she does while she is doing it.
Therefore, every time she counts a number she can count it faster than the previous one. The improvement it's not that spectacular, and to count one number still takes her 99.8% of the time it took to count the previous one.
This way, if counting to 1 took Sarah 1 second, the time it will take Sarah to count to n is: $1+1cdot 0.998 + 1cdot 0.998^2 + .... + 1cdot 0.998^n$
Since that's just a geometric series, it's sum to infinite is $frac11-0.998=500$ seconds.
That is, just thanks to keeping improving continuously, Sarah can count to infinite in 8 minutes and 20 seconds.
answered 2 days ago
PerePere
27316
edited 2 days ago
answered 2 days ago
PerePere
27316
answered 2 days ago
PerePere
27316
answered 2 days ago
PerePere
27316
27316
1
$begingroup$
I like this one! I actually didn’t expect another answer to come in with good mathematical arguments! +1
$endgroup$
– PerpetualJ
2 days ago
add a comment |
1
$begingroup$
I like this one! I actually didn’t expect another answer to come in with good mathematical arguments! +1
$endgroup$
– PerpetualJ
2 days ago
1
1
$begingroup$
I like this one! I actually didn’t expect another answer to come in with good mathematical arguments! +1
$endgroup$
– PerpetualJ
2 days ago
$begingroup$
I like this one! I actually didn’t expect another answer to come in with good mathematical arguments! +1
$endgroup$
– PerpetualJ
2 days ago
add a comment |
$begingroup$
The answer is:
She starts counting and for each number she takes half the time to count to the next number, through this method you can count to infinity in a finite time.
edited 2 days ago
Tahel
72011
answered 2 days ago
JamesttukJamesttuk
211
New contributor
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
The answer is:
She starts counting and for each number she takes half the time to count to the next number, through this method you can count to infinity in a finite time.
edited 2 days ago
Tahel
72011
answered 2 days ago
JamesttukJamesttuk
211
New contributor
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
The answer is:
She starts counting and for each number she takes half the time to count to the next number, through this method you can count to infinity in a finite time.
edited 2 days ago
Tahel
72011
answered 2 days ago
JamesttukJamesttuk
211
New contributor
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
The answer is:
She starts counting and for each number she takes half the time to count to the next number, through this method you can count to infinity in a finite time.
edited 2 days ago
Tahel
72011
answered 2 days ago
JamesttukJamesttuk
211
New contributor
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Tahel
72011
edited 2 days ago
Tahel
72011
edited 2 days ago
Tahel
72011
72011
answered 2 days ago
JamesttukJamesttuk
211
New contributor
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 days ago
JamesttukJamesttuk
211
answered 2 days ago
JamesttukJamesttuk
211
211
New contributor
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Jamesttuk is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
$begingroup$
Could this be the right approach (even if it is not the correct answer)?
Time is finite, yes, but continuous, so it contains an infinite number of individual positions. If we apply, for example, the function f: x -> 1/(10-x) to the interval of minutes [0,10] belonging to the Real Numbers, just before the 10 minutes we will have reached infinity.
answered 2 days ago
HermesHermes
5359
$endgroup$
add a comment |
$begingroup$
Could this be the right approach (even if it is not the correct answer)?
Time is finite, yes, but continuous, so it contains an infinite number of individual positions. If we apply, for example, the function f: x -> 1/(10-x) to the interval of minutes [0,10] belonging to the Real Numbers, just before the 10 minutes we will have reached infinity.
answered 2 days ago
HermesHermes
5359
$endgroup$
add a comment |
$begingroup$
Could this be the right approach (even if it is not the correct answer)?
Time is finite, yes, but continuous, so it contains an infinite number of individual positions. If we apply, for example, the function f: x -> 1/(10-x) to the interval of minutes [0,10] belonging to the Real Numbers, just before the 10 minutes we will have reached infinity.
answered 2 days ago
HermesHermes
5359
$endgroup$
Could this be the right approach (even if it is not the correct answer)?
Time is finite, yes, but continuous, so it contains an infinite number of individual positions. If we apply, for example, the function f: x -> 1/(10-x) to the interval of minutes [0,10] belonging to the Real Numbers, just before the 10 minutes we will have reached infinity.
answered 2 days ago
HermesHermes
5359
edited 2 days ago
answered 2 days ago
HermesHermes
5359
answered 2 days ago
HermesHermes
5359
answered 2 days ago
HermesHermes
5359
5359
add a comment |
add a comment |
$begingroup$
Did Sarah perhaps say once:
$limlimits_xtoinfty x = infty$
edited 2 days ago
trolley813
1,500411
answered 2 days ago
HamstirlyHamstirly
111
New contributor
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Sarah would have to say this very slowly to reach ten minutes, which would be impractical if @PerpetualJ was paying for every minute during the phone call!
$endgroup$
– Mr Pie
2 days ago
add a comment |
$begingroup$
Did Sarah perhaps say once:
$limlimits_xtoinfty x = infty$
edited 2 days ago
trolley813
1,500411
answered 2 days ago
HamstirlyHamstirly
111
New contributor
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Sarah would have to say this very slowly to reach ten minutes, which would be impractical if @PerpetualJ was paying for every minute during the phone call!
$endgroup$
– Mr Pie
2 days ago
add a comment |
$begingroup$
Did Sarah perhaps say once:
$limlimits_xtoinfty x = infty$
edited 2 days ago
trolley813
1,500411
answered 2 days ago
HamstirlyHamstirly
111
New contributor
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Did Sarah perhaps say once:
$limlimits_xtoinfty x = infty$
edited 2 days ago
trolley813
1,500411
answered 2 days ago
HamstirlyHamstirly
111
New contributor
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
trolley813
1,500411
edited 2 days ago
trolley813
1,500411
edited 2 days ago
trolley813
1,500411
1,500411
answered 2 days ago
HamstirlyHamstirly
111
New contributor
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 days ago
HamstirlyHamstirly
111
answered 2 days ago
HamstirlyHamstirly
111
111
New contributor
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Hamstirly is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Sarah would have to say this very slowly to reach ten minutes, which would be impractical if @PerpetualJ was paying for every minute during the phone call!
$endgroup$
– Mr Pie
2 days ago
add a comment |
$begingroup$
Sarah would have to say this very slowly to reach ten minutes, which would be impractical if @PerpetualJ was paying for every minute during the phone call!
$endgroup$
– Mr Pie
2 days ago
$begingroup$
Sarah would have to say this very slowly to reach ten minutes, which would be impractical if @PerpetualJ was paying for every minute during the phone call!
$endgroup$
– Mr Pie
2 days ago
$begingroup$
Sarah would have to say this very slowly to reach ten minutes, which would be impractical if @PerpetualJ was paying for every minute during the phone call!
$endgroup$
– Mr Pie
2 days ago
add a comment |
$begingroup$
Despite the puzzle being already solved, I have another take on this.
All she needs to do is
use a diverging function.
For instance, she could say
-log(3), -log(2), -log(1), -log(0)
Which is in agreement with the hint that she goes incredibly fast in the end.
answered 2 days ago
legrojanlegrojan
1814
$endgroup$
add a comment |
$begingroup$
Despite the puzzle being already solved, I have another take on this.
All she needs to do is
use a diverging function.
For instance, she could say
-log(3), -log(2), -log(1), -log(0)
Which is in agreement with the hint that she goes incredibly fast in the end.
answered 2 days ago
legrojanlegrojan
1814
$endgroup$
add a comment |
$begingroup$
Despite the puzzle being already solved, I have another take on this.
All she needs to do is
use a diverging function.
For instance, she could say
-log(3), -log(2), -log(1), -log(0)
Which is in agreement with the hint that she goes incredibly fast in the end.
answered 2 days ago
legrojanlegrojan
1814
$endgroup$
Despite the puzzle being already solved, I have another take on this.
All she needs to do is
use a diverging function.
For instance, she could say
-log(3), -log(2), -log(1), -log(0)
Which is in agreement with the hint that she goes incredibly fast in the end.
answered 2 days ago
legrojanlegrojan
1814
answered 2 days ago
legrojanlegrojan
1814
answered 2 days ago
legrojanlegrojan
1814
answered 2 days ago
legrojanlegrojan
1814
1814
add a comment |
add a comment |
$begingroup$
My answer is:
As Sarah got really fast, time stopped...according to Einstein's relativity..hence she did it....I know this sounds absurd but ...meh!
edited 2 days ago
Glorfindel
15k45788
answered 2 days ago
user669545user669545
1
New contributor
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
My answer is:
As Sarah got really fast, time stopped...according to Einstein's relativity..hence she did it....I know this sounds absurd but ...meh!
edited 2 days ago
Glorfindel
15k45788
answered 2 days ago
user669545user669545
1
New contributor
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
My answer is:
As Sarah got really fast, time stopped...according to Einstein's relativity..hence she did it....I know this sounds absurd but ...meh!
edited 2 days ago
Glorfindel
15k45788
answered 2 days ago
user669545user669545
1
New contributor
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
My answer is:
As Sarah got really fast, time stopped...according to Einstein's relativity..hence she did it....I know this sounds absurd but ...meh!
edited 2 days ago
Glorfindel
15k45788
answered 2 days ago
user669545user669545
1
New contributor
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Glorfindel
15k45788
edited 2 days ago
Glorfindel
15k45788
edited 2 days ago
Glorfindel
15k45788
15k45788
answered 2 days ago
user669545user669545
1
New contributor
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 days ago
user669545user669545
1
answered 2 days ago
user669545user669545
1
1
New contributor
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user669545 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1
$begingroup$
@MrPie All the way to infinity!
$endgroup$
– PerpetualJ
Apr 29 at 23:40
9
$begingroup$
This question feels a bit too broad. Are you sure there's one demonstrably correct answer to this one?
$endgroup$
– PiIsNot3
Apr 30 at 0:29
4
$begingroup$
An appropriate question for your username, @PerpetualJ.
$endgroup$
– Gareth McCaughan♦
Apr 30 at 0:59
13
$begingroup$
My concern is that there may be more than one valid answer, and without specifying further restrictions, the “correct” one becomes an arbitrary choice. There’s already many good answers that could potentially be correct, which feeds into my concern
$endgroup$
– PiIsNot3
Apr 30 at 4:06
5
$begingroup$
@PerpetualJ Several different answers already do so. As it stands, this seems to be too broad.
$endgroup$
– Deusovi♦
2 days ago