Ttdfjt

I'm new to latex and am using some stuff from a document my professor sent out.

I'm trying to define something in a paper I'm writing. Here is what I have:

documentclass[11pt]amsart
usepackageamssymb,latexsym,amsmath,amsthm,enumitem,hyperref
usepackagegraphics,graphicx,multicol,tikz,pgfplots,tkz- 
euclide,relsize,framed
usetikzlibrarycalc
tikzsetfontscale/.style = font=relsize#1

setlengthtopmargin-0.750in
setlengthtextheight9.5in
setlengthtextwidth6.5in
setlengthoddsidemargin0in
setlengthevensidemargin0in
allowdisplaybreaks
renewcommandlabelenumi(alphenumi)
renewcommandlabelenumiiromanenumii.
setlengtharraycolsep2pt

begindocument

sectionImportant Definitions and Theorems

subsectionDefinition [Sparsity]
The emphsparsity of $x in mathbbR^n$ is defined by 
beginequation
normx_0 = cardk in 1, 2, . . . , n : x_k neq 0
endequation

enddocument

However, when I run this I get an Undefined Control Sequence error and I'm not sure what that means or how to fix it, hence I have come for your merciful help. Thanks!

The command norm is not defined by default. A common way to define it is to use mathtools and DeclarPairedDelimiter, so that norm can be called

normx
norm[big]x
norm[Big]x
norm[bigg]x
norm[Bigg]x
norm*x

where the calls with the optional argument manually set the size of the delimiter; the *-form uses automatically extensible delimiter (to be used sparingly).

documentclass[11pt]amsart

% load here other needed packages
usepackageamssymb,mathtools

% set up for the document
setlengthtextheight9.5in
setlengthtextwidth6.5in
calclayout % <--- this is the proper way in amsart

% personal commands
DeclarePairedDelimiternormlVertrVert
DeclareMathOperatorcardcard

% theorem like environments
newtheoremtheoremTheorem[section]
theoremstyledefinition
newtheoremdefinition[theorem]Definition

begindocument

sectionImportant Definitions and Theorems

begindefinition[Sparsity]
The emphsparsity of $x in mathbbR^n$ is defined by 
beginequation
normx_0 = cardbiglk in 1, 2, dots, n : x_k neq 0bigr
endequation
enddefinition

enddocument

• Instead of abusing subsection I defined proper environments for theorems and definition (add the others you need).




• I also defined an operator name for the cardinality.




• The braces for delimiting the set definition should be and .




• Because of the nested sets, I used big for the outer braces (it's optional).




• ... should be dots.




• Instead of guessing at the appropriate values for the page parameters, just set the desired text height and width, then issue calclayout (a command proper of amsart) to set the others.

Adding this definition, based on mathtools (an extension of amsmath) works fine. I defined a znorm command which stretches to the size of its argument in its starred version. Alternatively, you can fine-tune the size of the norm symbols using an optional argument one of big, Big, bigg, Bigg.

Unrelated: you don't have yo load graphics if you load graphicx: the latter does it for you. Similarly, needless to load amsmathif you load mathtools.

documentclass[11pt]amsart
usepackageamssymb,mathtools,amsthm,enumitem,hyperref
usepackagegraphicx,multicol,tikz,pgfplots,tkz-euclide,relsize,framed
usetikzlibrarycalc
tikzsetfontscale/.style = font=relsize#1

setlengthtopmargin-0.750in
setlengthtextheight9.5in
setlengthtextwidth6.5in
setlengthoddsidemargin0in
setlengthevensidemargin0in
allowdisplaybreaks
renewcommandlabelenumi(alphenumi)
renewcommandlabelenumiiromanenumii.
setlengtharraycolsep2pt

DeclarePairedDelimiterXPPznorm[1]lVertrVert_0#1
DeclareMathOperatorcardcard

begindocument

sectionImportant Definitions and Theorems

subsectionDefinition [Sparsity]
The emphsparsity of $x in mathbbR^n$ is defined by
beginequation
znormx=cardbiglk in 1, 2, . . . , n : x_k neq 0bigrqquad znorm*fracxa
endequation

enddocument