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I am new to LaTex. The following is my proof. How do I code it so that it's not italic?

\\Proof: 

 \indent \forall A \in \mathcal{A}, let B_{A} \: be \: the \: collection \: of \: all \: subsets \: of \: B \: containing \: exactly \: 2^{n}
\\ \indent elements. \: Using \: the \: Axiom \: of \: Choice,
\\\indent let \: g: \mathcal{A} \rightarrow \bigcup_A\inT be \: a \: choice function \: and \: let \: g(a): B_A 
\\ \indent \forall A \in T, 
\\ \indent \indent A_{A}: = B_{A} \ \bigcup_{m<A} B_{m}
\\ \indent \forall A \in \mathcal{A}, A_{A} \: are \: obviously \: disjoint \: and \: nonempty. 
\\ \indent Using \: \: the \: Axiom \: of \: Choice \: again, 
\\ \indent let \: f: \: B \: \rightarrow \bigcup_{A<T} \: A_{A} \: be \: a \: choice \: function. 
\\ \indent Then \: f \: is \: a \: bijection,\: with \: its \: image \: and \: this \: image \: is \: a \: countable \: subset \:of \:B.
\\ \indent This \: f \: is \: a \: bijection \: with \: an \: infinitely \: countable \: subset \: of \: B. \:
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2  
Welcome to TeX.SX! Please make your code compilable (if possible), or at least complete it with \documentclass{...}, the required \usepackage's, \begin{document}, and \end{document}. That may seem tedious to you, but think of the extra work it represents for TeX.SX users willing to give you a hand. Help them help you: remove that one hurdle between you and a solution to your problem. –  Juri Robl Mar 5 at 20:03
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You are probably receiving a bunch of errors when you compile this proof... most likely due to the fact that you're using math content outside of math mode. –  Werner Mar 5 at 20:03
    
\documentclass{article} \usepackage[utf8]{inputenc} \title{The Axiom of Choice and its Consequences} \author{Samantha Dean } \date{March 3, 2014} \begin{document} \maketitle –  user47377 Mar 5 at 20:08
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@user47377 You should probably read some introduction to LaTeX, because your code is quite odd. Also have a look at ntheorem. –  Juri Robl Mar 5 at 20:27
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LaTeX defines math mode as formatted space delimited by \(...\) (inlined), or \[...\] (displayed). Inside this "region" of code, the user can insert specific macros to typeset mathematical operator, numbers, arrays et similia; an example is \int, \frac, \sum, \bigcup and others. In your non-MWE, the absence of these delimiters is one the main causes of the errors. –  Andrea L. Mar 5 at 20:31

1 Answer 1

I assume that the code snippet you've posted is an excerpt from a larger piece that's entirely in math mode. E.g., all those \: directives are interword spacers, right?

It's really important not to have the entire material in math mode, but only the formulas. In TeX/LaTeX, a "formula" can be something as short as a single character and as long as a multiline displayed equation.

Anyway, the following may serve your purposes. Note that the symbol $ is used to switch into and out of inline math mode. When not in math mode, there's no need to provide explicit interword spacers -- one or more spaces will do -- or explicit line breaks.

enter image description here

Addendum: As @DavidRicherby has pointed out in a comment, using the symbol : (colon) in math mode isn't optimal if the intent is to express a thought such as "for which" or "such that", as TeX will insert an equal amount of whitespace before and after the : symbol -- see above for three illustrations of this effect. In such cases, it's better to use the TeX macro \colon.

\documentclass{article} 
\usepackage{amsmath,amssymb,amsthm}
\begin{document}
\begin{proof} 
$\forall A \in \mathcal{A}$, let $B_{A}$ be the collection of all subsets 
of $B$ containing exactly $2^{n}$ elements. Using the Axiom of Choice,
let $g: \mathcal{A} \rightarrow \bigcup_A\in T$ be a choice function and let $g(a): 
B_A$ $\forall A \in T$, $A_{A}: = B_{A} \bigcup_{m<A} B_{m}$ $\forall A \in 
\mathcal{A}$, $A_{A}$ are obviously disjoint and nonempty. 

Using the Axiom of Choice again, let $f: B \rightarrow \bigcup_{A<T} A_{A}$ be a 
choice function. Then $f$ is a bijection, with its image and this image is a 
countable subset of $B$. This $f$ is a bijection with an infinitely countable subset 
of $B$. 
\end{proof} 
\end{document}
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+1 Nice cleanup! –  Jubobs Mar 5 at 21:06
    
THANK YOU SO MUCH! That helped me so much. I really appreciate it! I'm teaching myself latex and didnt know about the $ –  user47377 Mar 5 at 22:20
4  
Small comment: when defining a function "f from A to B", use f\colon A\to B. \to is just a shorthand but using \colon gives better typesetting (no space before the colon). –  David Richerby Mar 5 at 22:28
    
@DavidRicherby - Good point! –  Mico Mar 5 at 22:33

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