The file appendix.tex contains only the contents of Appendix A of the document. The main LaTeX file, MyDoc.tex, inserts the contents of appendix.tex into the document by using the commands
\appendix \input appendix.tex
Appendix A is just like any other section (note that it starts with a \section{} macro just like sections 1,2,3), except that it appears after the \appendix macro as shown above. So LaTeX doesn't number it as chapter 4, but restarts its section (or chapter) numbering using ``A'', ``B'', ``C'', etc.
A link to the actual file appendix.tex, and some comments about its contents, are at the bottom of this page.
\section{Math font styles} % file "appendix.tex"
Several extra font styles are available in math mode,
since there are so many typographical conventions
in various branches of mathematics.\footnote{By the way,
this is an appendix!}
In set theory (among other fields) one often uses
\emph{calligraphic} letters, e.g.,
\verb9$\mathcal{A}$9; \\
$$ \mathcal{A} ~ \mathcal{B} ~ \mathcal{C} ~ \mathcal{D} ~
\mathcal{E} ~ \mathcal{F} ~ \mathcal{G} ~ \mathcal{R} ~
\mathcal{S} ~ \mathcal{T} ~ \mathcal{Z} $$
In number theory, various number sets are often
indicated using
\emph{blackboard capital} letters, e.g.,
\verb9$\mathbb{R}$9; \\
$$ \mathbb{N} ~ \mathbb{Z} ~ \mathbb{Z}_{17} ~
~ \mathbb{R} ~ \mathbb{C} $$
Another style used now and then is
\emph{Fraktur} font letters, e.g.,
\verb9$\mathfrak{F}$9; \\
$$ \mathfrak{A} ~ \mathfrak{B} ~ \mathfrak{C} ~ \mathfrak{D} ~
\mathfrak{E} ~ \mathfrak{F} ~ \mathfrak{G} ~ \mathfrak{R} ~
\mathfrak{S} ~ \mathfrak{T} ~ \mathfrak{Z} $$
In vector algebra it is common to use \emph{boldface} letters
to indicate nonscalar values (vectors and matrices), e.g.,
\verb9$\mathbf{A}$9; \\
$$ \mathbf{A} ~ \mathbf{B} ~ \mathbf{C} ~ \mathbf{M} ~
\mathbf{v} ~ \mathbf{x} ~ \mathbf{y} ~ \mathbf{z} $$
One can get \emph{bold italic} letters for vector variables
by using, e.g.,
\verb9$\textbf{\em x}$9; \\
$$ \textbf{\em A B C D E F G s t u v w x y z} $$
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