deletions | additions       diff --git a/subsection_Functions_begin_tabular_lll__.tex b/subsection_Functions_begin_tabular_lll__.tex  index 18308eb..a851718 100644  --- a/subsection_Functions_begin_tabular_lll__.tex  +++ b/subsection_Functions_begin_tabular_lll__.tex 
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\verb!\sigma! & $\sigma$ &\verb!\gimel! & $\gimel$  \end{tabular}  \subsection{Set theory}  \begin{tabular}{lll}  \emph{description} & \emph{command} & \emph{output}\\  set brackets & \verb!\{1,2,3\}! & $\{1,2,3\}$\\  element of & \verb!\in! & $\in$\\  not an element of & \verb!\not\in! & $\not\in$\\  subset of & \verb!\subset! & $\subset$\\  subset of & \verb!\subseteq! & $\subseteq$\\  not a subset of & \verb!\not\subset! & $\not\subset$\\  contains & \verb!\supset! & $\supset$\\  contains & \verb!\supseteq! & $\supseteq$\\  union & \verb!\cup! & $\cup$\\  intersection & \verb!\cap! & $\cap$\\  big union &   \verb!\bigcup_{n=1}^{10}A_n! &  $\displaystyle \bigcup_{n=1}^{10}A_{n}$\\  big intersection & \verb!\bigcap_{n=1}^{10}A_n! &$\displaystyle \bigcap_{n=1}^{10}A_{n}$\\  empty set & \verb!\emptyset! & $\emptyset$\\  power set & \verb!\mathcal{P}! & $\mathcal{P}$\\  minimum & \verb!\min! & $\min$\\  maximum & \verb!\max! & $\max$\\  supremum & \verb!\sup! & $\sup$\\  infimum & \verb!\inf! & $\inf$\\  limit superior & \verb!\limsup! & $\limsup$\\  limit inferior & \verb!\liminf! & $\liminf$\\  closure & \verb!\overline{A}! & $\overline{A}$  \end{tabular}  \subsection{Calculus}  \begin{tabular}{lll}  \emph{description} & \emph{command} & \emph{output}\\  derivative & \verb!\frac{df}{dx}! & $\displaystyle \frac{df}{dx}$\\  derivative & \verb!\f'! & $f'$\\  partial derivative &   \begin{tabular}{l}  \verb!\frac{\partial f}!\\ \verb!{\partial x}!   \end{tabular}& $\displaystyle \frac{\partial f}{\partial x}$\\  integral & \verb!\int! & $\displaystyle\int$\\  double integral & \verb!\iint! & $\displaystyle\iint$\\  triple integral & \verb!\iiint! & $\displaystyle\iiint$\\  limits & \verb!\lim_{x\to \infty}! & $\displaystyle \lim_{x\to \infty}$\\  summation &   \verb!\sum_{n=1}^{\infty}a_n! &  $\displaystyle \sum_{n=1}^{\infty}a_n$\\  product &   \verb!\prod_{n=1}^{\infty}a_n! &  $\displaystyle \prod_{n=1}^{\infty}a_n$  \end{tabular}  \subsection{Logic}  \begin{tabular}{lll}  \emph{description} & \emph{command} & \emph{output}\\  not & \verb!\sim! & $\sim$\\  and & \verb!\land! & $\land$\\  or & \verb!\lor! & $\lor$\\  if...then & \verb!\to! & $\to$\\  if and only if & \verb!\leftrightarrow! & $\leftrightarrow$\\  logical equivalence & \verb!\equiv! & $\equiv$\\  therefore & \verb!\therefore! & $\therefore$\\  there exists & \verb!\exists! & $\exists$\\  for all & \verb!\forall! & $\forall$\\  implies & \verb!\Rightarrow! & $\Rightarrow$\\  equivalent & \verb!\Leftrightarrow! & $\Leftrightarrow$  \end{tabular}  \subsection{Linear algebra}  \begin{tabular}{lll}  \emph{description} & \emph{command} & \emph{output}\\  vector & \verb!\vec{v}! & $\vec{v}$\\  vector & \verb!\mathbf{v}! & $\mathbf{v}$\\  norm & \verb!||\vec{v}||! & $||\vec{v}||$\\  matrix&  \begin{tabular}{l}  \verb!\left[!\\  \verb!\begin{array}{ccc}!\\  \verb!1 & 2 & 3 \\!\\  \verb!4 & 5 & 6\\!\\  \verb!7 & 8 & 0!\\  \verb!\end{array}!\\  \verb!\right]!\end{tabular}&  $\displaystyle \left[\begin{array}{ccc}1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 0\end{array}\right]$\\  \\determinant&  \begin{tabular}{l}  \verb!\left|!\\  \verb!\begin{array}{ccc}!\\  \verb!1 & 2 & 3 \\!\\  \verb!4 & 5 & 6 \\!\\  \verb!7 & 8 & 0!\\  \verb!\end{array}!\\  \verb!\right|!  \end{tabular}&  $\displaystyle \left|\begin{array}{ccc}1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 0\end{array}\right|$\\  determinant & \verb!\det(A)! & $ \det(A)$\\  trace & \verb!\operatorname{tr}(A)! & $\operatorname{tr}(A)$\\  dimension & \verb!\dim(V)! & $\dim(V)$\\  \end{tabular}  \subsection{Number theory}  \begin{tabular}{lll}  \emph{description} & \emph{command} & \emph{output}\\  divides & \verb!|! & $|$\\  does not divide & \verb!\not |! & $\not |$\\  div & \verb!\operatorname{div}! & $\operatorname{div}$\\  mod & \verb!\mod! & $\operatorname{mod}$\\  greatest common divisor & \verb!\gcd! & $\gcd$\\  ceiling & \verb!\lceil x \rceil! & $\lceil x\rceil$\\  floor & \verb!\lfloor x \rfloor! & $\lfloor x \rfloor$\\  \end{tabular}  \subsection{Geometry and trigonometry}  \begin{tabular}{lll}  \emph{description} & \emph{command} & \emph{output}\\  angle& \verb!\angle ABC! & $\angle ABC$\\  degree& \verb!90^{\circ}! & $90^{\circ}$\\  triangle& \verb!\triangle ABC! & $\triangle ABC$\\  segment& \verb!\overline{AB}! & $\overline{AB}$\\  sine& \verb!\sin! & $\sin$\\  cosine& \verb!\cos! & $\cos$\\  tangent& \verb!\tan! & $\tan$\\  cotangent& \verb!\cot! & $\cot$\\  secant& \verb!\sec! & $\sec$\\  cosecant& \verb!\csc! & $\csc$\\  inverse sine& \verb!\arcsin! & $\arcsin$\\  inverse cosine& \verb!\arccos! & $\arccos$\\  inverse tangent& \verb!\arctan! & $\arctan$\\  \end{tabular}  \section{Symbols (in \emph{text} mode)}  The followign symbols do \textbf{not} have to be surrounded by dollar signs.  \begin{tabular}{lll}  \emph{description} & \emph{command} & \emph{output}\\  dollar sign & \verb!\$! & \$ \\  percent & \verb!\%! & \% \\  ampersand & \verb!\&! & \& \\  pound & \verb!\#! & \# \\  backslash & \verb!\textbackslash! & \textbackslash \\  left quote marks & \verb!``! & `` \\  right quote marks & \verb!''! & '' \\  single left quote & \verb!`! & ` \\  single right quote & \verb!'! & ' \\  hyphen & \verb!X-ray! & X-ray\\  en-dash & \verb!pp. 5--15! & pp. 5--15 \\  em-dash & \verb!Yes---or no?! & Yes---or no?   \end{tabular}  \section{Math vs. text vs. functions}  In properly typeset mathematics variables appear in italics (e.g., $f(x)=x^{2}+2x-3$). The exception to this rule is predefined functions (e.g., $\sin (x)$). Thus it is important to \textbf{always} treat text, variables, and functions correctly. See the difference between $x$ and x, -1 and $-1$, and $sin(x)$ and $\sin(x)$.   There are two ways to present a mathematical expression--- \emph{inline} or as an \emph{equation}.  \subsection{Inline mathematical expressions}  Inline expressions occur in the middle of a sentence. To produce an inline expression, place the math expression between dollar signs (\verb!$!). For example, typing \verb!$90^{\circ}$ is the same as $\frac{\pi}{2}$ radians! yields $90^{\circ}$ is the same as $\frac{\pi}{2}$ radians.  \subsection{Equations}  Equations are mathematical expressions that are given their own line and are centered on the page. These are usually used for important equations that deserve to be showcased on their own line or for large equations that cannot fit inline. To produce an inline expression, place the mathematical expression between the symbols \verb!\[! and \verb!\]!. Typing \verb!\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]! yields \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.\]    \subsection{Displaystyle}   To get full-sized inline mathematical expressions use \verb!\displaystyle!. Use this sparingly. Typing \verb!I want this $\displaystyle \sum_{n=1}^{\infty}! \verb!\frac{1}{n}$, not this $\sum_{n=1}^{\infty}! \verb!\frac{1}{n}$.! yields\\ I want this $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}$, not this $\sum_{n=1}^{\infty}\frac{1}{n}.$