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design/tpl: Begin symbol list at beginning of index

master
Mike Gerwitz 2021-05-10 16:50:30 -04:00
parent 176c7785e9
commit 4e7b882aed
2 changed files with 20 additions and 10 deletions
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27
design/tpl/sec/notation.tex
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@ -20,10 +20,10 @@ When you see any of these prefixed with ``0.'',
\subsection{Propositional Logic}
\index{boolean!false@\false{}}%
\index{boolean!true@\true{}}%
\index{boolean!FALSE@\tamefalse{}}%
\index{boolean!TRUE@\tametrue{}}%
\indexsym{\true,\false}{boolean}
\index{boolean!FALSE@\tamefalse{} (\false)}%
\index{boolean!TRUE@\tametrue{} (\true)}%
\indexsym\Int{integer}
\index{integer (\Int)}%
We reproduce here certain axioms and corollaries of propositional logic for
convenience and to clarify our interpretation of certain concepts.
@ -56,6 +56,7 @@ We further use $\equiv$ in place of $\leftrightarrow$ to represent material
and $\neg(p \logor q) \vdash (\neg p \logand \neg q)$.
\end{definition}
\indexsym\equiv{equivalence}
\index{equivalence!material (\ensuremath{\equiv})}
\begin{definition}[Material Equivalence]
$p\equiv q \vdash \big((p \logand q) \logor (\neg p \logand \neg q)\big)$.
@ -75,35 +76,41 @@ Consequently,
\subsection{First-Order Logic and Set Theory}
\index{first-order logic}
The symbol $\emptyset$ represents the empty set---%
the set of zero elements.
We assume that the axioms of ZFC~set theory hold,
but define $\in$ here for clarity.
\indexsym\in{set membership}
\index{set!membership@membership (\ensuremath{\in})}
\begin{definition}[Set Membership]
$x \in S \equiv \Set{x} \cap S \not= \emptyset.$
\end{definition}
\index{quantification|see {fist-order logic}}
\index{first-order logic!quantification (\ensuremath{\forall, \exists})}
\indexsym\forall{quantification, universal}
\indexsym\exists{quantification, existential}
\index{quantification!universal (\ensuremath{\forall})}
\index{quantification!existential (\ensuremath{\exists})}
$\forall$ denotes first-order universal quantification (``for all''),
and $\exists$ first-order existential quantification (``there exists''),
over some domain.
\index{disjunction|see {first-order logic}}
\index{first-order logic!disjunction (\ensuremath{\logor})}
\indexsym\logor{disjunction}
\index{disjunction (\ensuremath{\logor})}
\begin{definition}[Existential Quantification]\dfnlabel{exists}
$\Exists{x\in X}{P(x)} \equiv
\true \in \Set{P(x) \mid x\in X}$.
\end{definition}
\index{conjunction|see {first-order logic}}
\index{first-order logic!conjunction (\ensuremath{\logand})}
\indexsym\logand{conjunction}
\index{conjunction (\ensuremath{\logand})}
\begin{definition}[Universal Quantification]\dfnlabel{forall}
$\Forall{x\in X}{P(x)} \equiv \neg\Exists{x\in X}{\neg P(x)}$.
\end{definition}
\indexsym\emptyset{set empty}
\indexsym{\Set{}}{set}
\index{set!empty (\ensuremath{\emptyset, \{\}})}
\begin{remark}[Vacuous Truth]
By Definition~7, $\Exists{x\in\emptyset}P \equiv \false$

3
design/tpl/tpl.sty
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@ -120,3 +120,6 @@
\newcommand\bicompi[1]{{#1}^\bullet}
\let\xml\texttt
% Symbols appear at the beginning of the index
\newcommand\indexsym[2]{\index{__sym_#2@{\ensuremath{#1}}|see {#2}}}