lathalesians-nomenclature-analysis.tex

\nomenclature[a0000]{iff}{if and only if}
\nomenclature[a0010]{$\blacksquare$}{the Halmos symbol, which stands for \latin{quod erat demonstrandum}}
\nomenclature[a0020]{$A \defeq \set{1,2,3}$}{is equal by definition to (left to right)}
\nomenclature[a0030]{$\set{1,2,3} \eqdef A$}{is equal by definition to (right to left)}
\nomenclature[a0040]{$a_i \idwith b_i$}{is identified with}
\nomenclature[a0050]{$x \tendsto \infty$}{tends to}
\nomenclature[a0060]{$A \Implies B$}{implies, only if}
\nomenclature[a0070]{$A \ImpliedBy B$}{implied by, if}
\nomenclature[a0080]{$A \Iff B$}{if and only if}
\nomenclature[a0090]{$\N$}{natural numbers}
\nomenclature[a0100]{$\Nz$}{ditto, explicitly incl. 0}
\nomenclature[a0110]{$\Nnz$}{nonzero natural numbers}
\nomenclature[a0120]{$\Z$}{integers}
\nomenclature[a0130]{$\Zp$}{positive integers}
\nomenclature[a0140]{$\Znn$}{nonnegative integers}
\nomenclature[a0150]{$\Zn$}{negative integers}
\nomenclature[a0160]{$\Znz$}{nonzero integers}
\nomenclature[a0170]{$\Q$}{rationals}
\nomenclature[a0180]{$\Qp$}{positive rationals}
\nomenclature[a0190]{$\Qnn$}{nonnegative rationals}
\nomenclature[a0200]{$\Qn$}{negative rationals}
\nomenclature[a0210]{$\Qnz$}{nonzero rationals}
\nomenclature[a0220]{$\R$}{reals, $(-\infty, +\infty)$}
\nomenclature[a0230]{$\Rp$}{positive reals, $(0, +\infty)$}
\nomenclature[a0240]{$\Rnn$}{nonnegative reals, $[0, +\infty)$}
\nomenclature[a0250]{$\Rn$}{negative reals, $(-\infty, 0)$}
\nomenclature[a0260]{$\Rnz$}{nonzero reals, $\R \setminus \set{0}$}
\nomenclature[a0270]{$\Rx$}{extended reals, $[-\infty, +\infty]$}
\nomenclature[a0280]{$\Rpx$}{extended positive reals, $(0, +\infty]$}
\nomenclature[a0290]{$\Rnnx$}{extended nonnegative reals, $[0, +\infty]$}
\nomenclature[a0300]{$\Rnx$}{extended negative reals, $[-\infty, 0)$}
\nomenclature[a0310]{$\Rnzx$}{extended nonzero reals, $\Rx \setminus \set{0}$}
\nomenclature[a0320]{$\C$}{complex numbers}
\nomenclature[a0330]{$\Cnz$}{nonzero complex numbers}
\nomenclature[a0340]{$\emptyset$}{the empty set}
\nomenclature[a0350]{$\Collection{F}, \Collection{G}, \ldots$}{name of a collection}
\nomenclature[a0360]{$\Set{A}, \Set{B}, \ldots$}{name of a set}
\nomenclature[a0370]{$\collection{A,B,\ldots}$}{definition of a collection}
\nomenclature[a0380]{$\collection{O\in\Collection{T}}[O\text{ clopen}]$}{\ditto}
\nomenclature[a0390]{$\set{1,2,3}$}{definition of a set}
\nomenclature[a0400]{$\set{x\in\N}[x\text{ even}]$}{\ditto}
\nomenclature[a0410]{$\seqel{a_k}$}{name of element of a sequence}
\nomenclature[a0420]{$\seqel{a_k}[k\in\N]$}{\ditto}
\nomenclature[a0430]{$\seqel{a_k}[k=1][\infty]$}{\ditto}
\nomenclature[a0440]{$\sequence{2, 4, 6, \ldots}$}{definition of a sequence}
\nomenclature[a0450]{$\tuple{2, 4, 6}$}{definition of a tuple}
\nomenclature[a0460]{$x\in\N \st x\text{ even}$}{such that}
\nomenclature[a0470]{$\Z \sset \R$}{subset}
\nomenclature[a0480]{$\R \Sset \Z$}{superset}
\nomenclature[a0490]{$\Z \psset \R$}{proper subset}
\nomenclature[a0500]{$\R \pSset \Z$}{proper superset}
\nomenclature[a0510]{$\Set{A} \setdiff \Set{B}$}{set difference}
\nomenclature[a0520]{$\Set{A} \symmdiff \Set{B}$}{symmetric difference}
\nomenclature[a0530]{$\setcomplement{\Set{A}}$}{set complement}
\nomenclature[a0540]{$\Set{A} \times \Set{B}$}{the Cartesian product of the sets $A$ and $B$}
\nomenclature[a0550]{$\closure{\Set{A}}$}{closure}
\nomenclature[a0560]{$\interior{\Set{A}}$}{interior}
\nomenclature[a0570]{$X \embed Y$}{topological embedding}
\nomenclature[a0580]{$\functype{\C}{\Rnn}$}{function type}
\nomenclature[a0590]{$\functype[f]{\C}{\Rnn}$}{\ditto}
\nomenclature[a0600]{$\funcdefn{x}{x^2}$}{function definition}
\nomenclature[a0610]{$\funcdefn[f]{x}{x^2}$}{\ditto}
\nomenclature[a0620]{$f(\Set{A})$}{the image of the set $A$ under the function $f$}
\nomenclature[a0630]{$f^{-1}(\Set{A})$}{the inverse image of the set $A$ under the function $f$}
\nomenclature[a0640]{$\indfunc{\Set{A}}(x)$}{indicator function of a set}
\nomenclature[a0650]{$\zerofunc(x)$}{zero function}
\nomenclature[a0660]{$\argmin_{x\in \Set{A}} f(x)$}{arguments of the minima}
\nomenclature[a0670]{$\argmax_{x\in \Set{A}} f(x)$}{arguments of the maxima}
\nomenclature[a0680]{$\norm{x}_p$}{$p$-norm; in particular, when $p = 2$, Euclidean norm}