\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\groupAdd}[1] { +_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Analysis::Tao::03: Set theory
Cardinality of sets
Equal cardinality
We say that two sets \( X \) and \( Y \) have equal cardinality iff
[...].
Cardinality n
Let \( n \) be a natural number. A set \( X \) is said to have cardinality n
if it has equal cardinality with the set [...].
We also say that such a set has \( n \) elements.
Finite sets
A set is finite iff [...] for some natural number
\( n \); otherwise, the set is called infinite.
Notation: if \( X \) is a finite set, we use \( \#(X) \) to denote the
cardinality of \( X \).
