library/cardinal.tex


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\section{Cardinality}

\import{set.tex}
\import{ordinal.tex}
\import{function.tex}
\import{numbers.tex}

\begin{definition}\label{finite}
    $X$ is finite iff there exists a natural number $k$ such that
        there exists a bijection from $k$ to $X$.
\end{definition}

\begin{abbreviation}\label{infinite}
    $X$ is infinite iff $X$ is not finite.
\end{abbreviation}

\begin{definition}\label{cardinality}
    $X$ has cardinality $k$ iff $k$ is a natural number and 
    there exists a bijection from $k$ to $X$.
\end{definition}