\begin{definition}[Definition:Cardinality/Also known as]
Some authors prefer the term '''order''' instead of '''cardinality''', particularly in the context of finite sets.
{{AuthorRef|Georg Cantor}} used the term '''power''' and equated it with the term '''cardinal number''', using the notation $\overline {\overline M}$ for the '''cardinality''' of $M$.
Some sources cut through all the complicated language and call it the '''size'''.
Some sources use $\map {\#} S$ (or a variant) to denote '''set cardinality'''. This notation has its advantages in certain contexts, and is used on occasion on this website.
Others use $\map C S$, but this is easy to confuse with other uses of the same or similar notation.
A clear but relatively verbose variant is $\Card \paren S$ or $\operatorname{card} \paren S$.
{{BookReference|Introductory Real Analysis|1968|A.N. Kolmogorov|author2 = S.V. Fomin}} use $\map m A$ for the '''power''' of the set $A$.
Further notations are $\map n A$ and $\overline A$.
\end{definition}