# Definition:Cardinality/Also known as

## Definition

Some authors prefer the term **order** instead of **cardinality**, particularly in the context of finite sets.

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 $\operatorname{card} \paren S$.

1968: A.N. Kolmogorov and S.V. Fominâ€Ž: *Introductory Real Analysis* use $\map m A$ for the **power** of the set $A$.

Further notations are $\map n A$ and $\overline A$.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**cardinal number (cardinality)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**cardinal number (cardinality)**