# Definition:Cardinal

## Definition

Let $S$ be a set.

Associated with $S$ there exists a set $\map \Card S$ called the cardinal of $S$.

It has the properties:

$(1): \quad \map \Card S \sim S$

that is, $\map \Card S$ is (set) equivalent to $S$

$(2): \quad S \sim T \iff \map \Card S = \map \Card T$
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