MathGloss

Assuming the Axiom of Choice, the cardinality of a set $X$ is the least ordinal number $\alpha$ such that there exists a bijection between $X$ and $\alpha$.

There exists a well-ordering on the cardinal numbers under the relation $\vert A\vert \leq \vert B\vert$ if and only if there exists an injection from $A$ to $B$.

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