Definition:Comparable Sets/Cardinality

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Definition

Let $S$ and $T$ be sets.


Then $S$ and $T$ are comparable (in size) if and only if either:

$S$ can be put into one-to-one correspondence with a subset of $T$

or:

$T$ can be put into one-to-one correspondence with a subset of $S$

or both.


That is, if either $S$ is smaller than $T$ or $T$ is smaller than $S$.


Also see

  • Results about comparable sets can be found here.


Sources