Category:Definitions/Comparable Sets

This category contains definitions related to Comparable Sets.
Related results can be found in Category:Comparable Sets.

Comparable in Size

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 $S$.

Comparable by Subset Ordering

Let $S$ and $T$ be sets.

Then $S$ and $T$ are comparable (with respect to the subset ordering) if and only if either:

$S \subseteq T$

or:

$T \subseteq S$

or both.