Definition:Comparable Sets/Cardinality
Jump to navigation
Jump to search
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
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $1$: General Background: $\S 4$ Larger and smaller