Category:Finite Sets

From ProofWiki
Jump to navigation Jump to search

This category contains results about Finite Sets.
Definitions specific to this category can be found in Definitions/Finite Sets.

A set $S$ is defined as finite if and only if:

$\exists n \in \N: S \sim \N_{<n}$

where $\sim$ denotes set equivalence.

That is, if there exists an element $n$ of the set of natural numbers $\N$ such that the set of all elements of $\N$ less than $n$ is equivalent to $S$.

Equivalently, a finite set is a set with a count.