# Countable

(Redirected from Countability)
Definition: Countable
A set is countable if .

Equivalently, is countable of .

This last definition gives an intuitive definition of countability: if we have a surjection , then we can talk about could write , , etc., so that we can write in the form .

The fact that is surjective means that every element of is for some .

So the informal definition of countability is that is countable if its elements can be put in a (potentially infinite) sequence.