Cardinality

We recall the definitions for functions to injective, surjective, and bijective, and then use this to define when two sets have the same cardinality. We also use this to distinguish between finite and infinite sets. We finish with a proof that finite sets have a unique cardinality.

0:00, Intro
0:30, f-images and f-preimages
3:15, Definition of Injective
4:10, Definition of Surjective
5:06, Definition of Bijective
6:10, Example of a Surjective function that is not Injective
7:35, Example of a Bijective function
8:58, Example of a Injective function that is not Surjective
11:48, Example of a Bijective function
12:56, Theorem: Bijections are Invertible
15:48, Definition of Cardinality
19:30, Theorem: Finite Sets have a Unique Cardinality
20:33, Proof: Finite Sets have a Unique Cardinality