# Finite set

A finite set is like a package for a group of things. The package can be monstrously big to fit the amount of things it needs to hold but ultimately there is a limit to the amount of items in the package. This means that if you were to go by each item in this package one by one and count them you would eventually reach the last item. (Incidentally this number that you counted would be the cardinality of the set)

Create a diagram expressing what a finite set is.

examples, being the easiest way to understand what “finite set” means

More formally a Finite set is a set that also has a bijection with one of the natural numbers.

the same as saying the cardinality is finite

difference between “finite” and “hereditarily finite”: in particular, {N} is finite though N is infinite

Children:

• Category of finite sets

The category of finite sets is exactly what it claims to be. It’s a useful training ground for some of the ideas of category theory.

Parents:

• Set

An unordered collection of distinct objects.