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.