Verrrrry interesting...

I’d like to finish up the paradox series with a bit of mathematical humour, using proof by contradiction to show that all natural numbers are interesting.

Let U be the set of all uninteresting natural numbers:

U := { n ∈ N | n is not interesting }

Because the set of natural numbers is well ordered, any non-empty subset of the natural numbers must have a smallest element. But the “smallest uninteresting natural number” is certainly interesting! So there can be no smallest element of U, and, thus, U must be the empty set:

U = {}

∴   ∀ n ∈ N, n is interesting

A bit more mathematical humour to go along with that:

There are 3 kinds of people in the world: those who can count, and those who can’t.

There are 10 kinds of people in the world: those who understand the binary system, and those who don’t.

Aleph-null bottles of beer on the wall,
Aleph-null bottles of beer,
Take one down, pass it around,
Aleph-null bottles of beer on the wall...

And you thought mathematicians couldn’t be funny. Well!