Monday, October 27, 2008

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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!

Laurie said...

Q: What do you get if you divide the cirucmference of a jack-o-lantern by its diameter?
A: Pumpkin Pi!

Q: What does the zero say to the the eight?
A: Nice belt!

Q: What is the difference between a Ph.D. in mathematics and a large pizza?
A: A large pizza can feed a family of four...