### Wednesday, September 19. 2007

Theorem : All positive integers are equal.

Proof :

Sufficient to show that for any two positive integers, A and B, A = B. Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.

Proceed by induction.

If N = 1, then A and B, being positive integers, must both be 1. So A = B.

Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B.

### Wednesday, September 19. 2007

Q: What's purple and commutes?

A: An abelian grape.

Q: What's yellow, and equivalent to the Axiom of Choice?

A: Zorn's Lemon.

### Wednesday, September 19. 2007

A biologist, a statistician and a mathematician are on a photo-safari in africa. They drive out on the savannah in their jeep, stop and scout the horizon with their binoculars.

The biologist : "Look! There's a herd of zebras! And there, in the middle : A white zebra! It's fantastic ! There are white zebra's ! We'll be famous !"

The statistician : "It's not significant. We only know there's one white zebra."

The mathematician : "Actually, we only know there exists a zebra, which is white on one side."

### Wednesday, September 19. 2007

The shortest math joke ever: let epsilon < 0 (*)

### Wednesday, September 19. 2007

What is "pi"?

Mathematician: Pi is thenumber expressing the relationship between the circumference of a circle and its diameter.

Physicist: Pi is 3.1415927plus or minus 0.00000005

Engineer: Pi is about 3.

### Wednesday, September 19. 2007

The ark lands after The Flood. Noah lets all the animals out. Says, "Go and multiply." Several months pass. Noah decides to check up on the animals. All are doing fine except a pair of snakes. "What's the problem?" says Noah. "Cut down some trees and let us live there", say the snakes. Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?" "Certainly", say the snakes. "We're adders, and we need logs to multiply."

### Wednesday, September 19. 2007

Theorem: All positive integers are interesting.

Proof: Assume the contrary. Then there is a lowest non-interesting positive integer. But, hey, that's pretty interesting! A contradiction.