### What is “pi”?

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.

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.

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.

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.

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

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.

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.