The shortest math joke ever: let epsilon < 0 (*)
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Theorem : All positive integers are equal.
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.
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.
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.