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## Proof, Disproof, and Proof-dis!

The esteemed Notices of the AMS (January 2005) included an article by Paul Renteln and Alan Dundes, entitled "Foolproof: A Sampling of Mathematical Folk Humor." Below is an offering that focuses on logic and proof...Again, Enjoy or Boo & Hiss or even Scratch Your Head in Puzzlement!

Q: What is the difference between an argument and a proof?
A: An argument will convince a reasonable man, but a proof is needed to convince an unreasonable one.

Theorem: A cat has nine tails.
Proof: No cat has eight tails. A cat has one more tail than no cat. Therefore a cat has nine tails.

Theorem: All positive numbers are interesting.
Proof: Assume the contrary. Then there is a lowest noninteresting positive integer. But, hey, that's pretty interesting! A contradiction.

Theorem: 3 = 4?
Proof: Suppose a+b=c. This can also be written as 4a-3a+4b-3b = 4c-3c. After reorganizing: 4a+4b-4c = 3a+3b-3c. Factor out the constants: 4(a+b-c) = 3(a+b-c). Remove the same term on both sides: 4 = 3.