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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.

Credit: Matthew Holtz


An assemblage of the most gifted minds in the world were all posed the following question:

"What is 2 * 2 ?"

The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99".

The physicist consults his technical references, sets up the problem on his computer, and announces "it lies between 3.98 and 4.02".

The mathematician cogitates for a while, oblivious to the rest of the world, then announces: "I don't what the answer is, but I can tell you, an answer exists!".

Philosopher: "But what do you _mean_ by 2 * 2 ?"

Logician: "Please define 2 * 2 more precisely."

Accountant: Closes all the doors and windows, looks around carefully, then asks "What do you _want_ the answer to be?"

Computer Hacker: Breaks into the NSA super-computer and gives the answer.

Credit: Matthew Holtz


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