May 8, 2010

All numbers are interesting.

This is one of the 101 things - say, 101 is an interesting number, like 1729 - I learned about doin' science 'n' stuff.

Claim: Every number is interesting.

Stronger claim: There is a proof that every number is interesting.

Consider the numbers:
  • 0 is the unique identity operator for addition, which is interesting.
  • 1 is the unique identity operator for multiplication, which is interesting.
  • 2 is the only even prime, which is interesting.
  • 3 is the first odd prime, which is interesting.
  • 4 is the first square, which is interesting.
  • 5 is the first Pythagorean hypoteneuse (22 + 32 = 52), which is interesting.
  • 6 is the first perfect number, which is interesting.
  • etc.
  • ...
Suppose we go on inspecting numbers, and we do eventually find a number that is not interesting. Why, that number would be the first non-interesting number, which is interesting.

Therefore, by induction, all numbers are interesting. Q.E.D.
Observations: 1. This is a (humorous & paradoxical) proof, or (what mathematicians call) an argument, but it is not a story. 2. Wikipedia says it is related to the Berry paradox.

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