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© 1999-2010 by Francis Edward Su

From the Fun Fact files, here is a Fun Fact at the Medium level:

# All Numbers are Interesting

There are clearly many interesting whole numbers. For instance, 2 is the only even prime number, 3 is the first odd prime, 6 is a perfect number (the sum of the proper divisors is the number itself), etc.

But did you know that all whole numbers are interesting? We shall prove it here.

Suppose, for the sake of contradiction, that not all whole numbers are interesting. Using the well-ordering property of the whole numbers, among the non-interesting numbers there is a smallest non-interesting number N. But that would make N interesting, after all, a contradiction.

Therefore all numbers are interesting.

The Math Behind the Fact:
This is a rather amusing model of a proof by contradiction, and perhaps shouldn't be taken too seriously!

Su, Francis E., et al. "All Numbers are Interesting." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

Subjects:    other
Level:    Medium
Fun Fact suggested by:   Francis Su
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