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Interesting Numbers


Theorem: All positive integers are interesting.

Proof: Let X = {set of un-interesting positive integers}. Then by the well-ordering principle, set X has a least element, call it y. But, since y is “the least of the un-interesting positive integers,” that makes it quite interesting. Remove y from set X.

Now, this process and argument can be repeated until set X is empty, which means all of the positive integers must be interesting.