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In 1901, the British philosopher and mathematician Bertrand Russell uncovered a possible paradox that necessitated a modification to set theory. One version of Russell's Paradox involves a town with one male barber who, every day, shaves every man who doesn't shave himself, and no one else. Does the barber shave himself?
From The Math Book published by Sterling
Interesting number paradox
Did you know that all numbers are interesting?
Proof: Assume there exists a set of uninteresting numbers. This set would have a smallest number, which is interesting because it is the smallest uninteresting number. But a number cannot be both interesting and uninteresting, so the assumption that there exists a set of uninteresting numbers must be wrong and hence, all numbers must be interesting.