Not really reverse induction, but related: The principle of induction is equivalent to the axiom that all non-empty sets of natural numbers have a smallest element. And one can always convert proves from one technique to the other.
("If there were uninteresting numbers, there would be a smallest uninteresting number - but the smallest uninteresting number is itself interesting, producing a contradiction.")
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[ 5.5 ms ] story [ 29.0 ms ] threadAs an exercise, try out converting the "Interesting Number Paradox" (http://en.wikipedia.org/wiki/Interesting_number...) to use induction.
("If there were uninteresting numbers, there would be a smallest uninteresting number - but the smallest uninteresting number is itself interesting, producing a contradiction.")