- #1
Avichal
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The interesting number paradox is a semi-humorous paradox which arises from the attempt to classify natural numbers as "interesting" or "dull". The paradox states that all natural numbers are interesting. The "proof" is by contradiction: if there exists a non-empty set of uninteresting numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, producing a contradiction.
I don't want to talk about interesting being a subjective quality but the main paradox.
Since the first dull number is interesting, we classify it as interesting. But then the second dull number becomes the first dull number. So it is also interesting.
But if we look again, we have two new members to the interesting category both of which are interesting due to being the first dull number. But two numbers can't be first, right? So what is going on? I want a better understanding of this paradox.
Thank You!