The Interesting number paradox
Claim: There is no such thing as an uninteresting natural number.
Proof by Contradiction: Assume that you have a non-empty set of natural numbers that are not interesting. Due to the well-ordered property of the natural numbers, there must be some smallest number in the set of not interesting numbers. Being the smallest number of a set one might consider not interesting makes that number interesting. Since the numbers in this set were defined as not interesting, we have reached a contradiction because this smallest number cannot be both interesting and uninteresting. Therefore the set of uninteresting numbers must be empty, proving there is no such thing as an uninteresting number.
Claim: There is no such thing as an uninteresting natural number.
Proof by Contradiction: Assume that you have a non-empty set of natural numbers that are not interesting. Due to the well-ordered property of the natural numbers, there must be some smallest number in the set of not interesting numbers. Being the smallest number of a set one might consider not interesting makes that number interesting. Since the numbers in this set were defined as not interesting, we have reached a contradiction because this smallest number cannot be both interesting and uninteresting. Therefore the set of uninteresting numbers must be empty, proving there is no such thing as an uninteresting number.