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Interesting positive integers

Theorem. Every positive integer is interesting.

Proof. Assume towards a contradiction that there is an uninteresting positive integer. Then there must be a smallest uninteresting positive integer. But being the smallest uninteresting positive integer is interesting by itself. Contradiction!

2 kommentarer på “Interesting positive integers”

  1. den 12 Mar 2008 at 23:14Kristian

    Theorem 2: Every negative integer is interesting.

    Proof. Assume towards a contradiction that there is an uninteresting negative integer. Then there must be a biggest uninteresting positive integer. But being the biggest uninteresting negative integer is interesting by itself. Contradiction!

    Theorem 3: 0 is interesting.

    Proof. In being the only integer who is not positive or negative, one might conclude by intuition that it is indeed interesting, since it is a member of a singleton set.

    So by Theorem 1, 2 and 3:

    All possible integers are interesting.

    Sånn. Kan fortsette me å bevise dette for alle set som har et kjent minste eller største element tror eg? 😛 Men heile beviset spørs vel på koss du definere “interesting”.

  2. den 12 Mar 2008 at 23:14Kristian

    Og ja, kjeda meg litt der.

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