A Proof That All Natural Numbers Are Interesting

Posted by mathfail on April 7, 2012 Leave a comment (9) Go to comments

This is a proof that all natural numbers are interesting.

Suppose, for the sake of contradiction, that not all whole numbers are interesting. Using the well-ordering property of the whole numbers, among the non-interesting numbers there is a smallest non-interesting number N. But that would make N interesting, after all, a contradiction.

Therefore all numbers are interesting.

Thanks to Gerald for this submission!

Source: http://www.math.hmc.edu/funfacts/ffiles/20004.8.shtml

** Note: Some posts on Math-Fail are user-submitted and NOT verified by the admin of the site before publication. If you find this post to be distasteful, non-math related, ?or something worse?, then definitely leave a comment letting me know. Thanks very much! Mike **

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9 Comments.

Bill April 7, 2012 at 3:47 pm

I’m a fan of good jokes and all, but that’s the oldest one in the book.

http://en.wikipedia.org/wiki/Interesting_number_paradox

“224 (number), the smallest natural number which does not have its own Wikipedia article.”

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William April 8, 2012 at 12:08 pm

Doesn’t that just prove that there exisits natural numbers that are interesting, not that all natural numbers are intersting?

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- Secret Name April 8, 2012 at 6:09 pm
  
  No, he said “amongs the NON-interesting numbers”
  
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Secret Name April 8, 2012 at 6:10 pm

Interesting joke…

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MM April 9, 2012 at 8:11 am

After all, we can have “the smallest natural number, which wouldn’t be interesting otherwise”.

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Edigley Alexandre April 9, 2012 at 11:22 am

Math joke from the book “Almanac of mathematical curiosities” by Ian Stewart. The book is fantastic.

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Xtifr April 10, 2012 at 4:15 am

The problem is that once you declare that a given number is the smallest non-interesting number (which makes it interesting), it no longer is the smallest non-interesting number, which makes it no longer interesting, which makes it interesting, which makes it no longer interesting, which makes it….

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A Proof That All Natural Numbers Are Interesting

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