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In addition to the usual properties of nonnegative integers -- properties like the commutative properties of addition and multiplication, etc. -- there's one more, which I call it the "Interesting Number Property". The Interesting Number property states that every nonnegative integer is an interesting number. That is, it has a property that makes it interesting to mathematicians.
The proof of the Interesting Number Property is quite simple, really. It goes like this:
Suppose there is an uninteresting number. If so, there must be an uninteresting number that is smaller than all the other uninteresting numbers, by the Well-Ordering Principle. This Smallest Uninteresting Number is, by virtue of its unique position among uninteresting numbers, very interesting indeed -- a contradiction. Thus there are no uninteresting numbers.
The webmaster and author of this Math Help site is Graeme McRae.