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All numbers are "cool numbers."
Proof:
1. Assume that not all numbers are cool.
2. Divide the numbers into the set of cool numbers and the set of
not-cool numbers.
3. Now, consider the set of not-cool numbers. One of them is less than
all of the others, which means it is the lowest not-cool number in the
universe! Hey, that's pretty cool. Move it to the cool number set.
4. Repeat step 3 until the not-cool set is empty. This means that all
numbers are cool, QED.
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