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Why float('Nan') == float('Nan') is False

uri at speedy.net writes:

> There are more integers than odd numbers, and more odd numbers than prime
> numbers. An infinite set may be a subset of another infinite set although
> they may both have the same cardinality. Or in other words, the number of
> elements in each set is not equal. One has more elements than the other.
> AND, by induction you can also prove that the other one has more elements
> than the first one. So the number of elements in two infinite sets can't be
> equal. Even, if you compare the same set to itself.

You would expect that to be true, but it is not.  There are in fact the
same number of odd integers as integers, and the same number of primes
as integers.  Counterintuitive but true.