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> Or even better, use None instead of nan. ++ On Thu, Feb 14, 2019 at 3:26 AM Joe Pfeiffer <pfeiffer at cs.nmsu.edu> wrote: > 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. > I know it's a Python mailing list and not Math, and this thread is off-topic. But anyway, it depends how you define "more". There are infinite integers and odd numbers, and as I said you can't compare infinite "numbers" of elements. But, the set of odd numbers is a subset of the set of integers. If you take any big range, for example from 0 to google (10**100) - there are more integers in this range than odd numbers. There are integers which are not odd numbers but there are no odd numbers which are not integers. The set of integers which are not odd numbers is infinite. So in this sense, there are more integers than odd numbers. And also, there are more odd numbers than prime numbers (there is one prime number which is not odd, and many many odd numbers which are not prime). > There are in fact the same number of odd integers as integers, and the same number of primes as integers. If you mean that the "number" of odd integers is equal to the "number" of integers, it is not. They are both infinite and infinity is not a number. Two sets can have the same cardinality even if one set contains more elements than the other. At least in the sense I define "more". A cardinality is equal to the number of elements only for finite sets. For infinite sets the cardinality is not the number of elements, the number of elements is infinite. > -- > https://mail.python.org/mailman/listinfo/python-list >

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