3 ms·

Multiplying by the inverse is not the same as the division

• PaulHoule 2y ago
  Yes, "half of all floating-point numbers are in the interval [-1,1]" but measures over real numbers and other continuous spaces are about as toxic as you can get https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox In my mind the "real" numbers as described by Cantor ought to be called the phony numbers, whereas there is a lot more reality in the integers or the rationals in that every integer has a name. You could just as well say that "half of the reals are in the [-1, 1] range" in that you could say there is a 1:1 correspondence between x and 1/x or you could say there are as many reals in [-1, 1] as there are between [π, 2π].
  • Someone 2y ago
    > You could just as well say that "half of the reals are in the [-1, 1] range" in that you could say there is a 1:1 correspondence between x and 1/x That applies to the rationals, too, and for integers there’s the similar “there are as many odd integers as there are integers”. Infinities are weird, even the simplest one of aleph-zero.
• deleted 2y ago
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