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by thfuran
1153 days ago
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>For any infinite set, you could select unique values out of them indefinitely. Yes, but if you have a bijection between elements of that set and another, they're still the same size. Consider the strictly positive integers and the strictly negative integers: for any x, there's exactly one corresponding -x. Both sets are infinite, but they're the same size. Contrast that with, for example, the reals and the natural numbers: for each natural number n, there's not a corresponding real number but rather an infinite number of reals in [n, n+1). The sets are not the same size. |
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