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by AnimalMuppet
1760 days ago
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I think so? If I do it the "normal" way (repeating the [0, 1] interval infinitely many times), there are infinite times as many reals outside the [0, 1] interval as there are in it. But that "infinite times" is a countable infinity - the number of integers. How does "the number of reals in [0, 1] times the number of integers" compare to "the number of reals in [0, 1]"? Are they the "same" infinity? What if we use rationals instead of reals? We can do the same x 3 thing, right? But the number of rationals is countably infinite, and "3 times countably infinite" is the same as "countably infinite times countably infinite", isn't it? |
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