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Good Math by Mark C. Chu-Carroll

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The Continuum Hypothesis

Cantor proposed that the first infinite set larger than 0 was of size of the powerset of 0, which is the size of the set of reals. That proposition is known as the continuum hypothesis. If the continuum hypothesis is true, then

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The continuum hypothesis turns out to be a really sticky problem. In the model of numbers constructed from set theory (and thus, in all set-theoretic mathematics!), it’s neither true nor false. That is, you can choose to treat it as true, and all of ZFC mathematics will be fine, because you’ll never be able to prove a contradiction. But you also can take it as being false, and still you won’t ...

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