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Hurkyl

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It doesn't take all that much set-theoretic structure for Cantor's argument to be valid. (It even works in the universe of finite sets)

In what sense are you using the phrase "infinite construction"? And why should that be relevant to anything?

The argument is pretty much the same as Russell's paradox; assuming the problematic function exists (an injection [itex]\mathcal{P}(X) \to X[/itex]), you construct some set that has a self-contradictory membership relation in pretty much the same manner.

In what sense are you using the phrase "infinite construction"? And why should that be relevant to anything?

The argument is pretty much the same as Russell's paradox; assuming the problematic function exists (an injection [itex]\mathcal{P}(X) \to X[/itex]), you construct some set that has a self-contradictory membership relation in pretty much the same manner.

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There does not seem to be any need beyond mathematical induction, and the use of the excluded middle, (i.e. A or not A). We set things up in a countable way, and then rely upon proof by contradiction.

In fact, Euclid depends upon both of these principals in proving that the number of primes is infinite.

In fact, Euclid depends upon both of these principals in proving that the number of primes is infinite.

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Hurkyl

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CRGreathouse

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Are you asking about math without induction, like Robinson arithmetic?

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