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# Set theory watch

1. Quick question:

How do you show that X and P(X) i.e. the power set of X are not equipollent? (two sets are equipollent iff there is a one-one correspondence between them)

Thanks!
2. There is a proof known as the diagonal argument. Suppose such a bijection exists, call it f. What can you tell me about the set ?
3. hmm well i think im misunderstanding something

so the set of all subsets of X is larger than X, but this does not entail that there cannot be a one-one correspondence between the two sets, since f is a one-one function from X to Y iff it is into (so D(f) = X) and R(f) is a subset of Y..
4. My proof shows there can't be a bijection, which is equivalent to them not being equipollent.
5. ok just looked it up and get it now. thanks.

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