Prove for the following: a. Theorem: (Cantor-Schroder-Bernstein in the 1800s) For any set S, |S| <...

Prove for the following:

a. Theorem: (Cantor-Schroder-Bernstein in the 1800s) For any set S, |S| < |P(S)|.

b. Proposition N×N is countable.

c. Theorem: (Cantor 1873) Q is countable. (Hint: Similar. Prove for positive rationals first. Then just a union.)

Expert Solution

Colby Messinger answered 2 years ago

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