Show Q N 4SolutionAccording to Cantors Theorem for any set

Show |Q| = |N {4}|.

Solution

According to Cantor\'s Theorem, for any set A there is no surjective function AP(A). With A=N {4} this implies that P(N {4}) is not countable. So is uncountable. Similarly P(R) is uncountable, so there exists bijection between P(N {4}) and P(R)

Show |Q| = |N {4}|.SolutionAccording to Cantor\'s Theorem, for any set A there is no surjective function AP(A). With A=N {4} this implies that P(N {4}) is not c

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