Is the Boolean of a countable set equal to the continuum?

Question

Mathematics

Hello, can you explain why the power of the Boolean set of natural numbers = continuum? I understand that the boolean of a countable set is uncountable (follows from Cantor's theorem), but why precisely the power of the continuum? How can one define a bijection between a boolean and a continuum?
PS
If we consider the continuum hypothesis correct: from which it follows that c = aleph_1, and also assume that there is no such set B: aleph_0 = |A| < |B| < |2^aleph_0|.
Therefore, |2^aleph_0| = aleph_1 =c.

Answer 1

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