Show that the power set of a set A, finite or infinite, has too many elements to
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Show that the power set of a set A, finite or infinite, has too many elements to be able to be put in a one-to-one correspondence with A. Explain why this intuitively means that there are an infinite number of infinite cardinal numbers. Is the set of everything a logically acceptable concept? Why or why not?
For any set A, we denote by P(A) the collection of all subsets of A. For example, if A = {a, b, c, d}, then {a, b, d} ∈ P(A). The set P(A) is the power set of A.
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