(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A be the set of all sets.

#1.) Show that P(A) is a subset of A.

#2.) Find a contradiction.

2. Relevant equations

3. The attempt at a solution

#1.) We know that P(A) is a set. Therefore it must be in A, since A is the set of ALL sets.

#2.) I cannot figure out what to do here. I do not have a theorem that says that |P(A)| > |A|. I do have a theorem that states that there is no injection from P(A) to A and also that there is no surjection from A to P(A).

Since there is no injection from P(A) to A, does this alone mean that |P(A)| > |A| ?

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# The set of all sets contradiction

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