I'm attempting to teach myself topology from a textbook. I'm on the first chapter and came into some trouble with some of the set theory.(adsbygoogle = window.adsbygoogle || []).push({});

Here is what the textbook says.

We make a distinction between the object a, which is an elemant of a set A, and the one-element set {a}, which is a subset of A. To illustrate if A is the set {a,b,c}, then the following statements are all correct.

•a is an element of A

•{a} is a subset of A

•{a} is an element of P(A) where P(A) i the power set of A meaning that P(A) is the set of all subsets of A.

However according to the textbook the following statements are not true

•{a} is a member of A

•a is a subset of A

If the set {a}, simply contains a what is the difference between saying a is an "element" of A and a is a "subset" of A? If an object is an element of some set isn't it also a subset of that set? I also am having trouble understanding the idea of a power set. If P(A) is the set of all subsets then doesn't P(A)=A?

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# Basic set theory question

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