sorry, I'm sitting in class right now and my math teacher really doesn't know his stuff.
Say I have {a,b,c,{a,b}} \ P(a,b,c,{a,b}}. When pulling out the elements for the power set, I will eventually come to a {a}. Does this {a} = a from the original? I'm debating my teacher saying that these should be equal, since you're basically saying the element of a is = to the element of a. He keeps bringing up empty set is not equal to {empty set}.
Is this any better? Sorry