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I liked the cantor poster guy, this is actually a decent question on this board, I hate this board and usually idiots from pol post here but this is good. I love you babe.
Anyways, its fun because I just did this, I was doing combinatorics for some test and it was dumb, anyways. In HS i avoided the C^n_k thing, and had to confront it for a test. So I looked into it with my bigger cock from my college level studies.
Anyways I got to the power set, and went to set theory, and found something.
Point is this is nice because I did this recently, and the answer is this.
So for the Peano axioms. the empty set is defined as {} =0. And we assign 0, the natural number to be the empty set. We then defined 1 to be = 0 UI{0}. 2 to be 1U {1}... and so on.
So the natural number n is the succ of n-1.
So 2 being 1 U {1}, would be {0} U {1} = {0,1}
Now someone said this is an abuse of notation, but they're a dumb nigger, because based cantor.
So 2^N_0, is the set of all ordered pairs, with |N| entries, and each component will either be 1 or 0. |N| entries assuming N_0 is aleph null, the cardinality of the set of natural numbers.
Being, thing of R^n, notice how that is the set of ordered pairs, with n entries, all those entries being in the set R. That's what the X^Y should mean. At least if Y is an ordered set, I'm not going to assume nor look into that because I'm lazy. So let's just say Y has to be either a natural number, or the cardinality of the set of integers, rationals, or reals.
Ask me any questions for clarification, I could explain it better, but I'm lazy and wont try to be a perfectionist.
Anyways its the set { <x1,...> }, |N| entries, being the cardinality of natural numbers.
And x_i e {0,1}
