::[2] (note the brackets, it's an equivalence class) = {0,1}. A set cannot equal a scalar, and that's a fact. 
 ::A^B for {f|f: A->B} is, for the purposes of this article, the same as A x B, their Cartesian product. We should note that |{f|f:A->B}| = | A x B |, but don't get silly with equals signs for things that aren't equal, and don't use obscure notation AT ALL. Will you provide a citation rather than insisting that it's "standard"?