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Note that P(I(N)) is the power set of I(N), i.e. the collection of subsets of I(N).

For any subset X in I(N) and 1 <= n <= N, define h_n(X) to be 0 if n is not in X, and 1 if n is in X.

A natural bijection f: I(N) --> {0,1}^N is

f(X) = (h_1(X), h_2(X), h_3(X), ... , h_N(X)).

In other words, the elements in I(N) that are in the subset X identify which coordinates are 1's, and the elements in I(N) that are not in X identify which coordinates are 0's.

For example, if N = 7, then f({2, 3, 4, 6}) = (0, 1, 1, 1, 0, 1, 0).

Lord bless you today!

Define, F:{1,2,3,...,N} to {(a1,a2,a3,...,aN): an∈{0,1},1≤n≤N}, by...

F(n)=an.