For all real numbers x, floor(floor(x / 2) / 2) = floor(x / 4)

Proof:

Let n = floor(n / 2)		[a suggestion from the book I'm reading]

Case 1: n is even

If n is even, n can be written as 2k for some integer k by definition of even. Thus we can write:

floor(floor(x / 2) / 2) = floor(n / 2) = floor(2k / 2) = floor(k) = k		[by definition of floor]

[What do I do now with floor(x / 4) ?]