Let = {0,1}^N, = { ; (there exists ) s.t ( }. Recall that the function , given by is a bijection. Denote by the inverse function . Note that for ,

is the sequence with .

a) Construct an injection .

b) Construct an injection . (Hint: Interlace decimals)

The question is kind of confusing with all these notations, any help will be useful.