Constructing injection questions

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.

Re: Constructing injection questions

I am truly not sure what you are asking for?

Do you understand that is the set of infinite bit strings?

That is the set of infinite bit strings with at a finite collection of zeros?

Every number in has *binary representation*.

The set represent the binary representation that are unique.

Does that help?

Re: Constructing injection questions

sorry, I do not understand those terms, I think this question has things to do with decimal reprsentation