The easy way is to shift a countable set.
I'm looking for a injective function defined as f: [0,1]-->]0,1[.
How should I start?
I'm trying to start with what it implies:
x=y => f(x)=f(y) for all x,y in A.
It's not arctan(x) because im(arctan(x)) with x in[0,1] is not ]0,1[. So I rather think that f is only injective in [0,1].
I'm also thinking maybe I need to find f(x)^-1 first and then f(x), (since f is injective).
Thanks in advance!