>>11283841First off, my original claim was that there exists a function f:(0,1) -> (-inf,inf), not [0,inf), but I can also give you an example of such a function.
Second, you used a closed bracket for infinity which just shows how much of a brainlet you are.
Third, define the function f:(0,1) -> (-inf,inf)
by the function f(x) = tan[pi*(x-(1/2))].
This function is a bijection between (0,1) and (-inf, inf).
Fourth, learn some set theory you fucking normie. I would suggest reading a book by Halmos.