mapping of the real line to interval [0,1)

Question

What is a mapping (bijection) of the real line (−∞,∞) to the interval [0,1)? I'm trying out logs and exponentials but they don't seem to work?

Can you map the real line to $(0,1)?$ There are a number of functions that work for that. Then you just need to map $(0,1)$ to $[0,1)$. You can't do that continuously, but it is not hard to do. — Ross Millikan, May 13 '19 at 19:47
Thanks, I know how to map real line to (0,1), but dont know how (0,1) to [0,1). — user148733, May 13 '19 at 19:51
Possible duplicate of [How to define a bijection between $(0,1)$ and $(0,1]$?](https://math.stackexchange.com/questions/160738/how-to-define-a-bijection-between-0-1-and-0-1) Also [this one](https://math.stackexchange.com/questions/1233238/construct-an-explicit-bijection-f0-1-to-0-1-where-0-1-is-the-closed?rq=1) — Ross Millikan, May 13 '19 at 19:52
Or this one: [Explicit bijection between [0,1) and (0,1)](https://math.stackexchange.com/questions/1425492/explicit-bijection-between-0-1-and-0-1) — Jean-Claude Arbaut, May 13 '19 at 19:52

score 0 · Answer 1 · answered May 13 '19 at 19:43

0

What about the following function: $$f(x)=\tanh|x|$$

answered May 13 '19 at 19:43

Botond

This is not a bijection. – Ross Millikan May 13 '19 at 19:46
@RossMillikan bijectivity was not required in the original question. – Botond May 13 '19 at 19:47
In original required continuous and edited to bjection. – z100 May 13 '19 at 19:50
@Botond Im sorry, I changed the question, but thank you. – user148733 May 13 '19 at 19:52

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