I need a function such that for any real positive input, the output is an integer--AND is a different integer for each different input.
Does such a thing exist?
Correct me if I'm wrong, but this would not always produce an integer y for any real positive x.
Is there a proof or theorem somewhere that says or implies that if "the domain is an uncountable set and the range is countable" then there can be no "one to one map $\displaystyle \mathbb{R}^+ \rightarrow \mathbb{Z}$" ? I'd be very interested in that.
Thanks