Could you show me some bijection between the mathbb{R}-mathbb{Q} and mathbb{R}?

I was wondering if is there some "nice" bijective function that connects the irrationals and the reals.

1 Answer
Feb 7, 2018

"That is not possible"

Explanation:

"0 has to be in the range."
"Since 0 is in the range and 0 is a rational number, we cannot"
"have this."
"Think of it : the function must pass cross the X-axis, if not the"
"function would not be continuous everywhere."