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
MattyMatty
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."#

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