Cardinality of real numbers Given an open interval, say $(a,b]$, how do we show that it has the same cardinality as the set of real numbers? Or is there a bijective mapping in the 1st place?

The simplest proof sketch, in my opinion is:


*

*$|(a,b)| = \mathfrak{c}$

*$|(a,b]| = |(a,b)| + 1$

*$\mathfrak{c} + 1 = \mathfrak{c}$


where $\mathfrak{c}$ is the cardinality of the reals.
