I am trying to show that $|(0,1)| = $$|(0,1) \cup ${$2,3,4,5$}$|$ using the Schroder-Bernstein Theorem.
Therefore, I need to find injections
$f:(0,1) \rightarrow (0,1) \cup ${$2,3,4,5$} and
$g:(0,1) \cup ${$2,3,4,5$} $\rightarrow (0,1)$
(1) We can define $f(x)=x$ since we do not have to consider 2,3,4,5.
(2) We can define $g(x)= \frac{x}{6}$ in order to direct 2,3,4,5 to a number $\in (0,1)$
Therefore, by the Schroder-Bernstein Theorem, $|(0,1)| = $$|(0,1) \cup ${$2,3,4,5$}$|$
Is this valid?