bijection between reals and irrationals

[georgios]

1. The problem statement, all variables and given/known data

Prove that |R \ |Q ~ |R ... the irrationals are equinumerous to the reals

2. Relevant equations



3. The attempt at a solution

I can prove it using the Cantor Schroeder Bernstein theorem, but i was wondering if there
is a clever way of constructing the bijection explicitely ...
thanks,
g.
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution