This is just messing with my head for the past hour.
Question:
$|(0,1)| = |(0,1]|$. If you find a bijection, you don't need to prove that its a bijection.
So a Bijection is one-on-one. E.g $f(a_1) = f(a_2)$ then $a_1=a_2$ and $\operatorname{range} f = B$
In the above case It is bijective is true but is the statement true as well?
and what about if its $|[0,1]^2| = |[0,2]^2|$
Thanks Edit: Heres the exact wording of the question: http://i.stack.imgur.com/2MhxE.png