I have to sets: [-4;2) a nd (3,8). And I have to prove their equivalence using Cantor-Bernstein theorem and by constructing bijection between those two sets. I am stuck at which point I have to define, how to get set A, which belongs to [-4;2). I dont know what function I should use to get -4 and then upwards to 2.
Please help!
First, construct a bijection from $[-4,2)$ to $[0,1)$. That one should be easy.
Then, construct a bijection from $(3,8)$ to $(0,1)$. Should be just as easy as the first one.
Now, all you need is a bijection from $[0,1)$ to $(0,1)$. You can find that one by sending $x\mapsto x$, except you send $0$ to $\frac12$, and $\frac12\mapsto\frac13$, and $\frac13\mapsto\frac14$ and so on.
