1-1 Correspondence

1. Oct 10, 2004

Zurtex

I have to show that for the sets:

$$I = \left\{ x \; | \;0 \leq x \leq 1, x \; \epsilon \; \mathbb{R} \right\}$$
$$J = \left\{ x \; | \; 0 \leq x \leq 2, x \; \epsilon \; \mathbb{R} \right\}$$

That I and J are in 1 - 1 correspondence. I don't want to know how to prove this but a hint in the right direction would be really useful if possible.

2. Oct 10, 2004

TenaliRaman

Apply Schroeder Bernstein Theorem...

-- AI

3. Oct 10, 2004

Zurtex

Wow thanks!

Some serious maths rather than the kiddy version of infinite sets we have been learning lol.