Friday 31 January 2014

elementary set theory - Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) times (0, 1)$ have the same cardinality

Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
using the SB theorem?
Also how does one find a bijection on $f:(0, \infty) \to (0,1)$ such that they have the same cardiniality?

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...