# Cardinalities of Sets

1. May 10, 2014

### knowLittle

1. The problem statement, all variables and given/known data
Explain why $(0,1 )$ and $(0,2)$

I have proved that a function $f: (0,1 ) -> (0,2)$defined by f(x) =2x is bijective.

2. Relevant equations

3. The attempt at a solution
I could state that due to the sets relationship being bijective they have the same cardinality, but this is only true if both sets are finite. Here, (0,1) and (0,2 ) are infinite.

Any help?

2. May 10, 2014

### micromass

What is your definition of "having the same cardinality"?

3. May 10, 2014

### knowLittle

Nevermind, you are right. The definition of same cardinality or numerically equivalency doesn't restrict finite from infinite sets.

4. May 10, 2014

### micromass

Right! So you solved the problem correctly. Congratz!