# Homework Help: Infinite Sets

1. Apr 22, 2010

### nickmai123

1. The problem statement, all variables and given/known data

Using the Schroeder-Bernstein Theorem, prove that any two intervals of real numbers are numerically equivalent.

2. Relevant equations

Schroeder-Bernstein Theorem: Let $$A$$ and $$B$$ be sets, and suppose that there are injections from A into B and B into A. Then, there exists a bijective correspondence between A and B.

3. The attempt at a solution
None. I'm stuck. Can anyone help me with where to go?

2. Apr 22, 2010

### NeoDevin

If and only if two intervals are "numerically equivalent", there exists a bijective correspondence between A and B.

3. Apr 22, 2010

### JSuarez

Picture one of the intervals in the x-axis of the plane and the other in the y-axis. Can't you see the graph of an injective (in fact bijective) function between them?