Cardinality Question from Basic Analysis. Thanks for any help.

[snowfox2004]

Homework Statement

If the cardinality of A is less than or equal to the cardinality of the reals and the cardinality of B is less than or equal to the cardinality of the reals, I need to show that the cardinality of the union of A and B is less than or equal to the cardinality of the reals.

IE: Prove that if |A|</=|R| and |B|</=|R|, then |AUB|</=|R|.

Thanks for any help. I am in a basic analysis class, and we just started a small section on cardinality.

Homework Equations

The Attempt at a Solution

All I know is that based on my assumption, I know that there is a 1-1 function from A to the real numbers and another 1-1 function from B to the real numbers.

 

[Hurkyl]

Have you learned anything about the arithmetic of cardinal numbers?

 

[snowfox2004]

Nope, sorry.