Cardinality Question from Basic Analysis. Thanks for any help.

  • #1
snowfox2004
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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.
 

Answers and Replies

  • #2
Hurkyl
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  • #3
snowfox2004
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Nope, sorry.
 

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