# cardinality of sets

• May 13th 2013, 03:56 AM
rayman
cardinality of sets
If $A\subseteq B$ then $A\le B$ where $\le$ denotes here that the set A is less than or equinumerous with the set B.
How to do this? From the hypothesis we know that every element of A belongs to B so A cannot have more elements than B right? or do I understand it wrong?
• May 13th 2013, 04:05 AM
Plato
Re: cardinality of sets
Quote:

Originally Posted by rayman
If $A\subseteq B$ then $A\le B$ where $\le$ denotes here that the set A is less than or equinumerous with the set B.
How to do this? From the hypothesis we know that every element of A belongs to B so A cannot have more elements than B right? or do I understand it wrong?

All proofs depend upon the definitions and axioms one has to work with.

Usually in this case, show that there is an injection $f:A\to B~.$