For infinite sets A,B do we also have $A\subseteq B\rightarrow|A|\leq|B|$?

36 Views Asked by At

I know that for finite sets we have that $A\subseteq B\rightarrow|A|\leq|B|$ however does this necessarily hold for infinite sets as well?

For the purpose of this question we define an infinite set as a set for which there exists strict subset of equal cardinality to itself, and we define $|A|$ as the cardinality of A