# help to prove

• Apr 23rd 2008, 08:52 AM
dbhakta
help to prove
prove if a A is uncountable and A is a subset of B, then B is uncountable
• Apr 23rd 2008, 10:03 AM
ThePerfectHacker
Quote:

Originally Posted by dbhakta
prove if a A is uncountable and A is a subset of B, then B is uncountable

Since $A$ is uncountable it means $|A| > \aleph_0$. Since $A\subseteq B$ it means $|A|\leq |B|$ because the identity map on $A$ will be an injective function. Thus, $\aleph_0 < |A| \leq |B|$.