# Thread:

1. ## help to prove

prove if a A is uncountable and A is a subset of B, then B is uncountable

2. 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, $\aleph_0 < |A| \leq |B|$.
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