If $A$ is an uncountable set and $B \subset A$, $B \neq A$, how can i prove that $B$ is also uncountable?
If $A$ is an uncountable set and $B \subset A$, $B \neq A$, how can i prove that $B$ is also uncountable? I considered to take $a \in A$ and $B = A \setminus \{a\}$. But I don’t get anywhere, any help?
Solution 1:
That is not true.
You have that $\mathbb{N} \subset \mathbb{R}$ and $\mathbb{R}$ is uncountable and $\mathbb{N}$ is countable.