I don’t understand the reasoning statement in the box.
2026-03-28 22:24:57.1774736697
Why is $A$ uncountable?
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The statement in the box says the following:
If $X\subset A$ and $X$ is countable then $X \ne A$.
This shows that $A $ is uncountable since if you assume that $A$ is countable then $A\subset A$ so by the statement we proved, $A\ne A$ which is of course impossible.