Let $A$ be a subset of the real numbers, containing every integer, and such that for every $x$ and $y$ in A, there exists $z$ in A strictly comprised between them. Prove $A$ is uncountable.
2026-04-09 07:17:43.1775719063
Proving uncountability of a set
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Pick $A=\mathbb Q$. Then $A$ has the given property but $A$ is countable.