# Set of Rational Numbers is not G-Delta Set in Reals

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## Theorem

Let $\Q$ be the set of rational numbers.

Let $\left({\R, \tau}\right)$ be the real number line under the usual (Euclidean) topology.

Then $\Q$ is not a $G_\delta$ set in $\R$.

## Proof

## Sources

- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{II}: \ 30: \ 2$