“Elementary properties of closures”

From Terence Tao’s Analysis I, p213 of the hardcover second edition, Lemma 9.1.11.

Showing \(X\subset \overline{X}\). Let \(x\in X\), and let \(\epsilon >0\). We have \(\left|{x-x}\right| = 0 \leq \epsilon\), so we are done.

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