If $\forall \gamma>0$, $x>1-\gamma$, then $x\geq 1$?
I am confused about this simple thing. Can you help?
2026-05-17 04:38:59.1778992739
If $\forall \gamma>0$, $x>1-\gamma$, then $x\geq 1$?
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Assume by contradiction $x < 1$. Then there is $\varepsilon > 0$ such that $x = 1-\varepsilon$. However, by hypothesis you should have $x > 1-\varepsilon$. Contradiction. Hence $x \ge 1$.