I am studying analysis, and we're just getting to the topic of maxima and minima. I'm trying to find the maximum and minimum of the set $$S := (0,4] \cap \Bbb{Q}.$$ I know the minimum DNE, and I know why it doesn’t exist. But I don’t know why the maximum is $4$ and not $> 4,$ if the universal set extends past $4$? Any help would be appreciated. Please and thank you.
2026-04-12 22:53:43.1776034423
Max/min help please
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$\max S = 4$ since $4 \in (0, 4]$ and $4 \in \mathbb{Q}$ imply $4 \in S$, and there is no $x \in S$ for which $x > 4$.
$\min S$ does not exist. Suppose $\min S = x$. Then $y = x/2 < x$ and $y \in S$, a contradiction.