Find the $inf$ and $sup$ for $\{a + {1 \over {2a}}: a\in Q, 0.1 \leq a \leq 5\}$
I took a = 0.1 and a=5, the value is 5.1 and when a = 0.5 or a = 1, the value is 1.5
2026-03-30 17:09:41.1774890581
Find inf and sup for $\{a + {1 \over {2a}}: a\in Q, 0.1 \leq a \leq 5\}$
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using $AM-GM$ we get $$a+\frac{1}{2a}\geq \frac{2}{\sqrt{2}}$$