A set is open if it doesn't contain any of its boundary points. I think 0 is a boundary point here and I think it's the only one. So is the set open?
2026-04-05 17:56:52.1775411812
Is the set (0, $\infty$) open?
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You've hit the nail on the head. The only boundary point of $(0,\infty)$ is $0$, which is not in the set. Well done!