What is the correct way to answer to this question? I need to define a relation between the minimum of a set and the infimum of this set.
2026-03-29 12:52:11.1774788731
What is the relation between the minimum and the infimum of a set?
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The minimum, if it exists, will be equal to the infimum. A non-empty subset of $\mathbb{R}$ does not always have a minimum, but will always have an infimum.
For example, consider the interval $(0,1)$ which has no minimum or 'smallest' number since we can always get arbitrarily closer to $0$. But this set does have an infimum: its infimum is $0$. The infimum of a set does not need to belong to the set, whereas the minimum does.