Infimum

The infimum of a set is the largest number such that no numbers in the set are smaller. If the set has a minimum number, then this will be the infimum for the set.

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Example

Given the interval $I=\{x\in \mathbb{R}|0<x<1\}=(0,1)$. A minimum does not exist here (since we can always get slightly closer to $0$, but never reach $0$). However $0$ is the infimum for the set $I$ $\inf I=0$

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However, if the interval is $J=\{x\in \mathbb{R}|0\le x<1\}=[0,1)$, then the infimum is still $0$, but so is the minimum $\inf J=\min J=0$

Taken from SNL