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  "aliases": [
    "inf-sup",
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  "body": "\n## Summary\n\nIn mathematics, the **infimum** (abbreviated **inf**; : **infima**) of a [[subset|0BJR9QR08E]] $S$ of a [[partially ordered set|0QV2JS9RJ3]] $P$ is the greatest element in $P$ that is less than or equal to each element of $S,$ if such an element exists. If the infimum of $S$ exists, it is unique, and if *b* is a lower bound of $S$, then *b* is less than or equal to the infimum of $S$. Consequently, the term *greatest lower bound* (abbreviated as GLB) is also commonly used. The **supremum** (abbreviated **sup**; : **suprema**) of a subset $S$ of a partially ordered set $P$ is the least element in $P$ that is greater than or equal to each element of $S,$ if such an element exists. If the supremum of $S$ exists, it is unique, and if *b* is an upper bound of $S$, then the supremum of $S$ is less than or equal to *b*. Consequently, the supremum is also referred to as the *least upper bound* (or LUB).\n",
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  "name": "Infimum and supremum",
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