Infimum and Supremum

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The concept of infimum and supremum is quite simple actually, and in fact these concepts are dual to one another.

Lets take infimum for example:

We have a Partially Ordered Set \(T\) and a subset \(S \subset T\). The infimum is the greatest element in \(T\) that is less than or equal to all elements of \(S\). The supremum is similar in that it is the least element in \(T\) such that it is greater than or equal to all elements in \(S\).