Category:Definitions/Infima

This category contains definitions related to Infima.
Related results can be found in Category:Infima.

Let $\struct {S, \preccurlyeq}$ be an ordered set.

Let $T \subseteq S$.

An element $c \in S$ is the infimum of $T$ in $S$ if and only if:

$(1): \quad c$ is a lower bound of $T$ in $S$

$(2): \quad d \preccurlyeq c$ for all lower bounds $d$ of $T$ in $S$.