# Category:Infima

This category contains results about Infima in the context of Order Theory.

Definitions specific to this category can be found in Definitions/Infima.

Let $\left({S, \preceq}\right)$ 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 $S$
- $(2): \quad d \preceq c$ for all lower bounds $d$ of $T$ in $S$.

The **infimum** of $T$ is denoted $\inf T$.

If there exists an **infimum** of $T$ (in $S$), we say that **$T$ admits an infimum (in $S$)**.

## Pages in category "Infima"

The following 6 pages are in this category, out of 6 total.