# Category:Infima

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

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

Let $\struct {S, \preceq}$ 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 $S$.

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

## Pages in category "Infima"

The following 12 pages are in this category, out of 12 total.