# 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 $\struct {S, \preccurlyeq}$ 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 $S$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

### E

- Examples of Infima (7 P)

## Pages in category "Infima"

The following 22 pages are in this category, out of 22 total.

### E

### I

- Infima in Ordered Group
- Infimum in Ordered Subset
- Infimum is Unique
- Infimum of Empty Set is Greatest Element
- Infimum of Set of Reciprocals of Positive Integers
- Infimum of Singleton
- Infimum of Subgroups in Lattice
- Infimum of Subset Product in Ordered Group
- Infimum of Union of Bounded Below Sets of Real Numbers
- Inverse of Infimum in Ordered Group is Supremum of Inverses
- Inverse of Supremum in Ordered Group is Infimum of Inverses