# Definition:Infimum

## Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

**Infimum** may refer to:

## Also known as

Particularly in the field of analysis, the infimum of a set $T$ is often referred to as the **greatest lower bound of $T$** and denoted $\map {\operatorname {glb} } T$ or $\map {\operatorname {g.l.b.} } T$.

Some sources refer to the **infimum of a set** as the **infimum on a set**.

Some sources introduce the notation $\displaystyle \inf_{y \mathop \in S} y$, which may improve clarity in some circumstances.

## Also defined as

Some sources refer to the infimum as being ** the lower bound**.

Using this convention, any element less than this is not considered to be a lower bound.

## Also see

## Linguistic Note

The plural of **infimum** is **infima**, although the (incorrect) form **infimums** can occasionally be found if you look hard enough.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**greatest lower bound** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**greatest lower bound (g.l.b.; infimum)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**greatest lower bound (g.l.b.; infimum)** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**greatest lower bound** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**infimum (infima)**