# Definition:Infimum

## Disambiguation

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**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 $\map {\mathrm {glb} } T$ or $\map {\mathrm {g.l.b.} } T$.

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

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

Some older sources, applying the concept to a (strictly) decreasing real sequence, refer to an **infimum** as a **lower limit**.

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