# Definition:Infimum/Also known as

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## Definition

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**.

## Sources

- 1919: Horace Lamb:
*An Elementary Course of Infinitesimal Calculus*(3rd ed.) ... (previous) ... (next): Chapter $\text I$. Continuity: $2$. Upper or Lower Limit of a Sequence - 1964: Walter Rudin:
*Principles of Mathematical Analysis*(2nd ed.) ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: Real Numbers: $1.34$. Definition - 1970: Arne Broman:
*Introduction to Partial Differential Equations*... (previous) ... (next): Chapter $1$: Fourier Series: $1.1$ Basic Concepts: $1.1.2$ Definitions