Definition:Infimum/Also known as

From ProofWiki
Jump to navigation Jump to search

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 $\displaystyle \inf_{y \mathop \in S} y$, which may improve clarity in some circumstances.


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


Sources