Definition:Infimum

From ProofWiki
Jump to navigation Jump to search

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 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 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 refer to the infimum of a set as the meet of the set and use the notation $\bigwedge T$ or $\ds \bigwedge_{y \mathop \in T} y$.


Some sources introduce the notation $\ds \inf_{y \mathop \in T} y$, 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 see

  • Results about infima can be found here.


Linguistic Note

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


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Definition:Infimum&oldid=708453"