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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.