What does "infimum" mean?

(of a subset) the greatest element of the containing set that is smaller than or equal to all elements of the subset. The infimum may or may not be a member of the subset.

What is a synonym for "infimum"?

Common synonyms include: greatest lower bound, greatest lower bound, supremum.

Infimum

//ɪnˈfiːməm// noun

noun ·Rare ·Advanced level

Definitions

Noun

1
(of a subset) the greatest element of the containing set that is smaller than or equal to all elements of the subset. The infimum may or may not be a member of the subset.

Synonyms

All synonyms

greatest lower bound greatest lower bound supremum

Antonyms

All antonyms

supremum

Etymology

Borrowed from Latin infimum (“lowest part”), from infimus (“lowest”).

Related phrases

essential infimum

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.