greatest lower bound: meaning, definition, pronunciation and examples
C2Formal, Technical
Quick answer
What does “greatest lower bound” mean?
In mathematics, particularly order theory, the greatest element of a set that is less than or equal to every element of another specified set.
Audio
Pronunciation
Definition
Meaning and Definition
In mathematics, particularly order theory, the greatest element of a set that is less than or equal to every element of another specified set.
The most restrictive common limitation or baseline shared by all elements in a collection. By analogy, it can refer to the fundamental, non-negotiable shared characteristic or constraint within a group of items, concepts, or requirements.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or grammatical differences. The term is identical in both varieties within technical discourse.
Connotations
Purely technical; no cultural connotations differ between varieties.
Frequency
Extremely low frequency in general language, identical and stable high frequency within relevant academic/technical fields in both regions.
Grammar
How to Use “greatest lower bound” in a Sentence
The greatest lower bound of [SET/COLLECTION] is [ELEMENT/NUMBER].[SET/COLLECTION] has a greatest lower bound.To find/calculate the greatest lower bound for/of...Vocabulary
Collocations
Usage
Meaning in Context
Business
Virtually never used. A metaphorical extension might be: 'The greatest lower bound for project approval is a positive ROI.'
Academic
Core term in mathematics, computer science (especially in domain theory, static analysis), and engineering disciplines dealing with optimisation and constraints.
Everyday
Not used in everyday conversation.
Technical
Precise definition: For a subset S of a partially ordered set P, an element g in P is the greatest lower bound of S if 1) g ≤ x for all x in S (lower bound), and 2) for any other lower bound z of S, z ≤ g (greatest).
Vocabulary
Synonyms of “greatest lower bound”
Vocabulary
Antonyms of “greatest lower bound”
Watch out
Common Mistakes When Using “greatest lower bound”
- Using 'greatest lower bound' to mean 'very big lower limit' instead of its precise mathematical definition.
- Confusing it with 'least upper bound' (supremum).
- Treating it as three separate descriptive words rather than a single compound noun.
FAQ
Frequently Asked Questions
Not always. The minimum must be a member of the set itself, while the greatest lower bound need not be. If a minimum exists, it is equal to the greatest lower bound.
It is commonly abbreviated as GLB. In many mathematical texts, the equivalent term 'infimum' (abbreviated 'inf') is used.
Its use is almost exclusively technical. Any non-mathematical use is a deliberate metaphor, drawing on its precise meaning to describe a fundamental shared constraint or baseline.
The direct antonym is 'least upper bound' (also called 'supremum' or 'sup').
In mathematics, particularly order theory, the greatest element of a set that is less than or equal to every element of another specified set.
Greatest lower bound is usually formal, technical in register.
Greatest lower bound: in British English it is pronounced /ˈɡreɪtɪst ˈləʊə baʊnd/, and in American English it is pronounced /ˈɡreɪt̬ɪst ˈloʊɚ baʊnd/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[Metaphorical] The greatest lower bound of their demands was a commitment to transparency.”
Learning
Memory Aids
Mnemonic
Think of a group of people of different heights all reaching up to a shelf. The 'greatest lower bound' is the height of the tallest person who can still fit *under* all of their hands—it's the highest possible point that is still below everyone.
Conceptual Metaphor
A COMMON FLOOR / The HIGHEST BASELINE.
Practice
Quiz
In which field is the term 'greatest lower bound' a fundamental concept?