lower bound
C1Formal/Technical
Definition
Meaning
The minimum possible value or limit of something, especially in mathematical or statistical contexts.
A fundamental limit or constraint that cannot be undercut; a baseline or floor value in a range or set of possibilities.
Linguistics
Semantic Notes
Primarily a technical term from mathematics and computer science that has extended into general academic and business usage to denote a minimum limit. Often used in contrast to 'upper bound'.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or semantic differences. Spelling conventions follow local norms for 'lower' (e.g., 'analyse' vs. 'analyze' in surrounding text).
Connotations
Identical technical connotations. In general discourse, slightly more common in American academic/business writing.
Frequency
Equal frequency in technical contexts; slightly higher in American general academic prose.
Vocabulary
Collocations
Grammar
Valency Patterns
lower bound on [something]lower bound for [a quantity]lower bound of [a set/range]Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “[to] set/push the lower bound”
Usage
Context Usage
Business
Used in budgeting, forecasting, and risk analysis to indicate the worst-case scenario or minimum expected outcome (e.g., 'The lower bound for next quarter's revenue is £2 million').
Academic
A fundamental concept in mathematics, computer science (algorithm complexity), statistics (confidence intervals), and economics. Often used in proofs and theoretical models.
Everyday
Rare in casual conversation. May appear in discussions about estimates, ranges, or limits (e.g., 'The lower bound for the journey time is three hours in good traffic').
Technical
Precise term denoting the greatest element less than or equal to all elements of a set. Central to optimization, complexity theory, and numerical analysis.
Examples
By Part of Speech
adjective
British English
- The lower-bound estimate was deemed too pessimistic by the review board.
American English
- We need a lower-bound figure before proceeding with the analysis.
Examples
By CEFR Level
- For the test, you should study at least three hours—that's the lower bound.
- The report provides a lower bound for the project's cost, but the final amount could be higher.
- The researcher established a tight lower bound on the algorithm's time complexity, proving it cannot run faster than O(n log n).
Learning
Memory Aids
Mnemonic
Think of a 'bound' as a limit you cannot cross. The 'lower' one is the bottom limit—like the lowest step on a ladder you must stand on.
Conceptual Metaphor
LIMIT/BARRIER (A lower bound is a floor or a bottom line that you cannot go below.)
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating literally as 'низкая граница'—this is incorrect. Use 'нижняя граница' or 'нижняя оценка' for mathematical contexts.
- Do not confuse with 'нижний предел', which can be more general.
Common Mistakes
- Using 'lower boundary' interchangeably (a 'boundary' is a physical line, a 'bound' is a limit).
- Confusing 'lower bound' with 'minimum' (a minimum is an actual achieved value, a lower bound is a theoretical limit).
- Incorrect plural: 'lower bounds' (correct) vs. 'lowers bound' (incorrect).
Practice
Quiz
In which context is 'lower bound' most precisely defined?
FAQ
Frequently Asked Questions
Typically yes, especially in technical contexts. In metaphorical use, it can refer to a non-numerical minimum standard or limit.
A 'minimum' is the smallest value actually present or achieved in a set. A 'lower bound' is a value that is less than or equal to all elements in a set, but it may not be a member of the set itself.
No, 'lower bound' is a noun phrase. The related verb would be 'to bound' (as in 'to establish bounds'), but 'to lower-bound' is non-standard and should be avoided in formal writing.
Use the pattern 'lower bound on/for [quantity]'. Example: 'This theorem provides a new lower bound on the chromatic number of such graphs.'