singular point: meaning, definition, pronunciation and examples
C2+Academic, Technical, Scientific
Quick answer
What does “singular point” mean?
In mathematics, a point at which a given mathematical object is not defined or not "well-behaved", such as where a function is not analytic, a curve has a cusp, or a geometric object ceases to be a manifold.
Audio
Pronunciation
Definition
Meaning and Definition
In mathematics, a point at which a given mathematical object is not defined or not "well-behaved", such as where a function is not analytic, a curve has a cusp, or a geometric object ceases to be a manifold.
Can be used metaphorically in non-technical contexts to describe a unique, isolated, or critical moment of convergence, instability, or exceptional circumstance that stands apart from normal patterns.
Dialectal Variation
British vs American Usage
Differences
No significant differences in definition or core usage.
Connotations
Both varieties treat it as a highly technical term.
Frequency
Equally rare in general language; frequency identical in technical literature.
Grammar
How to Use “singular point” in a Sentence
The function has a singular point at X.The curve possesses a singular point.The analysis focuses on the singular point where Y occurs.Vocabulary
Collocations
Examples
Examples of “singular point” in a Sentence
verb
British English
- [Not applicable as a verb]
American English
- [Not applicable as a verb]
adverb
British English
- [Not applicable as an adverb]
American English
- [Not applicable as an adverb]
adjective
British English
- The equation's singular-point behaviour was chaotic.
- They studied the manifold's singular-point structure.
American English
- The singular-point analysis revealed a bifurcation.
- We need a singular-point classification theorem.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Standard term in mathematics, physics (e.g., general relativity), and engineering.
Everyday
Extremely rare. Possible metaphorical use: "The negotiation reached a singular point where compromise became impossible."
Technical
Primary context. Used in complex analysis, algebraic geometry, differential equations, dynamical systems.
Vocabulary
Synonyms of “singular point”
Strong
Neutral
Weak
Vocabulary
Antonyms of “singular point”
Watch out
Common Mistakes When Using “singular point”
- Using 'single point' interchangeably (a single point is just one point, not necessarily a *singular* one).
- Using it as a fancy synonym for 'turning point' in non-technical writing.
- Confusing it with 'singularity' in physics (which is related but broader).
FAQ
Frequently Asked Questions
In mathematics, 'singular point' is a specific type of singularity, often referring to a point on a curve or in a function's domain. 'Singularity' is a broader term that can refer to points, regions, or general conditions where properties are undefined or break down.
Yes, but it is a highly technical metaphor. Using it in everyday language will sound very academic or poetic, implying a precise, unique moment of critical change or exception.
A point where a function is undefined or misbehaves, but the function can be redefined at that single point to make it regular and continuous. The 'singularity' can be 'removed' by this redefinition.
It derives from the sense of 'unique', 'exceptional', or 'peculiar'. In this context, it means the point has exceptional, non-standard properties compared to the points around it.
In mathematics, a point at which a given mathematical object is not defined or not "well-behaved", such as where a function is not analytic, a curve has a cusp, or a geometric object ceases to be a manifold.
Singular point is usually academic, technical, scientific in register.
Singular point: in British English it is pronounced /ˌsɪŋɡjʊlə ˈpɔɪnt/, and in American English it is pronounced /ˌsɪŋɡjələr ˈpɔɪnt/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[No common idioms; term is technical]”
Learning
Memory Aids
Mnemonic
Think of a SINGLE (singular) unusual POINT on a map where the normal rules don't apply.
Conceptual Metaphor
A point of no return; a unique moment of breakdown or transformation; an exception that defines a rule.
Practice
Quiz
In which field is the term 'singular point' most precisely defined and frequently used?