null sequence
C1/C2 (Advanced)Formal, Technical, Academic
Definition
Meaning
A sequence (especially in mathematics) whose terms approach zero as the sequence progresses.
A sequence that converges to zero; also used metaphorically to describe a series of events or elements that diminish to nothingness or insignificance.
Linguistics
Semantic Notes
The term is almost exclusively used in technical contexts, particularly mathematics (analysis, calculus) and computer science. Its metaphorical use is rare and highly specialized.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning. Spelling remains consistent.
Connotations
Identical technical meaning in both varieties.
Frequency
Equally rare outside technical fields in both regions.
Vocabulary
Collocations
Grammar
Valency Patterns
The sequence (a_n) is a null sequence.To prove that (x_n) is a null sequence.A null sequence of real numbers.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “[No common idioms. Technical term.]”
Usage
Context Usage
Business
Extremely rare, potentially in highly technical financial modelling.
Academic
Primary context. Used in mathematics, engineering, and theoretical computer science lectures and papers.
Everyday
Virtually never used.
Technical
Standard term in mathematical analysis, signal processing, and algorithm design.
Examples
By Part of Speech
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 null-sequence property is fundamental to convergence tests.
American English
- We need a null-sequence argument to complete the proof.
Examples
By CEFR Level
- [Too advanced for A2]
- [Too advanced for B1]
- In calculus, a null sequence gets closer and closer to zero.
- The lemma states that the product of a bounded sequence and a null sequence is itself a null sequence.
- To demonstrate convergence, we first show that the tail of the series forms a null sequence.
Learning
Memory Aids
Mnemonic
Think of 'null' as zero and 'sequence' as a list. A 'null sequence' is a list of numbers that eventually gets as close to zero as you want.
Conceptual Metaphor
A JOURNEY TO NOTHINGNESS (The sequence travels towards the destination of zero).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid direct translation as 'нулевая последовательность' in non-mathematical contexts, as it will sound bizarre. In English, it is not used metaphorically like 'ничтожный ряд событий' might be in Russian.
Common Mistakes
- Using 'null sequence' to mean an empty sequence (a sequence with no terms). A null sequence has infinitely many terms that approach zero.
- Using it in general language to mean 'a series of unimportant events'.
Practice
Quiz
In which field is the term 'null sequence' primarily used?
FAQ
Frequently Asked Questions
No. An empty sequence has no terms. A null sequence has infinitely many terms, but their limit is zero.
Almost never. It is a technical term specific to mathematics and related disciplines.
For any arbitrarily small positive number, the absolute value of the terms eventually becomes and stays smaller than that number.
Conceptually related (both imply 'nothing'), but 'null sequence' is a precise mathematical term, while 'null and void' is a general legal idiom.