infinity
C1formal, academic, technical, literary
Definition
Meaning
The concept of having no limit, end, or boundary; an endless or immeasurable quantity.
A state or quality of being infinite; used in mathematics, physics, philosophy, and everyday language to express boundlessness, eternity, or an extremely large amount.
Linguistics
Semantic Notes
Primarily an abstract noun. In mathematics, it denotes a quantity greater than any assignable quantity. In general use, it often hyperbolically denotes a very large number or duration.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. The symbol ∞ is used identically in both varieties.
Connotations
Connotes boundlessness, eternity, and the sublime. In popular culture (e.g., 'Toy Story'), it can imply limitless potential.
Frequency
Slightly more frequent in American academic/scientific writing due to larger STEM output, but the difference is negligible.
Vocabulary
Collocations
Grammar
Valency Patterns
[Verb] + to infinity (e.g., stretch, go, continue)[Preposition] + infinity (e.g., for, towards, into)[Adjective] + infinity (e.g., mathematical, eternal, sheer)Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “to infinity and beyond”
- “a license/permit to infinity”
- “infinity pool (a swimming pool with an edge that appears to merge with the horizon)”
Usage
Context Usage
Business
Rare, except in hyperbolic marketing: 'Our new plan offers infinite possibilities.'
Academic
Common in mathematics, physics, philosophy: 'The sequence diverges to infinity.'
Everyday
Hyperbolic or metaphorical: 'I could look at this view for infinity.'
Technical
Precise mathematical/physical concept: 'The universe may be infinite in extent.'
Examples
By CEFR Level
- The children said they would love their new puppy to infinity.
- The line for the ride seemed to go on to infinity.
- In the clear desert sky, the stars appeared to stretch into infinity.
- The mathematician explained that some numbers are closer to infinity than others.
- The philosophical debate centred on whether the universe was finite or infinite.
- The artist used the infinity symbol to represent eternal love in her sculpture.
- The concept of infinity in calculus is foundational to understanding limits and asymptotic behaviour.
- His patience for bureaucratic delays was not infinite, and eventually he demanded a resolution.
Learning
Memory Aids
Mnemonic
Think of the number 8 lying on its side (∞). It has no beginning and no end, just like infinity.
Conceptual Metaphor
INFINITY IS A JOURNEY / INFINITY IS A CONTAINER (e.g., 'travel into infinity', 'filled with infinite possibilities').
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid calquing 'до бесконечности' as 'till infinity' in all contexts; 'indefinitely' or 'endlessly' may be more natural.
- Do not use 'infinity' as a direct equivalent for 'бесконечность' in abstract philosophical discourse without checking register.
Common Mistakes
- Using 'infinite' (adj.) and 'infinity' (n.) interchangeably (e.g., 'He has an infinity of patience' vs. 'He has infinite patience').
- Misspelling as 'infinety' or 'infinty'.
- Overusing in informal contexts where 'forever' or 'a lot' is sufficient.
Practice
Quiz
In which context is the term 'infinity pool' correctly used?
FAQ
Frequently Asked Questions
In common usage, it is not a number but a concept. In some branches of mathematics, such as projective geometry, it is treated as an abstract point or symbol (∞) with specific rules.
'Eternity' primarily refers to infinite time, especially in a philosophical or religious context. 'Infinity' is broader, encompassing limitless quantity, extent, or space, and is the preferred term in mathematics and science.
Yes, in advanced mathematics (set theory), one can speak of 'infinities' of different sizes (e.g., countable vs. uncountable infinities).
The symbol, called the lemniscate, was introduced by mathematician John Wallis in 1655. Its etymology is not certain, but it may derive from the Roman numeral for 1,000 (CIƆ), which was sometimes used to denote 'many', or from a geometric curve.