transfinite: meaning, definition, pronunciation and examples
C2/TechnicalFormal, Technical (Mathematics/Philosophy)
Quick answer
What does “transfinite” mean?
Being beyond or surpassing all finite magnitudes or numbers.
Audio
Pronunciation
Definition
Meaning and Definition
Being beyond or surpassing all finite magnitudes or numbers.
Relating to quantities (especially cardinal or ordinal numbers) that are infinite but can be compared or ordered; a concept in set theory dealing with different sizes of infinity.
Dialectal Variation
British vs American Usage
Differences
No significant spelling or meaning differences. Usage is identical across both variants as a highly technical term.
Connotations
In both regions, the term connotes high-level abstract mathematics. No regional connotative differences.
Frequency
Extremely rare in everyday language in both UK and US. Frequency is entirely tied to technical mathematical discourse.
Grammar
How to Use “transfinite” in a Sentence
Used attributively as an adjective (transfinite X)Used in the phrase 'of transfinite X' (e.g., theory of transfinite numbers)Vocabulary
Collocations
Examples
Examples of “transfinite” in a Sentence
adjective
British English
- Cantor's work on transfinite numbers revolutionised mathematics.
- The proof employed a method of transfinite induction.
American English
- The concept of transfinite cardinals is key to set theory.
- They debated the philosophical implications of transfinite arithmetic.
Usage
Meaning in Context
Business
Not used.
Academic
Core usage. Found in advanced mathematics, set theory, and theoretical computer science papers. Sometimes in metaphysics/philosophy.
Everyday
Virtually never used.
Technical
Primary domain. Describes a specific concept in Cantorian set theory.
Watch out
Common Mistakes When Using “transfinite”
- Using it as a synonym for 'very large' instead of its precise mathematical meaning.
- Spelling as 'transfinit' or 'trans-finite'.
- Incorrect stress: stressing the first syllable (TRANS-finite) instead of the second (trans-FIN-ite).
FAQ
Frequently Asked Questions
A number that is infinite but can be used in arithmetic and ordered in a sequence, such as the cardinal number ℵ₀ (aleph-null), which represents the size of the set of all natural numbers.
Not exactly. In mathematics, 'transfinite' specifically refers to infinite quantities (like cardinal and ordinal numbers) that can be compared and ordered, distinguishing different 'sizes' of infinity. In casual use, they might be conflated, but technically they belong to different conceptual frameworks.
The German mathematician Georg Cantor (1845–1918), the founder of modern set theory, introduced the term to describe his theory of infinite numbers.
Yes. ω (omega) is the smallest transfinite ordinal number. It comes after all the finite natural numbers 0, 1, 2, 3, ...
Being beyond or surpassing all finite magnitudes or numbers.
Transfinite is usually formal, technical (mathematics/philosophy) in register.
Transfinite: in British English it is pronounced /ˌtrænsˈfaɪ.naɪt/, and in American English it is pronounced /ˌtrænzˈfaɪ.naɪt/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[No common idioms for this technical term]”
Learning
Memory Aids
Mnemonic
Think of 'trans' (beyond) + 'finite' (limited). It refers to numbers that go **beyond** the **finite**.
Conceptual Metaphor
THE HIERARCHY OF INFINITY (different 'sizes' or 'levels' of infinity, like a ladder extending past the finite).
Practice
Quiz
In which field is the term 'transfinite' primarily used?