transfinite number: meaning, definition, pronunciation and examples
C2Formal, Academic, Technical
Quick answer
What does “transfinite number” mean?
A number that is larger than all finite numbers, used to describe the cardinality or size of infinite sets in set theory.
Audio
Pronunciation
Definition
Meaning and Definition
A number that is larger than all finite numbers, used to describe the cardinality or size of infinite sets in set theory.
In set theory, numbers introduced by Georg Cantor to describe and classify different sizes of infinity (aleph numbers, beth numbers). They generalize the concept of natural number into the infinite.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling follows regional norms for other words in the phrase.
Connotations
Purely mathematical, with no cultural variance.
Frequency
Exclusively used in advanced mathematical contexts in both regions.
Grammar
How to Use “transfinite number” in a Sentence
the transfinite number __ (e.g., aleph-null)transfinite number theorya transfinite number of elementsVocabulary
Collocations
Examples
Examples of “transfinite number” in a Sentence
adjective
British English
- Cantor developed transfinite number theory.
- The lecture covered transfinite arithmetic.
American English
- The textbook has a chapter on transfinite number systems.
- Her research focuses on transfinite cardinality.
Usage
Meaning in Context
Business
Not used.
Academic
Central term in advanced set theory, logic, and foundational mathematics.
Everyday
Never used.
Technical
Precise term for infinities of different sizes; used in mathematical proofs and discourse.
Vocabulary
Synonyms of “transfinite number”
Strong
Neutral
Weak
Vocabulary
Antonyms of “transfinite number”
Watch out
Common Mistakes When Using “transfinite number”
- Using it to mean 'a very large finite number'.
- Confusing it with 'infinitesimal' (which is infinitely small).
- Treating it as a synonym for 'infinity' as a single concept, rather than a class of distinct numbers.
FAQ
Frequently Asked Questions
Not exactly. 'Infinity' is a general concept. Transfinite numbers (like ℵ₀) are specific numbers that quantify different 'sizes' of infinity.
Yes. Aleph-null (ℵ₀) is the transfinite number representing the cardinality (size) of the set of all natural numbers.
No. Transfinite numbers are part of a separate number system used in set theory. They are not found on the standard real number line.
The German mathematician Georg Cantor introduced them in the late 19th century, revolutionizing the mathematical understanding of infinity.
A number that is larger than all finite numbers, used to describe the cardinality or size of infinite sets in set theory.
Transfinite number is usually formal, academic, technical in register.
Transfinite number: in British English it is pronounced /ˌtrænzˈfaɪnaɪt ˈnʌmbə/, and in American English it is pronounced /ˌtrænzˈfaɪnaɪt ˈnʌmbər/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think 'TRANScending FINITE numbers' to reach the concept of infinite sizes.
Conceptual Metaphor
INFINITY IS A NUMBER ON A LARGER SCALE. (A metaphorical extension of the number line beyond the finite.)
Practice
Quiz
What is a transfinite number?