cantor's paradox: meaning, definition, pronunciation and examples
Very LowFormal, Academic, Technical
Quick answer
What does “cantor's paradox” mean?
A logical paradox in set theory stating that there is no greatest cardinal number, because for any set, the set of all its subsets always has a strictly larger cardinality.
Audio
Pronunciation
Definition
Meaning and Definition
A logical paradox in set theory stating that there is no greatest cardinal number, because for any set, the set of all its subsets always has a strictly larger cardinality.
More broadly, it refers to the discovery that some totalities (like 'the set of all sets') cannot themselves be considered sets without leading to contradictions about their own size or membership, highlighting fundamental limitations in naive set theory.
Dialectal Variation
British vs American Usage
Differences
No significant differences in usage, spelling, or meaning. The term is international academic jargon.
Connotations
Identical technical connotations in both varieties.
Frequency
Equally rare and specialized in both UK and US academic English.
Grammar
How to Use “cantor's paradox” in a Sentence
[Subject] exemplifies Cantor's paradox.Cantor's paradox demonstrates [concept].One must confront Cantor's paradox when [action].Vocabulary
Collocations
Examples
Examples of “cantor's paradox” in a Sentence
adjective
British English
- Cantorian paradox theory
American English
- Cantorian paradox theory
Usage
Meaning in Context
Business
Not used.
Academic
Used in advanced mathematics, logic, and philosophy papers and discussions to describe foundational issues in set theory.
Everyday
Not used.
Technical
Core term in mathematical logic, set theory, and theoretical computer science.
Vocabulary
Synonyms of “cantor's paradox”
Neutral
Weak
Watch out
Common Mistakes When Using “cantor's paradox”
- Using 'Cantor paradox' without the possessive 's'.
- Confusing it with Russell's Paradox or the Barber Paradox, which are related but distinct.
- Using it as a general term for any contradiction.
FAQ
Frequently Asked Questions
It is named after the German mathematician Georg Cantor, who founded set theory in the late 19th century.
No, they are distinct. Cantor's paradox deals with the size of the 'set of all sets', while Russell's paradox deals with the 'set of all sets that do not contain themselves'.
It was addressed by modern axiomatic set theories (like Zermelo-Fraenkel set theory) which avoid the problematic 'set of all sets' by restricting the axiom of comprehension.
Yes, a basic understanding of different sizes of infinity (cardinalities) is essential to understand the core issue of the paradox.
A logical paradox in set theory stating that there is no greatest cardinal number, because for any set, the set of all its subsets always has a strictly larger cardinality.
Cantor's paradox is usually formal, academic, technical in register.
Cantor's paradox: in British English it is pronounced /ˈkæntɔːz ˈpærədɒks/, and in American English it is pronounced /ˈkæntərz ˈpærəˌdɑːks/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Cantor Counted: He tried to count ALL sets, but found the 'set of all sets' is too big to be a set itself—a paradox of totality.
Conceptual Metaphor
A CONTAINER TOO BIG TO CONTAIN ITSELF; A LIBRARY CATALOGUE THAT MUST LIST ITSELF.
Practice
Quiz
Cantor's paradox is primarily concerned with: