bijection: meaning, definition, pronunciation and examples
Very lowTechnical/academic
Quick answer
What does “bijection” mean?
A function between two sets that is both injective (one-to-one) and surjective (onto), establishing a perfect one-to-one correspondence where each element of the first set is paired with exactly one unique element of the second set, and vice versa.
Audio
Pronunciation
Definition
Meaning and Definition
A function between two sets that is both injective (one-to-one) and surjective (onto), establishing a perfect one-to-one correspondence where each element of the first set is paired with exactly one unique element of the second set, and vice versa.
In mathematics, a bijection is a mapping with a two-way perfect match between elements of two sets, allowing the sets to be considered the same size (cardinality) even if their elements are different. In computer science, it can refer to a reversible transformation between data structures.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling and pronunciation follow standard UK/US patterns for the suffix '-tion'.
Connotations
Identical technical connotations in both varieties.
Frequency
Equally rare and specialized in both UK and US English, confined to technical fields.
Grammar
How to Use “bijection” in a Sentence
There is a bijection between X and Y.We can define a bijection f: A → B.The map establishes a bijection.Vocabulary
Collocations
Examples
Examples of “bijection” in a Sentence
verb
British English
- [No standard verb form exists. One might say 'to biject', but it is non-standard and very rare.]
American English
- [No standard verb form exists. One might say 'to biject', but it is non-standard and very rare.]
adverb
British English
- [No standard adverb form exists.]
American English
- [No standard adverb form exists.]
adjective
British English
- The bijective mapping was central to the proof.
- They studied bijective functions in the module.
American English
- The bijective map was central to the proof.
- They studied bijective functions in the course.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Core term in pure mathematics, discrete mathematics, set theory, and theoretical computer science.
Everyday
Never used in everyday conversation.
Technical
Used in formal specifications, algorithm design (for reversible hashing or encoding), and logic.
Vocabulary
Synonyms of “bijection”
Strong
Neutral
Weak
Vocabulary
Antonyms of “bijection”
Watch out
Common Mistakes When Using “bijection”
- Using 'bijection' to mean any function or mapping.
- Confusing it with 'injection' (only one-to-one) or 'surjection' (only onto).
- Attempting to use it in non-technical contexts.
FAQ
Frequently Asked Questions
No, it is a highly specialized term used almost exclusively in mathematics, logic, and theoretical computer science.
An injection (one-to-one) maps distinct inputs to distinct outputs. A surjection (onto) covers the entire target set. A bijection is both, creating a perfect, reversible one-to-one pairing.
No, there is no standard verb form. The related adjective is 'bijective'.
It formally defines when two sets have the same 'size' or cardinality, which is fundamental to comparing infinite sets, defining isomorphisms, and creating lossless, reversible data transformations.
A function between two sets that is both injective (one-to-one) and surjective (onto), establishing a perfect one-to-one correspondence where each element of the first set is paired with exactly one unique element of the second set, and vice versa.
Bijection is usually technical/academic in register.
Bijection: in British English it is pronounced /baɪˈdʒɛkʃ(ə)n/, and in American English it is pronounced /baɪˈdʒɛkʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[No common idioms exist for this technical term]”
Learning
Memory Aids
Mnemonic
Think 'BI-JECTION' – a TWO-way (bi-) CONNECTION (jection) where every item has one unique partner and no one is left out.
Conceptual Metaphor
A perfectly coordinated dance partnership where every dancer from one group is paired with exactly one unique dancer from another group, and everyone has a partner.
Practice
Quiz
What is the primary field of use for the word 'bijection'?