noun

bijection

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Bijection (noun) means a function that pairs each element of one set with exactly one element of another set, with none left over on either side. Example: “The function that doubles every integer is not a bijection from the integers to the integers, because odd numbers are never reached.”

noun

technical A function that pairs each element of one set with exactly one element of another set, with none left over on either side.

"The function that doubles every integer is not a bijection from the integers to the integers, because odd numbers are never reached."

"Two finite sets have the same number of elements exactly when there is a bijection between them."

"The professor asked us to build a bijection between the positive integers and the even positive integers."

How to use bijection

Learner’s notes

In plain EnglishA perfect pairing between two sets where nothing is left out or doubled up.

When to use it

This is a technical term used in mathematics, especially set theory.

Memory tip

Think of it as a function that is both injective and surjective at once.

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Common pairings

a bijection between two sets construct a bijection establish a bijection an explicit bijection

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C2 · Advanced serendipity Fortunate discoveries made entirely by accident.

Gen Z slang rizz Charm — the ability to attract a romantic interest.

B2 · Intermediate empathy The capacity to share another person’s feelings.

C1 · Advanced nonchalant Casually calm and relaxed; unconcerned.

Internet slang delulu Delusional — believing something against the odds.

Etymology nostalgia Greek nostos “return home” + algos “pain”.

C2 · Advanced serendipity Fortunate discoveries made entirely by accident.

Gen Z slang rizz Charm — the ability to attract a romantic interest.

B2 · Intermediate empathy The capacity to share another person’s feelings.

C1 · Advanced nonchalant Casually calm and relaxed; unconcerned.

Internet slang delulu Delusional — believing something against the odds.

Etymology nostalgia Greek nostos “return home” + algos “pain”.

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Fill the gap

Can you complete this real example?

The function that doubles every integer is not a _____ from the integers to the integers, because odd numbers are never reached.

Etymology

The word comes from French bijection. It was introduced by the mathematician group Nicolas Bourbaki in their treatise Éléments de mathématique.

Origin: French

Synonyms

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bijective function one-to-one correspondence

Rhymes for bijection

region ablation allusion emulsion ideation novation diffusion elocution extension oxidation perfusion selection

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Frequently asked questions

What is a bijection in math?

A bijection is a function that is both one-to-one and onto. Every element in each set is matched with exactly one element in the other.

What is the difference between a bijection and an injection?

An injection only needs to send different inputs to different outputs. A bijection must also reach every element of the target set.

Is a bijection the same as a one-to-one correspondence?

Yes, the two terms mean the same thing. Both describe a function that is an injection and a surjection.

What is the meaning of bijection?

"bijection" (noun) means a function that pairs each element of one set with exactly one element of another set, with none left over on either side.