Noun

one-to-one (plural one-to-ones)

1. A personal relationship, especially a sexual one, between two people. Colloquial abbreviation: 121 or 1-2-1
2. (mathematics) injection; a mapping which takes no two points in the preimage to the same point in the image

Adjective

1. Involving direct communication between two people. Used especially to refer to situations in which one person is teaching one other person. (British)

Synonyms

• one-on-one (North America)

In mathematics, an injective function is a function which associates distinct arguments with distinct values; that is, every unique argument produces a unique result.

An injective function is called an injection, and is also said to be a one-to-one function (not to be confused with one-to-one correspondence, i.e. a bijective function).

A function f that is not injective is sometimes called many-to-one. (However, this terminology is also sometimes used to mean "single-valued", i.e. each argument is mapped to at most one value.)

A monomorphism is a generalization of an injective function in category theory.

Definition

Let f be a function whose domain is a set A. The function f is injective if for all a and b in A, if f(a) = f(b), then a = b; that is, f(a) = f(b) implies a = b. Equivalently, if a ≠ b, then f(a) ≠ f(b).