# One-to-One Relation

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An One-to-One Relation is a Binary Relation where an Argument Value is only in the Relation with one other Argument Value (and vice versa).

**AKA:**Injective Relation.**Context:**- It can be a Reflexive Relation.
- ...

**Example(s):**- A Property Relation can be one. E.g. for unique identifiers.
- A Successor Relation.
- One gene expresses one protein. “
*The Pseudomonas aeruginosa oprB gene encodes the carbohydrate-selective OprB porin, which translocates substrate molecules across the outer membrane to the periplasmic glucose-binding protein."* - A passport number refers to one person and one person has at most one passport number. (note though that not every person has a passport).
- “
*Brian Mulroney was succeeded by Kim Campbell who was succeeded by Jean Chrétien.*" - ...

**Counter-Example(s):****See:**Relation, One-to-One Function.

## References

### 2009

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Injective_function
- In mathematics, an injective function is a function which associates distinct arguments with distinct values.
- 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.