Definition:Injection/Also known as
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Injection
Authors who prefer to limit the jargon of mathematics tend to use the term:
- one-one (or 1-1) or one-to-one for injective
- one-one mapping or one-to-one mapping or one-to-one map for injection.
However, because of the possible confusion with the term one-to-one correspondence, it is standard on $\mathsf{Pr} \infty \mathsf{fWiki}$ for the technical term injection to be used instead.
E.M. Patterson's idiosyncratic Topology, 2nd ed. of $1959$ refers to such a mapping as biuniform.
This is confusing, because a casual reader may conflate this with the definition of a bijection, which in that text is not explicitly defined at all.
An injective mapping is sometimes written:
- $f: S \rightarrowtail T$ or $f: S \hookrightarrow T$
In the context of class theory, an injection is often seen referred to as a class injection.
Sources
- 1959: E.M. Patterson: Topology (2nd ed.) ... (previous) ... (next): Chapter $\text {II}$: Topological Spaces: $\S 9$. Functions
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 3.3$. Injective, surjective, bijective; inverse mappings: Definition $1$ (footnote)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): one-to-one function (one-to-one mapping, one-to-one map)