Definition 1. An injective function or injection is a function $f : X \to Y$ such that
\[\forall x, y \in X :\enspace f(x) = f(y) \enspace\rimp\enspace x = y.\]The set of all injections from $X$ to $Y$ is denoted by
\[\inj(X, Y).\]An injective function is also known as a one-to-one function.
References
- [1]
- Wikipedia contributors. Injective function. Wikipedia, The Free Encyclopedia.
- [2]
- Thomas Jech. Set Theory. 3rd Millennium ed, rev. and expanded. Springer, 2002. p. 11.