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== Definition ==
[[file:Injection.svg|thumb|An injective function, which is not also surjective]]
{{Further|topic=notation|Function (mathematics)#Notation}}
Let <math>f</math> be a function whose ___domain is a set <math>X.</math> The function <math>f</math> is said to be '''injective''' provided that for all <math>a</math> and <math>b</math> in <math>X,</math> if <math>f(a) = f(b),</math> then <math>a = b</math>; that is, <math>f(a) = f(b)</math> implies <math>a=b.</math> Equivalently, if <math>a \neq b,</math> then <math>f(a) \neq f(b)</math> in the [[Contraposition|contrapositive]] statement.
Symbolically,<math display="block">\forall a,b \in X, \;\; f(a)=f(b) \Rightarrow a=b,</math>
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