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* If <math>f : X \to Y</math> is injective and <math>A</math> and <math>B</math> are both subsets of <math>X,</math> then <math>f(A \cap B) = f(A) \cap f(B).</math>
* Every function <math>h : W \to Y</math> can be decomposed as <math>h = f \circ g</math> for a suitable injection <math>f</math> and surjection <math>g.</math> This decomposition is unique [[up to isomorphism]], and <math>f</math> may be thought of as the [[inclusion function]] of the range <math>h(W)</math> of <math>h</math> as a subset of the codomain <math>Y</math> of <math>h.</math>
* If <math>f : X \to Y</math> is an injective function, then <math>Y</math> has at least as many elements as <math>X,</math> in the sense of [[cardinal number]]s. In particular, if, in addition, there is an injection from <math>Y</math> to <math>X,</math> then <math>X</math> and <math>Y</math> have the same cardinal number. (This is known as the [[Cantor–Bernstein–Schroeder theorem]].) Repeated injections therefore have [[monotonic]] increasing cardinality of their codomains.
* If both <math>X</math> and <math>Y</math> are [[Finite set|finite]] with the same number of elements, then <math>f : X \to Y</math> is injective if and only if <math>f</math> is surjective (in which case <math>f</math> is bijective).
* An injective function which is a homomorphism between two algebraic structures is an [[embedding]].
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