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→Basic concepts: As a function is defined on its whole ___domain, its inverse is always surjective. |
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Because a function is trivially surjective when restricted to its image, the term [[partial bijection]] denotes a partial function which is injective.<ref name="Hollings2014-251">{{cite book|author=Christopher Hollings|title=Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups|url=https://books.google.com/books?id=O9wJBAAAQBAJ&pg=PA251|year=2014|publisher=American Mathematical Society|isbn=978-1-4704-1493-1|page=251}}</ref>
An injective partial function may be inverted to an injective partial function, and a partial function which is both injective and surjective has an injective function as inverse. Furthermore, a function which is injective may be inverted to
The notion of [[Transformation (function)|transformation]] can be generalized to partial functions as well. A '''partial transformation''' is a function <math>f : A \rightharpoonup B,</math> where both <math>A</math> and <math>B</math> are [[subset]]s of some set <math>X.</math><ref name="Hollings2014-251"/>
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