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Alsosaid1987 (talk | contribs) Added info on specialized arrows for injective function to match analogous information in the corresponding surjective function article. |
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Symbolically,<math display="block">\forall a,b \in X, \;\; f(a)=f(b) \Rightarrow a=b,</math>
which is logically equivalent to the [[Contraposition|contrapositive]],<ref>{{Cite web|url=http://www.math.umaine.edu/~farlow/sec42.pdf|title=Section 4.2 Injections, Surjections, and Bijections |last=Farlow|first=S. J.|author-link= Stanley Farlow |website=Mathematics & Statistics - University of Maine |access-date=2019-12-06 |url-status=dead |archive-url= https://web.archive.org/web/20191207035302/http://www.math.umaine.edu/~farlow/sec42.pdf |archive-date= Dec 7, 2019 }}</ref><math display="block">\forall a, b \in X, \;\; a \neq b \Rightarrow f(a) \neq f(b).</math>An injective function (or, more generally, a monomorphism) is often denoted by using the specialized arrows ↣ or ↪ (for example, <math>f:A\rightarrowtail B</math> or <math>f:A\hookrightarrow B</math>), although some authors specifically reserve ↪ for an [[inclusion map]].<ref>{{Cite web |title=What are usual notations for surjective, injective and bijective functions? |url=https://math.stackexchange.com/questions/46678/what-are-usual-notations-for-surjective-injective-and-bijective-functions |access-date=2024-11-24 |website=Mathematics Stack Exchange |language=en}}</ref>
== Examples ==
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