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Definition: Injective Function

A function \(f:A\mapsto B\) is called injective, (or injection, or embedding, or, less formally, one-to-one), if for all \(a_1,a_2\in A\) with $f(a_1)=f(a_2)$ it follows that $a_1=a_2.$ This corresponds to the left-unique property, in addition to the defining properties of a function.

By a contraposition argument the following definition is equivalent: For all \(a_1,a_2\in A\), it follows from $a_1\neq a_2$ that $f(a_1)\neq f(a_2).$


| | | | | created: 2014-07-11 19:59:54 | modified: 2020-06-01 07:41:41 | by: bookofproofs | references: [577], [979], [6823]

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Bibliography (further reading)

[6823] Kane, Jonathan: “Writing Proofs in Analysis”, Springer, 2016

[577] Knauer Ulrich: “Diskrete Strukturen – kurz gefasst”, Spektrum Akademischer Verlag, 2001

[979] Reinhardt F., Soeder H.: “dtv-Atlas zur Mathematik”, Deutsche Taschenbuch Verlag, 1994, 10