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 $f(a_1)\neq f(a_2).$
Chapters: 1
Corollaries: 2
Definitions: 3 4 5 6 7 8
Explanations: 9 10
Lemmas: 11
Proofs: 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Propositions: 32 33 34 35 36
Theorems: 37