◀ ▲ ▶Branches / Settheory / Definition: Total and Unique Binary Relations
The following properties of binary relations are fundamental to the concept of maps, which we will introduce later.
Definition: Total and Unique Binary Relations
Let \(V, W\) be (not necessarily different) sets and \(R\subseteq V\times W\) be a relation \(R\) is called:
 rightunique (also called functional, univalent or rightdefinite), if from $vRw_1$ and $vRw_2$ it follows that $w_1=w_2$ for the respective $v\in V$, $w_1,w_2\in W,$
 leftunique (also called injective), if from $v_1Rw$ and $v_2Rw$ it follows that $v_1=v_2$ for the respective $v_1,v_2\in V$, $w\in W,$
 unique if $R$ is rightunique and leftunique,
 lefttotal, if for all \(v\in V\) there is a \(w\in W\) with \(vRw\),
 righttotal, (also called surjective), if for all \(w\in W\) there is a \(v\in V\) with \(vRw\),
 total, if $R$ is lefttotal and righttotal.
 total, if $R$ is lefttotal and righttotal.
Mentioned in:
Chapters: 1
Definitions: 2 3 4 5 6 7 8
Explanations: 9 10
Lemmas: 11 12
Motivations: 13
Proofs: 14 15 16 17 18 19 20 21 22
Propositions: 23
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References
Bibliography
 Knauer Ulrich: "Diskrete Strukturen  kurz gefasst", Spektrum Akademischer Verlag, 2001