**Definition**: Extensional Relation

Let $V$ be a set and let $R\subseteq V\times V$ be a binary relation. $R$ is called **extensional** if all elements of $x\in V$ are uniquely determined by ordered pairs $(z,x)\in R,$ formally

$$\{z\in V\mid zRx\}=\{z\in V\mid zRy\} \Rightarrow x=y,$$

or, by contraposition,

$$\{z\in V\mid zRx\}\neq \{z\in V\mid zRy\} \Rightarrow x\neq y.$$

| | | | | created: 2019-02-01 08:03:02 | modified: 2019-02-16 17:11:14 | by: *bookofproofs* | references: [8055]

## 1.**Explanation**: Examples of Extensional Relations

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[8055] **Hoffmann, D.**: “Forcing, Eine EinfÃ¼hrung in die Mathematik der UnabhÃ¤ngigkeitsbeweise”, Hoffmann, D., 2018

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