Ordered Pair

set-theory

Definition

Ordered Pair

An ordered pair $(x,y)$ (for all sets $x$ and $y$) is an object with property:

$$\forall x\forall y\forall x^{\prime }\forall y^{\prime }:(x,y)=(x^{\prime },y^{\prime })⟹x=x^{\prime }\wedge y=y^{\prime }$$

Definitions

Kuratowski

Definition

Kuratowski's Ordered Pair

Define the ordered pair $(x,y)$ as:

$$(x,y):=\{\{x\},\{x,y\}\}$$

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