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== Ordered pair ==
{{main article|Ordered pair}}
First, consider the '''ordered pair'''. The reason that this comes first is technical: ordered pairs are needed to implement [[Relation (mathematics)|relations]] and [[Function (mathematics)|functions]], which are needed to
The first definition of the ordered pair was the definition <math>(x,y) \overset{\mathrm{def}}{=} \{\{\{x\},\emptyset\},\{\{y\}\}\}</math> proposed by [[Norbert Wiener]] in 1914 in the context of the type theory of [[Principia Mathematica]]. Wiener observed that this allowed the elimination of types of n-ary relations for <math>n>1</math> from the system of that work.
It is more usual now to use the definition <math>(x,y) \overset{\mathrm{def.}}{=} \{\{x\},\{x,y\}\}</math>, due to [[Kazimierz Kuratowski|Kuratowski]].
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