Difference between revisions of "Ordered pair"

Revision as of 22:19, 4 March 2015 (view source) Alec (Talk | contribs) (Created page with "An ordered pair <math>(a,b)=\{\{a\},\{a,b\}\}</math>, this way <math>(a,b)\ne(b,a)</math>. Ordered pairs are vital in the study of relations which leads to Fun...")		Revision as of 00:10, 11 March 2015 (view source) Alec (Talk | contribs) m Newer edit →
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		+	==Kuratowski definition==
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	An ordered pair <math>(a,b)=\{\{a\},\{a,b\}\}</math>, this way <math>(a,b)\ne(b,a)</math>.		An ordered pair <math>(a,b)=\{\{a\},\{a,b\}\}</math>, this way <math>(a,b)\ne(b,a)</math>.
	Ordered pairs are vital in the study of [[Relation|relations]] which leads to [[Function|functions]]		Ordered pairs are vital in the study of [[Relation|relations]] which leads to [[Function|functions]]
−	==Proof of existence==	+	===Proof of existence===
	It is easy to prove ordered pairs exist<br/>		It is easy to prove ordered pairs exist<br/>
	Suppose we are given <math>a,b</math> (so we can be sure they exist).		Suppose we are given <math>a,b</math> (so we can be sure they exist).

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Revision as of 00:10, 11 March 2015

Kuratowski definition

An ordered pair

$$(a,b)=\{\{a\},\{a,b\}\}$$ , this way $$(a,b)\ne(b,a)$$ .

Ordered pairs are vital in the study of relations which leads to functions

Proof of existence

It is easy to prove ordered pairs exist
Suppose we are given

$$a,b$$ (so we can be sure they exist).

By the axiom of a pair we may create

$$\{a,b\}$$ and $$\{a,a\}=\{a\}$$ , then we simply have a pair of these, thus $$\{\{a\},\{a,b\}\}$$ exists.

The axioms may be found here