Difference between revisions of "Ordered pair"
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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). | ||
Revision as of 00:10, 11 March 2015
Kuratowski definition
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 functions
Proof of existence
It is easy to prove ordered pairs exist
Suppose we are given [math]a,b[/math] (so we can be sure they exist).
By the axiom of a pair we may create [math]\{a,b\}[/math] and [math]\{a,a\}=\{a\}[/math], then we simply have a pair of these, thus [math]\{\{a\},\{a,b\}\}[/math] exists.
The axioms may be found here
Set Theory
