Cartesian product
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Revision as of 02:30, 8 December 2015 by Alec (Talk | contribs) (Created page with "{{Todo|Find references}} __TOC__ ==Definition== Given two sets, {{M|X}} and {{M|Y}} their ''Cartesian product'' is the set: * {{M|1=X\times Y:=\{(x,y)\ \vert\ x\in X\wedge y\i...")
TODO: Find references
Contents
Definition
Given two sets, [ilmath]X[/ilmath] and [ilmath]Y[/ilmath] their Cartesian product is the set:
- [ilmath]X\times Y:=\{(x,y)\ \vert\ x\in X\wedge y\in Y\}[/ilmath], note that [ilmath](x,y)[/ilmath] is an ordered pair traditionally this means
- [ilmath](x,y):=\{x,\{x,y\}\}[/ilmath] or indeed
- [ilmath]X\times Y:=\Big\{\{x,\{x,y\}\}\ \vert\ x\in X\wedge y\in Y\Big\}[/ilmath]
Set construction
TODO: Build a set that contains [ilmath]\{x,y\} [/ilmath]s, then build another that contains ordered pairs, then the Cartesian product is a subset of this set
