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gnome
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I freely admit that I am notationally challenged, so please help me out with this:
(from Enderton, A Mathematical Introduction to Logic)
[tex]\{x,y\} = \{y,x\}[/tex]
how does [itex]<x,y> = \{\{x\},\{x,y\}\} [/itex] define the ordered pair [itex]<x,y>[/itex]?
(from Enderton, A Mathematical Introduction to Logic)
I'm baffled. SinceThe ordered pair <x,y> of objects x and y must be defined in such a way that
[tex]<x,y>=<u,v> \mbox{ iff } x=u \qquad \mbox{ and } \qquad y=v[/tex]
Any definition that has this property will do; the standard one is
[tex]<x,y> = \{\{x\},\{x,y\}\}.[/tex]
[tex]\{x,y\} = \{y,x\}[/tex]
how does [itex]<x,y> = \{\{x\},\{x,y\}\} [/itex] define the ordered pair [itex]<x,y>[/itex]?
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