Implementation of mathematics in set theory: Difference between revisions

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Undid revision 620975765 by 5.69.140.243 (talk) actually, grammar forbids that change. Try this one.
Related definitions: This must have been a mistake. xRy usually refers to an ordered pair, which as noted above, can be implemented as a set but this would be ambiguous (which implementation?). R would be less ambiguous as a set, but not include y.
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The '''[[inverse relation|converse]]''' of <math>R</math> is the relation <math>\left\{\left(y, x\right) : xRy\right\}</math>.
 
The '''___domain''' of <math>R</math> is the set <math>\left\{x : \exists y \in \left(xRy\right)\right\}</math>.
 
The '''range''' of <math>R</math> is the ___domain of the converse of <math>R</math>.