Implementation of mathematics in set theory: Difference between revisions

Revision as of 18:56, 17 January 2013

Revision as of 18:38, 18 January 2013

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=== Properties and kinds of relations ===

Let ''R'' be some [[binary relation]]. ''R'' is:

*'''[[Reflexive relation|Reflexive]]''' if <math>''xRx'' \forallfor every ''x'' \existin ythe \,((xRy___domain \veeor yRx)range \leftrightarrowof xRx)</math>''R''.

* '''[[Symmetric relation|Symmetric]]''' if <math>\forall x,y \,(xRy \leftrightarrowto yRx)</math>.

* '''[[Transitive relation|Transitive]]''' if <math>\forall x,y,z \,(xRy \wedge yRz \rightarrow xRz)</math>.