Implementation of mathematics in set theory: Difference between revisions

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=== Special kinds of relation ===
 
Some properties of relations:
 
* A relation R is <strong>reflexive</strong> if <math>x R x</math> holds for all x in the ___domain of R.
 
* A relation R is <strong>symmetric</strong> if <math>x R y \leftrightarrow y R x</math> for all x and y.
 
* A relation R is <strong>transitive</strong> if <math>x R y \wedge y R z \rightarrow x R z</math> for all x,y,z.
 
* A relation R is <strong>antisymmetric</strong> if <math>x R y \wedge y R x \rightarrow x=y</math> for all x,y.
 
* A relation R is <strong>well-founded</strong> if for every set S which meets the field of R, there is x in S whose preimage under R does not meet S.
 
== Functions ==