vault backup: 2026-03-07 10:07:48

DAS/Relations.md

@@ -8,6 +8,7 @@
 | *symmetric*      | the given relation work both ways                                                                                     | $a = b => b = a$          |
 | *antisymmetric*  | the given relation only works both ways if $a$ and $b$ are the same                                                   | $a <= b, b <= a => a = b$ |
 
+
 ## Equivalence Relations
 A relation $R$ is called _equivalence relation_ when it is _transitive, reflexive and symmetric_.
 
@@ -38,3 +39,11 @@ Each possible sum creates it's own equivalence class. So there are $7$ equivalen
 > $[5]_(~) = {(2, 3), (3, 2)}$
 > $[6]_(~) = {(3, 3)}$
 
+## Binary Relation
+A binary relation is a relation $R$ between _exactly two_ elements $a in R$ and $b in R$. An example for a binary relation is $a <= b$
+## Orders
+An **Order** is a mathematical way to sort, rank or compare elements within a set, where some elements come "before" and "after" others.
+
+A _binary relation_ is called an order if it is...
+- a *reflexive relation*
+- a *antisymmetric relation*