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

.obsidian/workspace.json

@@ -93,7 +93,7 @@
       }
     ],
     "direction": "horizontal",
-    "width": 200
+    "width": 265.50418853759766
   },
   "right": {
     "id": "8a65bc0c1d4d98f2",
@@ -163,8 +163,19 @@
               "icon": "lucide-list",
               "title": "Outline"
             }
+          },
+          {
+            "id": "7cc839bdf6f45717",
+            "type": "leaf",
+            "state": {
+              "type": "git-view",
+              "state": {},
+              "icon": "git-pull-request",
+              "title": "Source Control"
             }
-        ]
+          }
+        ],
+        "currentTab": 4
       }
     ],
     "direction": "horizontal",
@@ -185,9 +196,9 @@
   },
   "active": "16b88a8bc6c6b6e0",
   "lastOpenFiles": [
-    "DAS/Relations.md",
-    "DAS/Set Theory.md",
     "DAS/Logic.md",
+    "DAS/Set Theory.md",
+    "DAS/Relations.md",
     "DAS/Functions.md",
     "mathe/notation.md",
     "Studium.md",

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*