diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 1ede617..a59930c 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -250,13 +250,13 @@
       "obsidian-git:Open Git source control": false
     }
   },
-  "active": "7a0e7b37bd89861d",
+  "active": "7d1b3d98021093a7",
   "lastOpenFiles": [
-    "DAS/Arithmetic.md",
+    "DAS/Set Theory.md",
     "DAS/Groups.md",
+    "DAS/Arithmetic.md",
     "DAS/merge.md",
     "DAS/export.css",
-    "DAS/Set Theory.md",
     "Formulas.md",
     "DAS/Functions.md",
     "DAS/Counting.md",
diff --git a/DAS/Groups.md b/DAS/Groups.md
index dc80f99..6bc5629 100644
--- a/DAS/Groups.md
+++ b/DAS/Groups.md
@@ -1,3 +1,7 @@
+Groups are Closures that have the following properties:
 
-## Internal Composition law
-$$
\ No newline at end of file
+1. **closure**: Every element which is a result of the binary operation of the group is part of the group
+2. **associativity**: changing the order of operations doesn't change the result
+3. **identity**: there is a neutral element ($0$ in addition, $1$ in multiplication)
+4. **inverses**: every element has a element when combined results in the identity element ($+5 + (-5) = 0$)
+   
\ No newline at end of file
diff --git a/DAS/Set Theory.md b/DAS/Set Theory.md
index a91505b..c84dee9 100644
--- a/DAS/Set Theory.md	
+++ b/DAS/Set Theory.md	
@@ -84,3 +84,8 @@ A := {1, 2, 3} \
 cal(P)(A) = {emptyset, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
 $$
 
+## Closures
+A **closed set** under the binary operation $*$ denoted by $forall a,b in S, a * b in S$
+"All $a * b$ from set $S$ are included in set $S$"
+
+A set can be closed under any binary operation ($+, -, *, \/$), depending on the set itself if it actually is closed or not. $NN$ for example is not closed under subtraction.