diff --git a/.obsidian/app.json b/.obsidian/app.json
index 6fd1af8..0e0990d 100644
--- a/.obsidian/app.json
+++ b/.obsidian/app.json
@@ -5,5 +5,6 @@
     "landscape": false,
     "margin": "0",
     "downscalePercent": 100
-  }
+  },
+  "alwaysUpdateLinks": true
 }
\ No newline at end of file
diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index d779651..26d5727 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -13,7 +13,7 @@
             "state": {
               "type": "markdown",
               "state": {
-                "file": "Algo/Séminaire/Chapter 4 - A bit of imperative.md",
+                "file": "Algo/Séminaire/Chapter 5 - Recursivity.md",
                 "mode": "source",
                 "source": false
               }
@@ -85,7 +85,7 @@
             "state": {
               "type": "backlink",
               "state": {
-                "file": "Algo/Séminaire/Chapter 4 - A bit of imperative.md",
+                "file": "Algo/Séminaire/Chapter 5 - Recursivity.md",
                 "collapseAll": false,
                 "extraContext": false,
                 "sortOrder": "alphabetical",
@@ -102,7 +102,7 @@
             "state": {
               "type": "outgoing-link",
               "state": {
-                "file": "Algo/Séminaire/Chapter 4 - A bit of imperative.md",
+                "file": "Algo/Séminaire/Chapter 5 - Recursivity.md",
                 "linksCollapsed": false,
                 "unlinkedCollapsed": true
               }
@@ -125,7 +125,7 @@
             "state": {
               "type": "outline",
               "state": {
-                "file": "Algo/Séminaire/Chapter 4 - A bit of imperative.md"
+                "file": "Algo/Séminaire/Chapter 5 - Recursivity.md"
               }
             }
           },
@@ -156,10 +156,14 @@
       "command-palette:Open command palette": false
     }
   },
-  "active": "c82ce15f72f65a11",
+  "active": "c473a791e2b34194",
   "lastOpenFiles": [
-    "Algo/Chapter 0 - A bit of imperative/0.1 - Print.md",
+    "Algo/Séminaire/assets/fact function response.png",
+    "Algo/Séminaire/assets/recursivite-meme.png",
+    "Pasted image 20230912155138.png",
+    "Algo/Séminaire/Chapter 5 - Recursivity.md",
     "Algo/Séminaire/Chapter 4 - A bit of imperative.md",
+    "Algo/Chapter 0 - A bit of imperative/0.1 - Print.md",
     "Algo/Séminaire/Untitled",
     "Algo/Séminaire/Introduction.md",
     "Algo/Séminaire/Chapter 1 - CAML basics.md",
@@ -183,8 +187,6 @@
     "Mathématiques/Séminaire/Logics/Pasted image 20230904100934.png",
     "Mathématiques/Séminaire",
     "Mathématiques/Séminaire/Logics/Pasted image 20230904100125.png",
-    "Mathématiques/Séminaire/Logics/Pasted image 20230904095003.png",
-    "Mathématiques/Séminaire/Logics/Pasted image 20230904094230.png",
     "2023-09-01.md",
     "Algo",
     "Mathématiques",
diff --git a/Algo/Séminaire/Chapter 4 - A bit of imperative.md b/Algo/Séminaire/Chapter 4 - A bit of imperative.md
index eb74e2b..660734d 100644
--- a/Algo/Séminaire/Chapter 4 - A bit of imperative.md	
+++ b/Algo/Séminaire/Chapter 4 - A bit of imperative.md	
@@ -72,6 +72,12 @@ Error: should have int type (*because of the hidden else*)
 
 # let print_even n = 
 	if n mod 2 = 0 then
-		print_int n ;
-		print_newline()
-		
\ No newline at end of file
+		begin
+			print_int n ;
+			print_newline()
+		end;; (*begin and end used to execute more than 1 function into a if*)
+val print_even : int -> unit = <fun>
+
+# print_even 4;;
+4
+-: unit = ()
diff --git a/Algo/Séminaire/Chapter 5 - Recursivity.md b/Algo/Séminaire/Chapter 5 - Recursivity.md
new file mode 100644
index 0000000..a4e1df5
--- /dev/null
+++ b/Algo/Séminaire/Chapter 5 - Recursivity.md	
@@ -0,0 +1,44 @@
+![[recursivite-meme.png]]
+### 5.1. Simple functions
+To create a recursive function we have to use this structure
+
+```Ocaml
+(*normal function*)
+# let f = expr -> 1) evaluate expr ; 2) create & link f to the result
+
+(*recursiv function*)
+# let rec f = expr -> 1) create f ; 2) evaluate expr ; 3) link f to the result
+```
+
+**Exmple with factorial function**
+```Ocaml
+# let rec fact = function 
+	| 0 -> 1
+	| n -> n * fact(n-1)
+
+# fact 4;;
+-: int = 24
+```
+![[fact function response.png]]
+> ⚠️ CAML have a call stack limite (it will block with stack overflow if the limit is reach)
+
+**Basic expression**
+```Ocaml
+let rec f params = 
+	if stop condition then 
+		stop expression
+	else
+		recursive expression 
+```
+
+To write a recurvise function we need two things
+1) There always is a stop case
+2) The parameters of a recursive call are different then its parent call, and go towards  the stop condition
+
+### 5.2. Down
+```Ocaml
+# let rec countdown n = 
+	if n = 0 then
+		print_int(0)
+	else
+		print_int(countdown (n-1));;
\ No newline at end of file
diff --git a/Algo/Séminaire/assets/fact function response.png b/Algo/Séminaire/assets/fact function response.png
new file mode 100644
index 0000000..7b70343
Binary files /dev/null and b/Algo/Séminaire/assets/fact function response.png differ
diff --git a/Algo/Séminaire/assets/recursivite-meme.png b/Algo/Séminaire/assets/recursivite-meme.png
new file mode 100644
index 0000000..352771d
Binary files /dev/null and b/Algo/Séminaire/assets/recursivite-meme.png differ