From bb73ee298ad87dcacc03ac21a3cb7daf0e5901de Mon Sep 17 00:00:00 2001
From: alexander <alexander@xstation>
Date: Sun, 14 Dec 2025 23:25:51 +0100
Subject: [PATCH] Fixed Incorrect Formula

---
 src/Analysis_rewrite.typ | 35 ++++++++++++++++++++++++++++++++---
 1 file changed, 32 insertions(+), 3 deletions(-)

diff --git a/src/Analysis_rewrite.typ b/src/Analysis_rewrite.typ
index e96d0f3..e1e9cab 100644
--- a/src/Analysis_rewrite.typ
+++ b/src/Analysis_rewrite.typ
@@ -44,12 +44,41 @@
   align(left, block(e))
 }
 
+#let colorAllgemein = color.hsl(105.13deg, 92.13%, 75.1%)
 #let colorFolgen = color.hsl(202.05deg, 92.13%, 75.1%)
 #let colorReihen = color.hsl(280deg, 92.13%, 75.1%)
 #let colorAbleitung = color.hsl(356.92deg, 92.13%, 75.1%)
 #let colorIntegral = color.hsl(34.87deg, 92.13%, 75.1%)
 
-#columns(5, gutter: 2mm)[
+#columns(4, gutter: 2mm)[
+  #subHeading(fill: colorAllgemein, it: [Allgemeins])
+  #grid(
+    columns: (auto, auto),
+    row-gutter: 2mm,
+    column-gutter: 3mm,
+    [Dreiecksungleichung], [
+      $abs(x + y) <= abs(x) + abs(y)$ \
+      $abs(abs(x) - abs(y)) <=  abs(x - y)$
+    ],
+    [Cauchy-Schwarz-Ungleichung], [
+      $abs(x dot y) <= abs(abs(x) dot abs(y))$
+    ],
+    [Geometrische Summenformel], [
+      #MathAlignLeft($ sum_(k=1)^(n) k = (n(n+1))/2 $)
+    ],
+    [Bernoulli-Ungleichung ], [
+      $(1 + a)^n >= 1 + n a$
+    ],
+    [Binomialkoeffizient], [
+      $binom(n, k) = (n!)/(k!(n-k)!)$
+    ],
+    [Binomische Formel], [
+      #MathAlignLeft($ (a + b)^n = sum^(n)_(k=0) binom(n,k) a^(n-k) b^k $)
+    ],
+    [Fakultäten], [$ 0! = 1! = 1 $],
+  )
+
+
   #subHeading(fill: colorFolgen, it: [Folgen])
   $ lim_(x -> infinity) a_n $
 
@@ -63,11 +92,11 @@
   #grid(columns: (1fr, 1fr),
     gutter: 1mm,
     row-gutter: 2mm,
-    align(top+center, [*Fallend*]), align(top+center, [*Fallend*]),
+    align(top+center, [*Fallend*]), align(top+center, [*Steigend*]),
     [$ a_(n+1) <= a_(n) $],
     [$ a_(n+1) >= a_(n) $],
-    [$ a_(n+1)/a_(n) > 1 $],
     [$ a_(n+1)/a_(n) < 1 $],
+    [$ a_(n+1)/a_(n) > 1 $],
   )
 
   *Konvergentz Allgemein*