From 23d0d936fc817961e0f8f19ca6033a51edb445fe Mon Sep 17 00:00:00 2001
From: markusde
Date: Mon, 24 Oct 2022 20:56:53 -0700
Subject: god is dead

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 entries/markusde/collatz/collatz.pdf | Bin 0 -> 86872 bytes
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 entries/markusde/collatz/collatz.tex |  21 +++++++++++++++++++++
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diff --git a/entries/markusde/collatz/collatz.pdf b/entries/markusde/collatz/collatz.pdf
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+\documentclass[12pt]{article}
+\usepackage[landscape]{geometry}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+\renewcommand{\phi}{\varphi}
+\begin{document}
+
+\noindent The least fixed point of 
+\begin{align*}
+    h & : (\mathbb{Z}_\bot \to \mathbb{Z}_\bot) \to (\mathbb{Z}_\bot \to \mathbb{Z}_\bot) \\
+    h(F)(n) & = 
+    \begin{cases}
+        1 & n = 1 \\
+        (\phi^{n/2} + (-\phi)^{-n/2})\, F_{n/2} & n \textrm{ is even} \\
+        \sqrt[3]{\frac{\phi^{3n+1}-\phi F_{3n+1}}{10} + \frac{\sqrt{25 \phi^{3n+1} - 25\phi F_{3n+1} - 20}}{50}} + \sqrt[3]{\frac{\phi^{3n+1}-\phi F_{3n+1}}{10} - \frac{\sqrt{25 \phi^{3n+1} - 25\phi F_{3n+1} - 20}}{50}} & \textrm{otherwise} \\
+    \end{cases}
+\end{align*}
+is the Fibonacci sequence if and only if the Collatz conjecture is true.
+
+\end{document}
-- 
cgit v1.2.3-70-g09d2


From 781b027bc09bcda00f93a0f0ee749a25ff657cde Mon Sep 17 00:00:00 2001
From: markusde
Date: Mon, 24 Oct 2022 21:05:09 -0700
Subject: god is dead 2

---
 entries/markusde/collatz/collatz.pdf | Bin 86872 -> 87475 bytes
 entries/markusde/collatz/collatz.tex |   2 +-
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--- a/entries/markusde/collatz/collatz.tex
+++ b/entries/markusde/collatz/collatz.tex
@@ -8,7 +8,7 @@
 
 \noindent The least fixed point of 
 \begin{align*}
-    h & : (\mathbb{Z}_\bot \to \mathbb{Z}_\bot) \to (\mathbb{Z}_\bot \to \mathbb{Z}_\bot) \\
+    h & : (\mathbb{N}_\bot \to \mathbb{Z}_\bot) \to (\mathbb{N}_\bot \to \mathbb{Z}_\bot) \\
     h(F)(n) & = 
     \begin{cases}
         1 & n = 1 \\
-- 
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