From d92ae7d86a083bd3fc360606ae3b8ce38fa60f27 Mon Sep 17 00:00:00 2001
From: "David A. Madore" <david+git@madore.org>
Date: Wed, 9 Mar 2016 15:50:14 +0100
Subject: Start writing an intuitive introduction to ordinals.

---
 notes-mitro206.tex | 134 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 134 insertions(+)

(limited to 'notes-mitro206.tex')

diff --git a/notes-mitro206.tex b/notes-mitro206.tex
index 2c4cf75..ba84960 100644
--- a/notes-mitro206.tex
+++ b/notes-mitro206.tex
@@ -3165,6 +3165,140 @@ $G/\equiv$, on a bien $f(x) = f(x')$ ssi $x\equiv x'$).
 %
 %
 
+\section{Introduction aux ordinaux}
+
+\subsection{Explication intuitive}
+
+\thingy Les ordinaux sont une sorte de nombres, totalement ordonnés et
+même « bien-ordonnés », qui généralisent les entiers naturels en
+allant « au-delà de l'infini » : les entiers naturels
+$0,1,2,3,4,\ldots$ sont en particulier des ordinaux (ce sont les plus
+petits), mais il existe un ordinal qui vient après eux, à
+savoir $\omega$, qui est lui-même suivi de
+$\omega+1,\omega+2,\omega+3,\ldots$, après quoi vient $\omega\cdot 2$
+(ou simplement $\omega 2$), et beaucoup d'autres choses.
+
+\begin{center}
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+\draw[fill] (9.88471,0.02306) -- (9.88471,-0.02306) -- (10.00000,0.00000) -- (9.88471,0.02306);
+\end{scope}
+\node[anchor=north] at (0.00000,-2.00000) {$0$};
+\node[anchor=north] at (0.40000,-1.60000) {$1$};
+\node[anchor=north] at (0.72000,-1.28000) {$2$};
+\node[anchor=north] at (0.97600,-1.02400) {$3$};
+\node[anchor=north] at (2.00000,-1.60000) {$\omega$};
+\node[anchor=north] at (2.32000,-1.28000) {$\scriptscriptstyle \omega+1$};
+\node[anchor=north] at (3.60000,-1.28000) {$\omega2$};
+\node[anchor=north] at (4.88000,-1.02400) {$\omega3$};
+\end{tikzpicture}
+\\{\footnotesize (Une rangée de $\omega^2$ allumettes.)}
+\end{center}
+
+\thingy On pourra ajouter les ordinaux, et les multiplier, et même
+élever un ordinal à la puissance d'un autre, mais il n'y aura pas de
+soustraction ($\omega-1$ n'a pas de sens, en tout cas pas en tant
+qu'ordinal, parce que $\omega$ est le plus petit ordinal infini).
+
+
 %
 %
 %
-- 
cgit v1.2.3

