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saundersp
2024-08-05 00:35:49 +02:00
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contents/number_theory.tex
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@ -86,7 +86,7 @@ Chaque application généré de $g_c$ avec $c \in \N^*$ est injective avec $\N$,
\begin{itemize} \label{theorem:totally_ordered_natural_numbers}
\item{L'ensemble est totalement ordonnée : $\forall n \in \N, \exists k \suchas k = n + 1 \land n < k$}
\item{On peut diviser l'ensemble en deux ensembles distincts : $\forall n \in \N, \exists! k \in \N \suchas n := \begin{cases} 2k & \text{pair} \\ 2k+1 & \text{Impair} \end{cases}$}
\item{On peut diviser l'ensemble en deux ensembles distincts : $\forall n \in \N, \exists! k \in \N \suchas n := \begin{cases} 2k & \text{paire} \\ 2k+1 & \text{Impaire} \end{cases}$}
\end{itemize}
\begin{theorem_sq}
@ -172,8 +172,7 @@ $\functiondef{(p,q)}{P_1^{\frac{p}{|p|} + 1}P_2^pP_3^q}$
\langsubsection{Construction de Cayley–Dickson}{Cayley–Dickson's construction}
%\citeannexes{wikipedia_cayley_dickson}
\citeannexes{project_vae}
Source: \citeannexes{wikipedia_cayley_dickson}
\langsubsection{Coupes de Dedekind}{Dedekind's cuts}
%TODO Complete subsection
@ -181,7 +180,7 @@ $\functiondef{(p,q)}{P_1^{\frac{p}{|p|} + 1}P_2^pP_3^q}$
\langsection{Construction des complexes $(\C)$}{Construction of complex numbers}
%TODO Complete section
\citeannexes{wikipedia_complex_numbers}
Source: \citeannexes{wikipedia_complex_number}
$\C = (a,b) \in R, a + ib ~= \R $
@ -223,7 +222,7 @@ $\forall((a,b),(c,d)) \in \C, a + ib \Rel_L c + id := \begin{cases}
\section{Construction des quaternions $(\Hq)$}
\citeannexes{wikipedia_quaternion}
Source: \citeannexes{wikipedia_quaternion}
\langsubsection{Table de Cayley}{Multiplication table}
%TODO Complete subsection
@ -245,7 +244,7 @@ $\forall((a,b),(c,d)) \in \C, a + ib \Rel_L c + id := \begin{cases}
\section{Construction des octonions $(\Ot)$}
\citeannexes{wikipedia_octonion}
Source: \citeannexes{wikipedia_octonion}
\langsubsection{Table de multiplication}{Multiplication table}
%TODO Complete subsection
@ -283,7 +282,7 @@ Où $\delta_{ij}$ est le symbole de Kronecker et $\epsilon_{ijk}$ est un tenseur
\section{Construction des sedenions $(\Se)$}
\citeannexes{wikipedia_sedenion}
Source: \citeannexes{wikipedia_sedenion}
\langsubsection{Table de multiplication}{Multiplication table}
%TODO Complete subsection