saundersp/notebook
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Fixed some notations mistakes

Browse Source
This commit is contained in:
saundersp
2024-08-05 00:35:07 +02:00
parent 55ac1c6c20
commit 1a17854c3c
4 changed files with 35 additions and 17 deletions
Download Patch File Download Diff File Expand all files Collapse all files

10
contents/number_theory.tex
View File

@ -139,9 +139,9 @@ $\forall (p,q) \in \Q, \forall n \in \N^*, \frac{p}{q} \Leftrightarrow \frac{p \
\langsubsection{Opérateurs}{Operators}
%TODO Complete subsection
$\forall ((p,q), (a,b)) \in \Q^2, \frac{p}{q} + \frac{a}{b} = \frac{pb + aq}{qb}$
$\forall ((p,q), (a,b)) \in \Q, \frac{p}{q} + \frac{a}{b} = \frac{pb + aq}{qb}$
$\forall ((p,q), (a,b)) \in \Q^2, \frac{p}{q} \cdot \frac{a}{b} = \frac{pa}{qb}$
$\forall ((p,q), (a,b)) \in \Q, \frac{p}{q} \cdot \frac{a}{b} = \frac{pa}{qb}$
$\forall (p,q) \in \Q, \forall k \in \Z, (\frac{p}{q})^k = \frac{p^k}{q^k}$
@ -183,7 +183,7 @@ $\functiondef{(p,q)}{P_1^{\frac{p}{|p|} + 1}P_2^pP_3^q}$
\citeannexes{wikipedia_complex_numbers}
$\C = (a,b) \in R^2, a + ib ~= \R^2 $
$\C = (a,b) \in R, a + ib ~= \R $
$i^2 = -1$
@ -204,7 +204,7 @@ $i^2 = -1$
\langsubsection{Relations binaries}{Binary relations}
%TODO Complete subsection
$\forall ((a,b), (c,d)) \in \C^2, a = c \land b = d \Leftrightarrow a + ib = c + id$
$\forall ((a,b), (c,d)) \in \C, a = c \land b = d \Leftrightarrow a + ib = c + id$
\langsubsection{Opérateurs}{Operators}
%TODO Complete subsection
@ -213,7 +213,7 @@ Il est impossible d'avoir une relation d'ordre dans le corps des complexes mais
\subsubsection{Ordre lexicographique}
$\forall((a,b),(c,d)) \in \C^2, a + ib \Rel_L c + id := \begin{cases}
$\forall((a,b),(c,d)) \in \C, a + ib \Rel_L c + id := \begin{cases}
a < c & \implies a + ib < c + id \\
\otherwise & \begin{cases}
b < d & \implies a + ib < c + id \\