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Update 1-preliminaries.tex
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pitmonticone committed Jun 14, 2024
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Expand Up @@ -8,16 +8,15 @@ \chapter{Preliminaries}

\section{Notation}

% In this section, we define the notation and symbols that will be consistently used in this work.
% Familiarity with these symbols is crucial for understanding the formal arguments and proofs presented later.
In this section, we define the notation and symbols that will be consistently used in this work.

\begin{tabular}{>{\centering}m{1.8cm} m{5.8cm}}
\toprule
\textbf{Symbol} & \multicolumn{1}{c}{\textbf{Description}} \\
\midrule
$\lnot$ & Logical negation \\
$\land$ & Logical conjunction \\
$\lor$ & Logical inclusive disjunction \\
% $\lnot$ & Logical negation \\
% $\land$ & Logical conjunction \\
% $\lor$ & Logical inclusive disjunction \\
$:=$ & Definition \\
$\forall$ & Universal quantification \\
$\exists$ & Existential quantification \\
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% \end{center}

\newpage

\section{Definitions}

In this section, each definition is articulated as clearly as possible to maximise clarity and precision.
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The \textit{$n$-th cyclotomic extension field} or \textit{$n$-th cyclotomic field} is a field $X(\zeta_n)$ obtained by adjoining $\zeta_n$ to $X$.
\end{definition-pre}

\newpage
\section{Results}

In this section, we state some preliminary results that are crucial for the development of our formal proofs.
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