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packages/macros.sty : Added convinences macros

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saundersp
2024-11-07 05:29:13 +01:00
parent 94cdd07e84
commit aafcec6a3e
5 changed files with 46 additions and 36 deletions
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12
contents/set_theory.tex
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@ -13,7 +13,7 @@ $S = \{a,b,c\}$
\langsubsection{Extensionnalité}{Extensionality}
$\forall A\forall B(\forall X(X \in A \Leftrightarrow X \in B) \Rightarrow A = B)$
$\forall A\forall B(\forall X(X \in A \equivalence X \in B) \implies A = B)$
\langsubsection{Spécification}{Specification}
%TODO Complete subsection
@ -32,9 +32,9 @@ Unite all elements of two given sets into one.
$n,m \in \N$
$A = \{a_0, \cdots, a_n\}$
$A := \{a_0, \cdots, a_n\}$
$B = \{b_0, \cdots, b_m\}$
$B := \{b_0, \cdots, b_m\}$
$A \union B = \{a_0, \cdots, a_n, b_0, \cdots, b_m\}$
@ -47,7 +47,7 @@ $A \union B = \{a_0, \cdots, a_n, b_0, \cdots, b_m\}$
\subsection{Power set}
%TODO Complete subsection
For a set $S$ such that $\card{S} = n \equivalence \card{\mathbf{P}(S)} = 2^n$
For a set $S$ such that $\card{S} = n \implies \card{\mathbf{P}(S)} = 2^n$
\langsubsection{Choix}{Choice}
%TODO Complete subsection
@ -77,9 +77,9 @@ If the domain is the same as the codomain then the function is an endormorphsim
\subsection{Notation}
$A \longrightarrow B$
$\functiondef{A}{B}$
$ x \longrightarrow f(x)$
$\function{f}{x}{f(x)}$
\langsubsection{Injectivité}{Injectivity} \label{definition:injective}