design/tpl (Monoids and Sequences): Add missing index entries
Forgot in previous commit.master
parent
8d54420656
commit
9fd57872ed
|
@ -323,6 +323,8 @@ Given that, we have $f\bicomp{[]} = f\bicomp{[A]}$ for functions returning
|
|||
|
||||
|
||||
\subsection{Monoids and Sequences}
|
||||
\index{abstract algebra!monoid}
|
||||
\index{monoid|see abstract algebra, monoid}
|
||||
\begin{definition}[Monoid]\dfnlabel{monoid}
|
||||
Let $S$ be some set. A \emph{monoid} is a triple $\Monoid S\bullet e$
|
||||
with the axioms
|
||||
|
@ -337,6 +339,8 @@ Given that, we have $f\bicomp{[]} = f\bicomp{[A]}$ for functions returning
|
|||
\end{align}
|
||||
\end{definition}
|
||||
|
||||
\index{abstract algebra}
|
||||
\index{abstract algebra!semigroup}
|
||||
Monoids originate from abstract algebra.
|
||||
A monoid is a semigroup with an added identity element~$e$.
|
||||
|
||||
|
@ -350,6 +354,8 @@ When the sequence has one or zero elements,
|
|||
as $x_0 \bullet e = x_0$ in the case of one element
|
||||
or $e \bullet e = e$ in the case of zero.
|
||||
|
||||
\indexsym\cdots{sequence}
|
||||
\index{sequence}
|
||||
Generally,
|
||||
given some monoid $\Monoid S\bullet e$ and a sequence $\Fam{x}jJ\in S$
|
||||
where $n<|J|$,
|
||||
|
@ -378,6 +384,7 @@ If $x=\Set{1}$,
|
|||
If $x=\Set{}$,
|
||||
we have $0$.
|
||||
|
||||
\index{conjunction!monoid}
|
||||
\begin{lemma}
|
||||
$\Monoid\Bool\land\true$ is a monoid.
|
||||
\end{lemma}
|
||||
|
@ -388,6 +395,7 @@ If $x=\Set{}$,
|
|||
as in $\true \land p \equiv p \land \true \equiv p$.
|
||||
\end{proof}
|
||||
|
||||
\index{disjunction!monoid}
|
||||
\begin{lemma}
|
||||
$\Monoid\Bool\lor\false$ is a monoid.
|
||||
\end{lemma}
|
||||
|
|
Loading…
Reference in New Issue