Fixed math in some blog posts

This commit is contained in:
Brandon Rozek 2021-07-26 09:52:41 -04:00
parent c717c72d08
commit 17165847cd
6 changed files with 8 additions and 1 deletions

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@ -36,6 +36,7 @@ This element maps $0 \rightarrow 1$, $1 \rightarrow 2$, and $2 \rightarrow 0$.
A good way to check if something similar to the above is an element of a symmetric group is pay attention to the second row. Make sure that it only contains the elements of the set you care about (ex: $\mathbb{Z}_3$) and that there are no repeats.
Let's look at an example of composing two elements from this symmetric group.
$$
\begin{pmatrix}
0 & 1 & 2 \\
@ -46,12 +47,13 @@ $$
0 & 1 & 2 \\
0 & 2 & 1 \\
\end{pmatrix}
=
\=
\begin{pmatrix}
0 & 1 & 2 \\
1 & 0 & 2 \\
\end{pmatrix}
$$
The main thing to remember here is that you must compose from right to left.
$0 \rightarrow 0$ and then $0 \rightarrow 1$, so ultimately $0 \rightarrow 1$.