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Fixed math in some blog posts
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@ -36,6 +36,7 @@ This element maps $0 \rightarrow 1$, $1 \rightarrow 2$, and $2 \rightarrow 0$.
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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.
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Let's look at an example of composing two elements from this symmetric group.
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$$
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\begin{pmatrix}
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0 & 1 & 2 \\
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@ -46,12 +47,13 @@ $$
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0 & 1 & 2 \\
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0 & 2 & 1 \\
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\end{pmatrix}
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=
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\=
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\begin{pmatrix}
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0 & 1 & 2 \\
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1 & 0 & 2 \\
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\end{pmatrix}
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$$
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The main thing to remember here is that you must compose from right to left.
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$0 \rightarrow 0$ and then $0 \rightarrow 1$, so ultimately $0 \rightarrow 1$.
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