When it's said that the group of permutations $S_n$ acts on $A=\{1,...,n\}$, how does an element $\sigma_i \in S_n$ act on a single element $a \in A$? In other word, how does a permutation of numbers from $A$ actually act on a single natural number from $A$? I think I got confused conceptually.
2026-04-02 14:12:01.1775139121
$S_n$ acting on set of natural numbers
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If $n=4$ the permutation $(1,2,3)$ acts on $1$ by sending it to $2$, it acts on $4$ by sending it to $4$.