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Set of Permutation and Identity Permutation
I have a "basic" math question that seems easy but I couldn't figure out.
Assume I have $L$ = {0,1,2,3,4,5,6,7,8,9} and $M$ = set of all
permutations on set $L$.
From the description above, I know that the $L$ = 10 and $M$ = 10!
Now let $J$ = $M$ \ {id} where id is an identity permutation i.e id($x$) = $x$ for all $x$ in $L$.
What is $J$?
Would it make more sense if I set the value of $x$ first?
Also, X \ Y means set of X "subtract" with set of Y
I may be misinterpreting your question, but I'm assuming that by $M\{id\}$, you're referring to the quotient space $M/{id}$. If that is the case, we know by Lagrange's theorem that $M/\{id\}=M/\{id\}=10!/1=10!$.
Let me know if I misinterpreted the problem.

I may be misinterpreting your question, but I'm assuming that by $M\{id\}$, you're referring to the quotient space $M/{id}$. If that is the case, we know by Lagrange's theorem that $M/\{id\}=M/\{id\}=10!/1=10!$.
Let me know if I misinterpreted the problem.
20171214 07:12:18