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# Set of Permutation and Identity Permutation

2017-12-14 05:21:39

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.

2017-12-14 07:12:18