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#1 2013-02-04 20:20:52

Still Learning
Guest

Is this a group ?

Is ({0,n} ,~) a group where x~yneutralx-y| and n is any postive real number?

#2 2013-02-04 20:26:21

Still Learning
Guest

Re: Is this a group ?

Sorry there will be "= |" in place of the smiley

#3 2013-02-04 20:31:12

Fistfiz
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Re: Is this a group ?

~ is not associative: (x~y)~z!=x~(y~z). For example, take x=5, y=3, z=1. You have:

(5~3)~1 = ||5-3|-1| = 1 != 3 = |5-|3-1|| = 5~(3~1)

so ({0,n} ,~) is not a group, if I understood what you meant.


30+2=28 (Mom's identity)

#4 2013-02-04 21:00:14

Still Learning
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Re: Is this a group ?

Yes,but ~ is associative when you only use 0 and n,does that count?

#5 2013-02-04 21:17:00

anonimnystefy
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Re: Is this a group ?

Yes, that is a group. It is even an Abel's group.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
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#6 2013-02-04 22:05:13

Fistfiz
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Re: Is this a group ?

Still Learning wrote:

Yes,but ~ is associative when you only use 0 and n,does that count?

Ok, I thought that {0,n} was {0,1,...,n}


30+2=28 (Mom's identity)

#7 2013-02-04 22:43:16

bob bundy
Moderator

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Re: Is this a group ?

hi Still Learning

You have to show it obeys the four properties of a group:  closure, identity, inverses, asociativity.

I've made a group combination table (see below).

From that it is obvious that closure holds, it has an identity (o)  and all members are self inverse.

So what about associativity ?  This is often the hardest to prove.  You have to show that

a(bc) = (ab)c for all a b and c in the set.

As Stefy has pointed out, commutativity holds (ab = ba) so it is fairly easy to cover all cases by using that property.

I'll use * for a tilda as I cannot see that symbol above, and show one example:

0*(0*n) = 0* n = n

(0*0)*n = 0 * n = n

I'll leave the rest to you.

Bob


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#8 2013-02-05 04:23:57

Still Learning
Guest

Re: Is this a group ?

Ok,but i want to know if the operation has to be always associative or it has to be associative only for the set?

#9 2013-02-05 05:22:34

bob bundy
Moderator

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Re: Is this a group ?

That question has already been answered by Fistfiz in post 3.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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