Math Is Fun Forum

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Is the system a group?

Solve the problem.
Decide whether the system is a group. If it is not a group, identify which of the following properties it fails to satisfy: closure, associativity, identity, inverse. Even integers; multiplication

    a.     Not a group; identity, inverse, associative           b.     Not a group; closure           c.     Not a group; identity, inverse           d.     Group

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Is the system a group?

Focus on the identity.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: Is the system a group?

I went ahead and answered that it is a group.

But as far as identity, I guess not cause you'd need a one or a zero. I am probably wrong.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Is the system a group?

Well, you are wrong.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: Is the system a group?

I now realize that there is no zero. You would need a zero for Identity I guess, but Jane which do you think is the answer and why?

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Is the system a group?

You need to find an identity.  That is, an element e where a * e = a for all a.  Now that can be really hard to do.  But, you can simplify the process.  If it has to work for all a's, then it must work for at least one a.  So you pick an element a, lets pick 2.  So we need to find an e such that:

2 * e = 2

What must e be?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: Is the system a group?

But how does that account for the rest of the properties?

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Is the system a group?

If you show one property doesn't hold, it doesn't matter whether or not other properties hold.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: Is the system a group?

Select and option.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: Is the system a group?

Select and option.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: Is the system a group?

The official answer is C. Now to figure out why. I'll be back.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Is the system a group?

I’ve figured out that you still haven’t got a clue exactly what a group is. Please re-read your lecture notes on the definition of a group. Look at various examples of groups – that should hopefully also help.

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: Is the system a group?

No  need to figure it out.It is stated clearly in my last post. Thanks for the advice. You might benefit from reading your lecture notes also.

Hey! I look like you now.

Last edited by rune2402 (2007-11-15 22:52:03)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Is the system a group?

Rune, you are starting to be very rude.  We are here to help you, please be nice in return.

Do you understand why the set does not have an identity under multiplication?  For inverses, since it's closed and the inverse is outside of the set, then this leads us to conclude there can't be inverses.  If there were, the set would not be closed.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

rune2402

Banned

Registered: 2007-10-23

Posts: 32

Re: Is the system a group?

I am rude.? screw off, and die. Look at the rude comment beore mine you $%^$?

I will not be back. You people are &$&%

Quote:

I’ve figured out that you still haven’t got a clue exactly what a group is.

I had already figured it out geniuses, but before i could post i was insulted. Thanks for being an $^%& Mr.moderator.

Just like an &$&%

Please cancel my account.

Last edited by rune2402 (2007-11-16 09:35:57)