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#1 2007-04-04 10:37:19
- Stanley_Marsh
- Member
- Registered: 2006-12-13
- Posts: 345
explain
What is " In
, the group of integer modulo 6 "?Numbers are the essence of the Universe
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#2 2007-04-04 11:49:45
- Zhylliolom
- Real Member
- Registered: 2005-09-05
- Posts: 412
Re: explain
It's just the group of integers modulo 6... The group operation is addition.
Last edited by Zhylliolom (2007-04-04 11:49:58)
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#3 2007-04-04 12:18:00
- Stanley_Marsh
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- Registered: 2006-12-13
- Posts: 345
Re: explain
Does that mean , the residues? integers modulo 6? shoundnt it belike this a congruent to b modulo m ?
Numbers are the essence of the Universe
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#4 2007-04-04 12:22:37
- Zhylliolom
- Real Member
- Registered: 2005-09-05
- Posts: 412
Re: explain
Yes, residues are the same thing. Everything is done mod 6 here, so 5 + 5 = 4, 2[sup]5[/sup] = 2, etc. From this you can see that it is actually a group.
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#5 2007-04-04 13:07:45
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: explain
If you want to be really explicit, you write them as:
{[0], [1], [2], [3], [4], [5]}
The equivalence classes of 0, 1, 2, 3, 4, 5, and 6. But when you start working with them, you very quickly find this extremely annoying, and so you drop the [].
"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..."
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