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#1 2006-09-04 12:15:47

confused94
Member
Registered: 2006-08-26
Posts: 7

cayley table

Cayley table for the binary operation multiplication Modulo 10, for the sub set of integers {2,4,6,8}...
HERE

Correct?

Last edited by confused94 (2006-09-04 12:18:06)

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#2 2006-09-04 13:40:54

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: cayley table

Did it specify whether the operation was multiplication or addition?  If it didn't, you should normally assume addition as Z10 is a group under addition and Z10 is not under multiplication.

If it is multiplication, it's correct.


"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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#3 2006-09-04 23:37:59

confused94
Member
Registered: 2006-08-26
Posts: 7

Re: cayley table

Yes, multiplication.
How do you find the identity element? Under multiplication, the identity element is 1. What about here? Also how to find inverses? eg inverse of 2.

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#4 2006-09-05 02:20:40

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: cayley table

You want to find a row where the numbers appear in the order that they occur in the very top.  Note that there won't always be an identity element when you combine a set with an operation.  However, there is one here.

To find an inverse, start by picking a number on the very left column.  Then look along that number's row till you find the identity.  Once there, look up to the very top row and same column.  That number is the inverse.


"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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