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You are not logged in. #1 20080723 02:46:49
Division mod nTrackback from here:
"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..." #2 20080723 03:51:45
Re: Division mod nIf you drop the condition that division means "multiplication by multiplicative inverse", then you can end up turning modular arithmetic into a Wheel. If, on the other hand, you drop the distributive property (which I believe is required to prove that 0*a = 0, but not certain), then you'd probably be studying something that hasn't been looked at all too much before. I know of no name for a ring without the distributive property. "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..." #3 20080724 08:32:03
Re: Division mod nSince distributivity is the only ring axiom to mention both addition and multiplication, a ring without distributivity is nothing more than an abelian group and a semigroup that happen to be defined on the same set. #4 20080724 09:57:43
Re: Division mod nRight, it's the relation between multiplication and addition that gives a ring its interesting properties. "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..." #5 20080724 14:20:12
Re: Division mod nWow, thanks for giving this so much attention. I see now why division by zero is still a "nono" in modular arithmetic. I admit (begrudgingly) that the "wheel" stuff is way over my head, but I'm very appreciative that attention was given to my question. Thanks. There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. 