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Divide by zero

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abyaly:
Dividing by zero isn't new. Making up a new number that allows division by zero isn't an issue. If you look for them, I'm sure you can find plenty of number systems where you can "divide by zero". The problem is that we want the real numbers to be a field.


Like in every field, the additive identity (in this case 0), behaves in an unhappy way when we use it in multiplication. Namely, multiplying anything by zero just gives us zero again. So we can't undo multiplication by zero in a consistent way.


So the the real challenge for you isn't just to divide by zero. It's to divide by zero while still keeping your new number system similar enough to the usual one. But I still won't use it, since I think every single one of the field properties is more valuable than division by zero.

triclops200:
That's what I was doing (I'm a clever 16 y/o  )... It didn't work out, unfortunatly. I gave an example where it did, but that was just chance that out of all the equations that it could work, I hit it. I tried... I will probably try again tomarrow, this time from a different angle, but I have serious doughts that it can be done. Though getting one example is a positive step in that direction. But the problem is: The new set of imaginary numbers will have to contain rules that either conflict with real number 0 rules or make an endless set of imaginary 0 rules.

bacillus:
Okay, so you're saying dividing by zero results in the entire real number set?

triclops200:
No, it equals an undefined imaginary number which has some similarities to the real number set and follows alot of correlations, but is undefinable and utterly hard to work out...
1/0 = 10
2/0 = 20
0/2 = 0 right? well it also equals, in my rules, (which were incorrect, but it was still a beautiful system untill I figured that out) 02
0/3= 0 and = 03
0*2 = 0 and 02
0*3 = 0 and 03
I actually got a correct answer from it once, using 0 as a value, but I tried 4 more similar equations and none of them were correct. I am going to start again tommarrow, but I am making no promises on weather it can be done.

Houshalter:
 I am almost through with algebra 2 at my school and I still can't figure out what your talking about. But this does give me an idea. Ever hear of AM? Its an old artificial intellegence program that did math. Theres also automated theorem proving, which I guess is similiar. My idea is to use a program like that and set it loose on trying to come up with useful concepts and properties related to division by zero. Or you can always do what you did and waste 9 hours of your life.

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