0/0 exists in the 0 ring

{0} is a ring under multiplication. 0 is the multiplicative identity and additive identity.

we have 0 x 0 = 0
so 0/0 = 0 and everythign works fine!

But how many times must we multiply zero by something to get zero? It could be any number, and thus INFINITY! :O

>>2

Or it can be zero!

why dont you divide it by 0 to make it 0

A RING IS AN ABELIAN GROUP UNDER ADDITION THAT IS ALSO CLOSED, ASSOCIATIVE, AND DISTRIBUTIVE UNDER MULTIPLICATION.  {0} IS A RING

AN INTEGRAL DOMAIN IS A COMMUTATIVE (UNDER MULT.) RING, WITH UNITY AND NO ZERO DIVISORS.
CONSEQUENTLY, {0} IS ALSO AN INTEGRAL DOMAIN, WHERE 0 ACTS AS UNITY.  NOTE: THERE ARE NO NON-ZERO ELEMENTS.

ALL FINITE INTEGRAL DOMAINS ARE FIELDS, SO {0} IS A FIELD AS WELL.

>>5
The definition of integral domain demands that 0 != 1.

>>6
unity is an element, u, such that for all r in R,
ur = ru = r

let u = 0 in {0}
then for all r in {0},
0*r = r*0 = 0 = r


why not ;[[[[

>>2
You miss the whole point...  The only defined number in the ring is 0, and hence 0/0 must be 0.

>>7
I didn't say that the definition implies that 0 != 1, I said it demands that 0 != 1. That's just stated as part of the definition of an integral domain. If you ignore that part of the definition though, then yes, the trivial ring is a field in which you can divide by zero.

In fields, 0 != 1 by definition. {0} fails.

In any case, if you want to divide by zero you don't have to break axioms. Just work on the CPL.

This board is awesome

0 is awesome
It's a very weird number mathematically

>>9
ah, the book i got my definition from didnt state that =(

>>1
Here's your problem. Sure your ring can have multiplication as one of it's operations, but that doesn't mean division is defined. And if division -is- defined, then it's not the same division that we'd normally use to divide real number quantities. Simply put, division is only defined on Rx(R-{0}), assuming that (a,b)=a/b. So, in order to have division on your ring, you're going to have to define an operation other than the one we're all familiar with.

Have fun with your new operation :P

>>14
WHAT ABOUT DIVIDE BY i NOT IN R\{0}

i want to fuck 0

0 = nullity

{0} is not a ring in the first place, but even if it was, there's a reason we call these "trivial".

0/0 = X

X . 0 = 0

X  can be any number

0/0 = can be every number

>>19
Your logic is absolutely terrible. I can go ahead and say that 4/2=3. Therefore, 2*3=4! Tadaa! I've proved centuries of math wrong!

Oh wait, 0/0 doesn't equal a complex number. Ha, how about that.

>>18

Just because it's trivial doesn't mean that we don't care what is or isn't true.

That being said, the only way for 0/0 to equal 0 is to redefine what '/' is. If you just redefine it so that 0/0=0, then you're just fine.

Only then, noone is impressed since I can just redefine any operation to yield any results I'd like whenever I'd like, so darn. Looks like you're no closer to your quest of proving the last two millenia of mathematicians wrong.

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