0 divided by 0

[SubJunk]

This isn't even a mathematical question you realise.

Just because it's numerical doesn't mean it's mathematical, and regardless of what category it fits into it's the stupidest thing i've ever heard, ever.

That equation just doesn't exist and never would in mathematics.

[Sayonara]

3*0 = 0

 

if you devide both side by 0' date=' what do you get????[/quote']

Nothing, because you can't divide by zero.

 

 

Non-mathsy explanation:

 

A division operation such as y/x returns the number of instances of x required to total y.

 

No number of zeros can total a non-zero number, so zero can't be used as a denominator.

[albertlee]

Well, I think the reason why this does not make any sense is much more about mathematical reasonning....

 

for eg, 3/0 does not make sense, because in any mathematical equation, you cannot devide any number into a complete nothing.....

 

it is like if I sell you a slice of meat, and you "chop" it into as many pieces as possible, every piece may become very very small, but there is still something..

 

Albert

[123rock]

That all depends on what you are trying to do by claiming a definition of 0/0.

 

NB thinking about 0 fitting into 0 some number of times is not mathematics' date=' and has no place in the discussion at all. Simply there is no way to define 0/0 in side any field, or ring, that is consistent with the axioms of a field, where consistent has the obvious meaning.[/quote']

 

That's exactly what I'm trying to explain but people keep contradicting me with the x*0=0 is the same as x=0/0 bogus sh*t.

[123rock]

Definitions are arbitrary. You do not "prove" definitions' date=' nor do you "prove" something that has been arbitrarily designated as undefined. The only requirement in math is that a definition be "well-defined," meaning it doesn't lead to some logical inconsistency or absurdity. 0/0 cannot be well-defined, so it is left as undefined.

 

 

It leads to all sorts of contradictions. Here, have fun with this one:

Let 0/0 = 0.

Then:

-infinity = ln(0) = ln(0/0) = ln(0) - ln(0) = -infinity - -infinity = infinity - infinity[/quote']

 

I'm sorry but ln(0)=undefined. Does that mean that 0 is undefined?

 

Besides what does this have to do with anything? Natural logs are a function that 0 is subjected to. I can say that f(0)=1. What's f(0)? 0+1. That's irrational

[AL]

OK, that was admittedly a bad example on my part. I didn't give it enough thought; ln(0) is not defined from R->R, and I should have known better. Also not sure what you're trying to say about functions.

 

But moving right along, there are still plenty of valid reasons why 0/0 = 0 is not well-defined. Try this one:

Let c be a nonzero constant, and let 0/0 = 0. Then:

0/0 = 0

(0*c)/0 = 0

0*(c/0) = 0

c/0 = 0/0

c/0 = 0

c = 0*0

c = 0

Contradiction.

[granDODyssey]

to quote .."this is nature's way of telling us ...we are doing something wrong"

see...we invented Zero.....it's not even "natural number"....now it turns back and bite "us"(sound similar?).

go back to the basic ...what is zero...can you show me zero monkey? no you can't ...i bet!!

[MandrakeRoot]

Zero is a natural number according to most conventions. It all depends on whether or not you find it usefull to include it in this set.

 

Mandrake

[123rock]

OK' date=' that was admittedly a bad example on my part. I didn't give it enough thought; ln(0) is not defined from R->R, and I should have known better. Also not sure what you're trying to say about functions.

 

But moving right along, there are still plenty of valid reasons why 0/0 = 0 is not well-defined. Try this one:

Let c be a nonzero constant, and let 0/0 = 0. Then:

0/0 = 0

(0*c)/0 = 0

0*(c/0) = 0

c/0 = 0/0

c/0 = 0

c = 0*0

c = 0

Contradiction.[/quote']

 

that's valid if you assume 0/0=1

 

See:

 

c/0=0/0

c/0=0

c=0*0 --> can be translated as [c/0][0]=0*0 ---> c*0/0=0*0 and thus 0/0=1 is proven to be valid by c=0 as 0 being c's only solution which contradicts the definition of a variable. This can be shown to be a contradiction for all numbers, except for 0.

 

 

Whether 0 is a natural number or not DOESN'T MATTER. I don't see how that was included upon the discussion.

 

Edit: Also you assume that 0*(c/0)=0 is the same as c/0=0*0; Again, that's only true if you are assuming that 0/0=1.

 

0/0 doesn't equal 1 because if 0/0=1, then (0/0)(2)=1(2); 0/0=2, and thus 1=2, which is a contradiction.

[123rock]

This isn't exactly a proof that 0/0=0, since we arrive at [0/0]/0=0/0, since 1/0=0/0, but 1 doesn't equal 0, but it's a step forward.

 

 

x and y do not equal x/0

 

0/0=0^x/0^y

 

0^2x-x/0^y

 

[0^2x/0^x]/0=0/0

 

[0/0]/0=0/0