0 divided by 0

[123rock]

Nope, not another boring, theological quest to find the value of 0/0, but in fact to disprove its existence...

 

The simple proof that 0/0 doesn't equal any positive, negative, or imaginary number, then for example:

0/0=1, then 0/0(2)=1(2), making 1=2, if 0/0=2, we substitute 1 for 0/0.

 

Now 0/0=0, this doesn't hold, so 0/0 might as well equal 0, nobody knows.

 

This can be proven to not be able to be disproven by:

 

a = b

a^2 = b^2

a^2 - b^2 = ab - b^2

(a+b)(a-b) = b(a-b)

a+b=b

b+b=b

2b=b

2=1;

 

This would be true that 0/0 cannot equal 0, but on line 5, a+b=b, we can subtract each side to get that a=0, in which case nothing can be proven for 2=1

 

 

Now for the big bonanza: 1/0=0/0

 

 

To prove that 0/0=1/0

We have to assume that 0/0=0/0, otherwise this doesn't work.

 

0/0=(1-1)/(1-1)

 

1/1-1 - 1/1-1=0/0

 

(1/1-1)(1+1/1+1)-1/1-1=0/0

 

(1+1/1-1)-1/1-1=0/0

 

2/0 - 1/0=0/0

 

1/0=0/0 QED

 

 

 

1/0=0/0!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[Aeschylus]

Divison by zero is simply not defined, so your proof is worthless.

[123rock]

if 1-1=0, then 1/0-1/0=1-1/0. You can simply think of this as 1-1=0, then dividing by 0 when everything is defined.

When the denominators are the same, the numerators can be subtracted added, etc, thus there is no reason to think that the same ratio can't be subjected to arithmetic.

 

The only way 0/0 is undefined is if you try to evaluate it. 0/0(2) is not undefined, but 0/0. Theological proof like it is undefined so you can't prove it's defined is the most inconsistent, and the way many theorems have been proven is by proving the inverse of the false assumption. One such case is sqrt.of 2=a/b. Since sqrt. of 2 is irrational, a/b cannot describe it, but it is assumed that it can be described by a/b, thus proven not true. Same here, we assume that 0/0=1, and prove that it can't, and thus arrive that 0/0 may or may not equal 0, infinity, or just undefined.

Mathematics is not about going with the flow and accepting proofs, but finding them, and thus show me why 0/0 is undefined and not simply 0?

Since 0/0=1/0, then i guess 1/0=0, if 0/0=0, but then does that make sense?

[Dave]

if 1-1=0' date=' then 1/0-1/0=1-1/0. You can simply think of this as 1-1=0, then dividing by 0 when everything is defined.

When the denominators are the same, the numerators can be subtracted added, etc, thus there is no reason to think that the same ratio can't be subjected to arithmetic.

 

The only way 0/0 is undefined is if you try to evaluate it. 0/0(2) is not undefined, but 0/0. Theological proof like it is undefined so you can't prove it's defined is the most inconsistent, and the way many theorems have been proven is by proving the inverse of the false assumption. One such case is sqrt.of 2=a/b. Since sqrt. of 2 is irrational, a/b cannot describe it, but it is assumed that it can be described by a/b, thus proven not true. Same here, we assume that 0/0=1, and prove that it can't, and thus arrive that 0/0 may or may not equal 0, infinity, or just undefined.

Mathematics is not about going with the flow and accepting proofs, but finding them, and thus show me why 0/0 is undefined and not simply 0?

Since 0/0=1/0, then i guess 1/0=0, if 0/0=0, but then does that make sense?[/quote']

 

?

 

I read the first sentence and got confused. I don't even know what you're trying to talk about other than 0/0.

[Aeschylus]

Basically can not be a member of the field of real numbers. I'll show ou if you want, but you might like to try and construct the proof yourself by looking at the field axioms.

[RICHARDBATTY]

The simple fact as I see it is you cannot divide nothing, it is ilogical so any answer will also be ilogical. But then my dog is better than me at math hang on I'll ask him.

[RICHARDBATTY]

He says if 0/0=1 what does the 1 signify?. Answer nothing.

[123rock]

Ok, so if 10/5 is 2, what does the 2 signify?

It's a process of evaluation.

 

if 0/0=0/0 by definition, then 1-1/0=0/0 by arithmetic. What proof can you show me that 1-1 doesn't equal 0?

Mathematicians have said 0/0 is undefined because they have found that it's undefined through standard mathematical processes not the other way around, saying that you can't use standard mathematical processes to show what 0/0 is because it's undefined and thus is undefined. This is faulty logic Aeschylus.

 

P.S.: Tell your dog good job.

[RICHARDBATTY]

Ok' date=' so if 10/5 is 2, what does the 2 signify?

It's a process of evaluation.

 

if 0/0=0/0 by definition, then 1-1/0=0/0 by arithmetic. What proof can you show me that 1-1 doesn't equal 0?

Mathematicians have said 0/0 is undefined because they have found that it's undefined through standard mathematical processes not the other way around, saying that you can't use standard mathematical processes to show what 0/0 is because it's undefined and thus is undefined. This is faulty logic Aeschylus.

 

P.S.: Tell your dog good job.[/quote'] 2 Signifys two ones. As I said I'm no good at math so I can't realy argue math with any one but it seems simple in my simpleton like capacity.

EDIT. Rex says thanks and any time. The outcome of the arguement is logical, its the question that does not make sense. Its like saying if I put one nothing on top of one nothing I get a pile of nothing.

[ydoaPs]

anything divided by 0 is undefined. end of discussion.

[RICHARDBATTY]

anything divided by 0 is undefined. end of discussion.

Aww daaad I was playing with that.

[123rock]

ok, the ratio of 1 to 0 isn't a function since it would have to equal to 0/0 as well as x/0, thus 1/0 isn't R, or i, may or may not be 0, infinity or undefined.

[Dave]

ok, the ratio of 1 to 0 isn't a function since it would have to equal to 0/0 as well as x/0, thus 1/0 isn't R, or i, may or may not be 0, infinity or undefined.

 

Any number divided by zero will yield an undefined result. There's nothing "special" about this operation, it's just undefined.

[matt grime]

Ok' date=' so if 10/5 is 2, what does the 2 signify?

It's a process of evaluation..[/quote']

 

it signifies they are in the same equivalence of elements in the localization of the real numbers, don't know if that's the same thing as an evaluation. that 0/0 is not in the real numbers is a simple matter of deduction from the axioms of a field (and 0/0 is not a member of any field where 0 is the additive identity and 1/x means the multiplicative inverse) it is not theological, it is just logical.

 

anyone who says you can't divide by zero for hand wavy arguments is explaineing something about the way we apply maths, not about the mathematics itself. at a basic level this is acceptable, but if people don't accept it you may need to cite the proper reasons.

[Guest Doron Shadmi]

x/0 result depends on the Axiomatic system which is used.

 

For example, by Monadic Mathematics, which is based on Complementary Set Theory x/0 = {__}.

 

For more details please look at: http://www.geocities.com/complementarytheory/My-first-axioms.pdf

[YT2095]

surely ANYTHING divided by Zero (or nothing) negates the division symbol/function ? and so your original quantity remains unaltered

 

 

 

same applies to Multiplication, Subtraction and Addition with Zero

[Guest Doron Shadmi]

Hi YT2095,

 

0 is not {} but the cardinal of {}, which is notated as |{}| = 0.

[123rock]

ok 1/0=2/0 because

1/0(2/2)=1/0

2/0=1/0

We are not evaluating x/0. We are just operating on the numerator and denominator which are still defined values.

[bishnu]

what are you trying to prove...its a meaningless assertion to say that 2/0=1/0

okay they are both undefined...you cant have different magnitudes of undefined...but here are someweird things i think about 0/0. It seems it has a differnet value in different ways it is used. look at the function x/x,now for continoutiy reasons you might conclude that 0/0 is 1 for that graph, 0/x for continoutiy you might assume 0/0 is 0 and for x/0 you would assume that it is undefined.

[123rock]

well I know that x/0 is undefined, and I'm not saying that 2=1 because that would be a contradiction to the whole proof that 2=1. I guess it would be logical to express 1/0 as how many times 0 goes into 1, but that obviously doesn't work for 0, since it would be R and i, so it's better to use a pure mathematical proof rather than kindergarden taught logic of how to skip steps to get the same results because they obviously don't work for x/0.

 

If the same arithmetic principles for x/0 didn't apply as they do for all numbers, i.e. x/0-x/0=0/0 then the proof that 0/0 isn't R, and i is useless, as 0/0=1. Since you can't multiply 0/0 by anything, or substitute it with anything, 0/0 will have different values yet since you couldn't substitute 0/0 by anything, by definition 0/0 wouldn't be 0/0 and thus the problem.

 

What I mean is that 1/0-1/0=0/0 is a perfectly legal operation.

[123rock]

what are you trying to prove...its a meaningless assertion to say that 2/0=1/0

okay they are both undefined...you cant have different magnitudes of undefined...but here are someweird things i think about 0/0. It seems it has a differnet value in different ways it is used. look at the function x/x' date='now for continoutiy reasons you might conclude that 0/0 is 1 for that graph, 0/x for continoutiy you might assume 0/0 is 0 and for x/0 you would assume that it is undefined.[/quote']

 

What? 0/0=1, then all of a sudden it's 0?

[YT2095]

it all looks quite perverted logic to me, Zero = 0 aka NOTHING, and any "proof" to the contrary must be flawed somehow. Hovever convincing it may seem to be on paper.

 

I`m no maths student/grad of schollar in this field, but Zero is just that, Nothing, or at best a symbol to represent "No Content" as in the number 10 = 1 TENS unit and Zero content in the ONES unit, and so on into the kazillions

[Aeschylus]

it all looks quite perverted logic to me' date=' Zero = 0 aka NOTHING, and any "proof" to the contrary must be flawed somehow. Hovever convincing it may seem to be on paper.

 

I`m no maths student/grad of schollar in this field, but Zero is just that, Nothing, or at best a symbol to represent "No Content" as in the number 10 = 1 TENS unit and Zero content in the ONES unit, and so on into the kazillions [/quote']

 

Zero is the additve identity that is for any number:

 

a + 0 = a

 

also:

 

a + (-a) = 0

[YT2095]

Zero is the additve identity that is for any number:

 

a + 0 = a

 

also:

 

a + (-a) = 0

I agree, and have no problem with your logic in the above truths

 

I don`t find them at all helpfull in my understanding of this thread though (

[Aeschylus]

I agree' date=' and have no problem with your logic in the above truths

 

I don`t find them at all helpfull in my understanding of this thread though ([/quote']

 

You see a + 0 = a is what defines zero (in a field), so using this (and the other field axioms) you can show that divison by zero is undefined.