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0 divided by 0


123rock

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123Rock's biggest problem is that you cant look at a rational number, ie 1/0 as having two independent quantities of 1 and 0 and then trying to compare that to 2/0 or 2 and 0.

 

Rational numbers are used to exactly express a quotiant (sp?) of a real number.

 

1/0 has no value because (useing the def'n of divisor) there is no q such that 1 = q*0, and you cant compare something that lacks a value.

 

Any number divided by zero does no exist because there isnt any number, a, such that 0|a so your comparing nothing when you write '1/0=2/0'.

 

Hence 1/0=2/0 is meaningless

 

edit - also you need to justify several of the algebraic steps in your proof

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I never said that you have to evaluate 1/0, or x/0. While still a fraction, x/0 applies to the same laws of arithmetic as all other fractions.

 

0/0=x and x * 0=0 are not the same equations because multiplying each side by zero in 0/0 (0)=x *0 implies that 0/0 is 1.

 

If 0/0=0/0, which would be the only way that it can be undefined, otherwise 0/0 can equal whatever we want it to equal, then 1-1/0=0/0

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I never said that you have to evaluate 1/0' date=' or x/0. While still a fraction, x/0 applies to the same laws of arithmetic as all other fractions.

 

0/0=x and x * 0=0 are not the same equations because multiplying each side by zero in 0/0 (0)=x *0 implies that 0/0 is 1.

 

If 0/0=0/0, which would be the only way that it can be undefined, otherwise 0/0 can equal whatever we want it to equal, then 1-1/0=0/0[/quote']

 

you could put 1, 7, or 43 billion in for x, and it would still be undefined.

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fraction, x/0 applies to the same laws of arithmetic as all other fractions.

 

you cannot use arithmetic laws on something that does not exist. x/0 is not a fraction because fractions have a quantity and can therefore be compared. Do you see what i'm saying? It has no value because it does not exist, there is no quantity so even though you can write in a fraction form it is still not a fraction.

 

Saying x/0 is a fraction means that you are expressing some number, a, whereby 0*x=a. Remember, fractions are rational numbers which means the denominator and the numerator have a ratio equating them. Look over divisior rules as they apply number theory and the def'n of rational numbers....or just look at my previous post.

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Guest jaydeschizo

err... afaik using normal algabraic(sp?) mathematics you cant divide by 0 in any case, and any way you made a mess up in your example:

a = b

a^2 = b^2

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

(a+b)(a-b) = b(a-b) here you divide both sides by a-b, but if a=b a-b is always 0, thus you say that 0/0 = 1 because you: (a+b)(a-b)/(a-b)=b(a-b) => (a+b)*1 = b*1

a+b=b

b+b=b

2b=b

2=1;

 

 

so to cut the cake: to prove that 0/0 doesnt exist you asume that 0/0 = 1 thats useless, in calulating with 0 u can only use limit cases... lim 1/0 = infinite... lim 0/0 = 1 is afaik unproven but most logical... but ill have to ask my teachers to be sure...

 

maybe this has already been said, but my scientific english is a disaster anyway

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i think its easier to prove x/0 doesnt exist using number theory, simply put

 

1. x/0 => there exists q, an element of R, such that x = q*0, x!=0

2. since there is no such q x/0 does not exist

3. for x=0, 0/0 is trivial for 123's example and indeed for anything else

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i think its easier to prove x/0 doesnt exist using number theory' date=' simply put

 

1. x/0 => there exists q, an element of R, such that x = q*0, x!=0

2. since there is no such q x/0 does not exist

3. for x=0, 0/0 is trivial for 123's example and indeed for anything else[/quote']

 

if x/0=q, x*q=0 is not a valid reevaluation, because you are multiplying each side by 0, and thus assuming that 0/0 is 1.

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err... afaik using normal algabraic(sp?) mathematics you cant divide by 0 in any case' date=' and any way you made a mess up in your example:

a = b

a^2 = b^2

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

(a+b)(a-b) = b(a-b) here you divide both sides by a-b, but if a=b a-b is always 0, thus you say that 0/0 = 1 because you: (a+b)(a-b)/(a-b)=b(a-b) => (a+b)*1 = b*1

a+b=b

b+b=b

2b=b

2=1;

 

 

so to cut the cake: to prove that 0/0 doesnt exist you asume that 0/0 = 1 thats useless, in calulating with 0 u can only use limit cases... lim 1/0 = infinite... lim 0/0 = 1 is afaik unproven but most logical... but ill have to ask my teachers to be sure...

 

maybe this has already been said, but my scientific english is a disaster anyway[/quote']

 

That's only true if you evaluate x/0.

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you cannot use arithmetic laws on something that does not exist. x/0 is not a fraction because fractions have a quantity and can therefore be compared. Do you see what i'm saying? It has no value because it does not exist' date=' there is no quantity so even though you can write in a fraction form it is still not a fraction.

 

Saying x/0 is a fraction means that you are expressing some number, a, whereby 0*x=a. Remember, fractions are rational numbers which means the denominator and the numerator have a ratio equating them. Look over divisior rules as they apply number theory and the def'n of rational numbers....or just look at my previous post.[/quote']

 

Everything has to be proven, except of course axioms. It was proven by arithmetic laws that x/0 does not exist, but these same arithmetic laws cannot be used when we are trying to get a different fraction?

 

is 1-1/0 not equal to 0/0? Yes, because 1-1=0. 0/0(2/2)=0/0; 0/0(x)=0/0

 

Again, if arithmetic laws could not be used on 0/0, then 0/0 does not equal 0/0, which is not something that the axiom x=x accepts, or 1=1

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if x/0=q, x*q=0 is not a valid reevaluation, because you are multiplying each side by 0, and thus assuming that 0/0 is 1.

 

thats not what i wrote, look again...i am useing number theory, the def'n of divisor in specific....i proved that x/0 does not exist and because it does not exist it cannot be compared to other expressions nor is it a fraction.

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is 1-1/0 not equal to 0/0? Yes, because 1-1=0. 0/0(2/2)=0/0; 0/0(x)=0/0

 

The initial statement is non-logical since 0/0 is undefined. How are you supposed to manipulate something which has not been defined?

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err... afaik using normal algabraic(sp?) mathematics you cant divide by 0 in any case' date=' and any way you made a mess up in your example:

a = b

a^2 = b^2

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

(a+b)(a-b) = b(a-b) here you divide both sides by a-b, but if a=b a-b is always 0, thus you say that 0/0 = 1 because you: (a+b)(a-b)/(a-b)=b(a-b) => (a+b)*1 = b*1

a+b=b

b+b=b

2b=b

2=1;

 

 

so to cut the cake: to prove that 0/0 doesnt exist you asume that 0/0 = 1 thats useless, in calulating with 0 u can only use limit cases... lim 1/0 = infinite... lim 0/0 = 1 is afaik unproven but most logical... but ill have to ask my teachers to be sure...

 

maybe this has already been said, but my scientific english is a disaster anyway[/quote']

 

your "proof" is over before it starts

 

if a=b, then [math]a^2-b^2=0[/math]

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  • 2 weeks later...
your "proof" is over before it starts

 

if a=b' date=' then [math']a^2-b^2=0[/math]

 

That's the disproof that 0/0=1. If 0/0 doesn't equal 1, then 0/0(x) does not equal x, which is true for all numbers except for x=0. I never said that was a proof. Why not take me seriously Dave? The simple arithmetic is right there.

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The initial statement is non-logical since 0/0 is undefined. How are you supposed to manipulate something which has not been defined?

 

Something has to be proven to be undefined before you can say it is. Besides, it's not a relatively hard question to imagine, of how many times 0 fits into 0, or how many monkeys can put zero bananas into zero baskets. I guess in that case it's undefined, but tautology is not mathematics, and before you can state that something is undefined solely based on a mathematical dictionary definition, you have to show it.

 

Edit: Also, if you state that 0/0=0 and no other number, it leads to absolutely no contradictions whatsoever

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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, 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.

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Something has to be proven to be undefined before you can say it is. Besides, it's not a relatively hard question to imagine, of how many times 0 fits into 0, or how many monkeys can put zero bananas into zero baskets. I guess in that case it's undefined, but tautology is not mathematics, and before you can state that something is undefined solely based on a mathematical dictionary definition, you have to show it.

Definitions are arbitrary. You do not "prove" definitions, 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.

 

Edit: Also, if you state that 0/0=0 and no other number, it leads to absolutely no contradictions whatsoever

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

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