Dividing Zero By Zero

@guigus,

guigus wrote:

Owen phil wrote:

x/y =df (the z: x = y*z).

0/0 = (the z: 0 = 0*z).

But, 0 = 0*z is true for all z. That is, 0/0 is not unique, therefore 0/0 does not exist...even though it is defined.

Similarly, 1/0 does not exist because there is no z such that 1 = 0*z.
1/0 = (the z: 1 = 0*z).

x/0 does not exist for all x.

Plain and simple: zero divided by zero is any number, which is why it is said to be undefined. Even more simple (instead of more complicated, got it?): division is a series of subtractions. So 6/2 means how many times I can subtract 2 from 6, which is 3 times. Then, 0 / 0 means how many times I can subtract zero from zero, which is 1, 5, 96, or whatever number of times I wish. That is, any number of times. That's the meaning of the term undefined: zero divided by zero is any number I wish, which makes any number the same as any other. Now it is another thing entirely to say that 0 / 0 "does not exist:" on the contrary, the quotient of 0 / 0 exists, precisely, as any result I wish.

Your view that 0/0 is equal to any number, is indeed 'simple' and it is contradictory.
(0/0=1 and 0/0=2) implies (1=2). But, (1=2) is a contradiction...therefore
(0/0=1 and 0/0=2) is false. (got it yet?)

"The" quotient of n/0 must be unique. (got it yet?)

n/0=m, is contradictory for all m and all n. Therefore, n/0 cannot exist.

2 Replies

@Owen phil,

Owen phil wrote:

Your view that 0/0 is equal to any number, is indeed 'simple' and it is contradictory.

Zero divided by zero being any number is not my view: it is a mathematical result:

1) No number multiplied by zero equals a number that is different from zero.

2) Any number multiplied by zero is identical to zero.

So zero divided by zero is any number.

As I already explained, division is a series of subtractions, so asking for the quotient of six divided by two is the same as asking how many times two can be subtracted from six until we get to zero. And if you ask how many times zero can be subtracted from zero until you get to zero, then the answer is just "as many times as you wish": it can be two, three, nine, twenty-two, or any other number of times. In other words: zero divided by zero is any number: it is indeterminate.

Owen phil wrote:

(0/0=1 and 0/0=2) implies (1=2). But, (1=2) is a contradiction...therefore
(0/0=1 and 0/0=2) is false. (got it yet?)

Of course it is a contradiction, but it is also a rigorous mathematical result. No wonder it has been a nightmare to mathematicians for centuries.

Owen phil wrote:

"The" quotient of n/0 must be unique. (got it yet?)

The fact that mathematics depends on the distinctness of each number is no guarantee that numbers themselves enjoy the privilege of inherent distinction. Your assertion is just an article of faith, not mathematical in nature, and false.

Owen phil wrote:

n/0=m, is contradictory for all m and all n. Therefore, n/0 cannot exist.

You mean mathematics cannot stand contradiction. However, it also produces this patent contradiction: zero divided by zero is any number, by which all numbers are the same, which ultimately destroys mathematics itself. No matter how painful it is to you to accept that mathematics produces such a contradiction, you must accept it in order to stay faithful to the rigor of mathematics itself.

(The division of zero by zero is painfully uncomfortable to all those who believe the absolute truth of the universe to be mathematical, since it remembers us this cannot be the case.)

0 Replies

@Owen phil,

Owen phil wrote:

(0/0=1 and 0/0=2) implies (1=2). But, (1=2) is a contradiction...therefore
(0/0=1 and 0/0=2) is false.

Let me point out the flaw in this reasoning. The assertion that "(0/0=1 and 0/0=2) implies (1=2)" is perfectly correct, as "0/0=1" and "0/0=2" are as well. And it is also perfectly correct the observation that "1=2" is a contradiction. However, that contradiction neither falsifies "0/0=1" nor "0/0=2," since it points to not a single mathematical flaw in either one of them. In fact, we have not one, but rather two contradictions here:

1) The contradiction of "1=2."
2) The contradiction between "1=2" and each one of the mathematical results that produced it, each of which alone is perfectly non-contradictory.

Indeed, 0/0=1 is in itself correct, since 1*0=0, as 0/0=2 is in itself correct, since 2*0=0: the problem resides between these two possible quotients. What we have here is a contradiction within mathematics itself -- an extremely-deep-reaching contradiction, since it makes all numbers identical to each other, hence all mathematical operations also identical to each other, which utterly destroys mathematics completely.

0 Replies

So the division of zero by zero falsify all numbers, by making any of them identical to any other. However, it can only do so if any number is different from any other number, hence true: all numbers must be true to be false -- they must be different from each other for there to be possible to divide zero by zero with a single, particular quotient -- and false to be true -- their being different from each other validates the division of zero by zero, as thus their falsity.

What is false is not zero divided by zero, but all numbers, by virtue of this division, which however depends on all numbers being different from each other, hence true: numbers must be true to be false and false to be true.

1 Reply

@guigus,

you are definitely the chosen O!

1 Reply

@guigus,

guigus wrote:

So the division of zero by zero falsify all numbers, by making any of them identical to any other. However, it can only do so if any number is different from any other number, hence true: all numbers must be true to be false -- they must be different from each other for there to be possible to divide zero by zero with a single, particular quotient -- and false to be true -- their being different from each other validates the division of zero by zero, as thus their falsity.

What is false is not zero divided by zero, but all numbers, by virtue of this division, which however depends on all numbers being different from each other, hence true: numbers must be true to be false and false to be true.

Wow! I agree with solipsister here.
Your misunderstanding of: truth, falsity, identity, numbers, division..etc. is shocking!

guigus:
"So the division of zero by zero falsify all numbers, by making any of them identical to any other."

What?

guigus:
"all numbers must be true to be false -- "

What?

guigus:
"-- their being different from each other validates the division of zero by zero, as thus their falsity."

What?

Why do you maintain that 'numbers' are true or false?
Why do you maintain that 'division' is true or false?
Why don't you understand that 'propositions' are the only things that are true or false?

I give up...your nonsense is not worthy of wasting time by replying.

Have a nice day.

2 Replies

@guigus,

guigus wrote:

contrex wrote:
In mathematics zero has 2 different roles to play. 1. To provide the symbol for the empty set. 2. To serve as a place holder symbol in a positional number system.

It is not a "number".

You are definitely not a mathematician. ....

This is hilarious! You obviously wouldn't know a mathematician if you tripped over one. Nor would you know a philosopher, btw, having just "discovered" a paradox mentioned by Epimenides the Cretan 25 centuries ago.

On L'Hopital's rule (really discovered by Bernoulli) you're only 3 centuries late - maybe you should start with pictures Smile

http://mathworld.wolfram.com/images/eps-gif/LHospitalsRule2_1000.gif

Quote:

While both f(x) and g(x) approach infinity as x->infinity, the limit of the ratio is bounded inside the interval [1/e,e], while the limit of f^'(x)/g^'(x) approaches 0.

http://mathworld.wolfram.com/LHospitalsRule.html

3 Replies

@Owen phil,

Owen phil wrote:

...I give up...your nonsense is not worthy of wasting time by replying....

The idea is to refer him to some elementary source of apparent paradoxes, so he spares us additional nonsense by first looking up if his next great "discovery" was already noted by someone else - usually a long, long time ago, judging by his level of ignorance. This is a list of 275 such paradoxes:
http://search.wolfram.com/?query=mathematical%20paradoxes&collection=tryonall
If the link can't be accessed directly, go to wolfram.com, search for "mathematical paradoxes" on "all sites". Good luck.

1 Reply

@solipsister,

solipsister wrote:

you are definitely the chosen O!

You have been watching Matrix too much.

0 Replies

@Owen phil,

Owen phil wrote:

guigus wrote:

So the division of zero by zero falsify all numbers, by making any of them identical to any other. However, it can only do so if any number is different from any other number, hence true: all numbers must be true to be false -- they must be different from each other for there to be possible to divide zero by zero with a single, particular quotient -- and false to be true -- their being different from each other validates the division of zero by zero, as thus their falsity.

What is false is not zero divided by zero, but all numbers, by virtue of this division, which however depends on all numbers being different from each other, hence true: numbers must be true to be false and false to be true.

Wow! I agree with solipsister here.
Your misunderstanding of: truth, falsity, identity, numbers, division..etc. is shocking!

Let us see how is that...

Owen phil wrote:

guigus wrote:

"So the division of zero by zero falsify all numbers, by making any of them identical to any other."

What?

What what?

Owen phil wrote:

guigus wrote:

"all numbers must be true to be false -- "

What?

What what?

Owen phil wrote:

guigus wrote:

"-- their being different from each other validates the division of zero by zero, as thus their falsity."

What?

What what?

Owen phil wrote:

Why do you maintain that 'numbers' are true or false?

A number is a class of similar classes (two classes are similar if they have a one-to-one relationship between their elements). For example, the class of all classes with two elements is the number two. According to this, if two different numbers are identical, then they violate the definition of a number, hence are false numbers. This is what a false number means.

Owen phil wrote:

Why do you maintain that 'division' is true or false?

I did not mention the falsity of mathematical operations, just the falsity of numbers, although all numbers being identical to each other cause all mathematical operations also to be identical to each other, hence false (a division that is rather a multiplication is no longer a division, hence is false).

Owen phil wrote:

Why don't you understand that 'propositions' are the only things that are true or false?

I understand that propositions can be true or false only by referring to something true or false, respectively.

Owen phil wrote:

I give up...your nonsense is not worthy of wasting time by replying.

Then why are you replying?

Owen phil wrote:

Have a nice day.

You too.

0 Replies

@High Seas,

High Seas wrote:

guigus wrote:

contrex wrote:
In mathematics zero has 2 different roles to play. 1. To provide the symbol for the empty set. 2. To serve as a place holder symbol in a positional number system.

It is not a "number".

You are definitely not a mathematician. ....

This is hilarious! You obviously wouldn't know a mathematician if you tripped over one. Nor would you know a philosopher, btw, having just "discovered" a paradox mentioned by Epimenides the Cretan 25 centuries ago.

On L'Hopital's rule (really discovered by Bernoulli) you're only 3 centuries late - maybe you should start with pictures

Quote:
While both f(x) and g(x) approach infinity as x->infinity, the limit of the ratio is bounded inside the interval [1/e,e], while the limit of f^'(x)/g^'(x) approaches 0.

http://mathworld.wolfram.com/LHospitalsRule.html

Sorry, we are not talking about the division between two functions, but about the division of zero by zero. Zero is not a function: it is a number.

0 Replies

@High Seas,

High Seas wrote:

Owen phil wrote:
...I give up...your nonsense is not worthy of wasting time by replying....

The idea is to refer him to some elementary source of apparent paradoxes, so he spares us additional nonsense by first looking up if his next great "discovery" was already noted by someone else - usually a long, long time ago, judging by his level of ignorance. This is a list of 275 such paradoxes:
http://search.wolfram.com/?query=mathematical%20paradoxes&collection=tryonall
If the link can't be accessed directly, go to wolfram.com, search for "mathematical paradoxes" on "all sites". Good luck.

The division of zero by zero is not a mathematical paradox, it is an indeterminate mathematical operation. What I am showing is that, by making all numbers identical to each other (which it recognizably does), it makes numbers false, as also that it can do that only as long as numbers are different from each other, hence true. This is not a mathematical paradox, but a philosophical contradiction: the division of zero by zero is where mathematics ceases to be mathematics and becomes something else.

1 Reply

A summary:

1. The division of zero by zero is any number, since:
1.1. Any number multiplied by zero results in zero.
1.2. Division is defined as the inverse of multiplication.

2. By being any number, the quotient of zero divided by zero makes any number the same as any other number, hence a false number, since true numbers cannot be both different and identical to each other.

3. The division of zero by zero depends on true numbers for its formulation as resulting in any particular number, so numbers must be true to be false.

4. Since the mathematical definition of division must validate any particular quotient of the division of zero by zero, numbers must be false to be true.

0 Replies

The division of zero by zero is like the Liar paradox -- both manifest my first philosophical category, Variability (http://able2know.org/topic/160606-3#post-4349462):

If any truth were untrue, then it would not be a truth: every truth must be true. And yet, since the truth of a being is a true being, for any truth to be true it must have itself as a truth, which must be different from it. So its truth must be different from itself, hence untrue. But if the truth of a truth is untrue, then the truth it makes true is also untrue: any truth becomes its falsity, which makes every truth variable. Conversely, any falsehood must have itself as a true falsehood, by which it is also a truth. Yet still, since any truth must be false, the truth of no falsehood has any truth: any falsehood becomes the truth it falsifies, which makes every falsehood also variable. Finally, since any truth must be false and its falsity must be this truth it falsifies, if any being is true, then it must be false, and if it is false, then it must be true. Even though any being is either true or false, hence either a being, once true, or nothing, once false: as it varies between true and false, its variability between a being and nothing becomes all being.

1 Reply

@guigus,

If you're too lazy to look at the ratio of the 2 equations I posted - which really is a division of 0 by 0 within the interval noted, as is obvious from the graph - and too lazy to read the posts of the other people here, at least try to keep this simple fact in mind: Our distant ancestor who came up with the wheel was a genius; any of us who wastes his time - and the time of others - in an effort to re-invent the wheel is a fool.

Do you really think you've come up with anything original on this thread? The questions you raise are as old as mathematics and have been answered many times over the centuries. Try reading a book on the subject before posting any more confused statements; this is a very good one:

http://g-ecx.images-amazon.com/images/G/01/ciu/b5/0d/8a52603809a0a7fccfb48110.L._SL500_AA300_.jpg

1 Reply

@guigus,

guigus wrote:

The division of zero by zero is like the Liar paradox -- both manifest my first philosophical category, Variability (http://able2know.org/topic/160606-3#post-4349462):
.....

I see my friend Joe from Chicago already attempted to explain elementary logic to you without success. Please therefore forget about answering any of my posts on mathematics - they require some elementary reasoning capacity which you lack. Maybe watching Bonzo here will show you the way:

http://www.wired.com/images_blogs/wiredscience/images/2007/12/03/mathchimp.jpg

http://www.wired.com/wiredscience/2007/12/are-you-smarter/

1 Reply

@High Seas,

High Seas wrote:

If you're too lazy to look at the ratio of the 2 equations I posted - which really is a division of 0 by 0 within the interval noted, as is obvious from the graph - and too lazy to read the posts of the other people here, at least try to keep this simple fact in mind: Our distant ancestor who came up with the wheel was a genius; any of us who wastes his time - and the time of others - in an effort to re-invent the wheel is a fool.

Do you really think you've come up with anything original on this thread? The questions you raise are as old as mathematics and have been answered many times over the centuries. Try reading a book on the subject before posting any more confused statements; this is a very good one:

First, let me thank you for the complements. Second, and again, I am talking about zero divided by zero, and not about an infinitesimal divided by an infinitesimal. Zero is zero, nothing, zip. You can go to http://mathworld.wolfram.com/DivisionbyZero.html so there you can read:

Quote:

Although division by zero is not defined for reals, limits involving division by a real quantity which approaches zero may in fact be well-defined.

I am not talking about dividing something that approaches zero by something that approaches zero: I am talking about dividing zero itself by zero itself.

0 Replies

@High Seas,

High Seas wrote:

guigus wrote:

The division of zero by zero is like the Liar paradox -- both manifest my first philosophical category, Variability (http://able2know.org/topic/160606-3#post-4349462):
.....

I see my friend Joe from Chicago already attempted to explain elementary logic to you without success. Please therefore forget about answering any of my posts on mathematics - they require some elementary reasoning capacity which you lack. Maybe watching Bonzo here will show you the way:

http://www.wired.com/wiredscience/2007/12/are-you-smarter/

Unfortunately, Joe from Chicago did not try to teach me anything that I didn't already knew (neither was he willing to learn anything).

So then, are you going to use your administrator privileges to block me from answering to your posts? Aren't you going to be fired for that? Never mind, I will just ignore your advice, as also your lovely "jokes," and keep answering to any posts I wish -- I hope you don't mind. Let me just remind you that your post above lacks any reference to my reasoning whatsoever, or any proper reasoning or argumentation: offenses are no kind of reasoning -- which suggests you to be the one who lacks any reasoning capacity.

1 Reply

Let us go by small steps. Please point out a flaw in the following reasoning:

Quote:

The division of zero by zero is any number, since:
1. Any number multiplied by zero results in zero.
2. Division is defined as the inverse of multiplication.

0 Replies

@guigus,

guigus wrote:

Unfortunately, Joe from Chicago did not try to teach me anything that I didn't already knew (neither was he willing to learn anything).

So then, are you going to use your administrator privileges to block me from answering to your posts? ...

Your "reality" exists only in your imagination. For instance: what is your source for thinking I have administrator privileges on this site? Finally: it's not only Joe who refused to "learn" from your magical thinking; it's also I who asked you to please not address me any longer, I won't bother replying.

1 Reply

Dividing Zero By Zero

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