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Atlas3

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- #1

Atlas3

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- #2

member 587159

- #3

Atlas3

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- #4

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What does "if you have a zero, and zero goes into zero, you have exactly one zero" mean?

- #5

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A proof of what? That if you perform a meaningless operation that you can pretend that the answer is valid?... those two examples are a proof...

- #6

Atlas3

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@Atlas3, you are, in military parlance, pissing up a rope.

- #8

fresh_42

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Zero isn't part of the multiplicative group of our ring. Hence the question about division by zero is as meaningful as whether there are unicorns and to which species they belong. It is not "forbidden", it is simply not existent. Now one can ask, if we can extend the multiplicative group by the zero of the additive group, to which the answer is no, as we will run into contradictions:

$$

0^{-1}\cdot 0 \stackrel{(1)}{=} 1 \text{ and } 0^{-1}\cdot 0 \stackrel{(2)}{=}0^{-1}\cdot (1+(-1))\stackrel{(3)}{=}0^{-1}\cdot 1 + (- 0^{-1}\cdot 1)\stackrel{(4)}{=}0

$$

- definition of the multiplicative inverse
- definition of the additive neutral
- distribution law
- definition of the additive inverse

- #9

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I think the argument is as follows:

Because ##0 = 1 \times 0## then ##\frac{0}{0} = 1##

One problem with this argument is that we also have:

Because ##0 = 2 \times 0## then ##\frac{0}{0} = 2##

Etc.

- #10

symbolipoint

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No. That division process goes on forever, with no stopping point. Division By Zero is meaningless and is undefined.

- #11

Atlas3

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Thank you for the better topic Title. I appreciate the moderation.

- #12

Mark44

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This is exactly why the expression ##\frac 0 0## is meaningless. We in mathematics are picky about arithmetic -- we like any division problem to have only one answer.I think the argument is as follows:

Because ##0 = 1 \times 0## then ##\frac{0}{0} = 1##

One problem with this argument is that we also have:

Because ##0 = 2 \times 0## then ##\frac{0}{0} = 2##

Etc.

- #13

Atlas3

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- #14

fresh_42

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##a \cdot 0 = 0## is due to the distributive law in a ring. It

- #15

Atlas3

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These kind of questions must have bored the crap out of the posters/moderators with such strange notions. However, I did ask a simple thing. Is it useful? Not one comment to the question. I have been schooled instead. I think the title is useful if you knew where to put it. I also received replies stating the state of the nature of the question. Comments followed up by phrases of military parlance of urinating in a vertical fashion are amusing. I suppose it is hard to have an option about things that were left undefined since the 1500's. Thanks to those that took the time to distribute the proofs. It read a bit condescending but I can live with it. Thank you.This is exactly why the expression ##\frac 0 0## is meaningless. We in mathematics are picky about arithmetic -- we like any division problem to have only one answer.

- #16

jbriggs444

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It is all right for many different expressions to all yield the same result. A bit inevitable, perhaps. There are so many expressions and so few results.What about the converse? 2 x 0 = 0 3 x 0 = 0 has many many problems and the same answer.

It is not all right for one expression to yield many different results. We normally require each expression [with no free variables] that produces a result must produce the same result every time it is evaluated.

- #17

fresh_42

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I think you have got more answers than the question deserved, esp. as there are already dozens of such threads which can easily be found by a forums search. The short answer is: ##\dfrac{0}{0} =1## is not useful, because it will result in logical contradictions. Instead you have been explained why these contradictions will arise. I bet you would had been equally unsatisfied by a simple "**No!**" which is **a complete answer** and barely better than *not one comment to the question*, that wouldn't had *schooled you*, and didn't contain *phrases of military parlance.* Furthermore, this

I consider your criticisms unfair, because - as I pointed out - seemingly there will be no answer which would have pleased you. But I will respect your wish: next time I will try to answer your questions by a simple yes, no, correct or false. It will save me a lot of time, I only wished you would had said this right from the beginning.

The question itself is as if you had asked: "What if I fly a plane under water, will it increase gas mileage?" Please ask yourself how you would have answered to such a question.

doesn't make sense either, as there is no such option.I suppose it is hard to have an option about things that were left undefined since the 1500's.

I consider your criticisms unfair, because - as I pointed out - seemingly there will be no answer which would have pleased you. But I will respect your wish: next time I will try to answer your questions by a simple yes, no, correct or false. It will save me a lot of time, I only wished you would had said this right from the beginning.

The question itself is as if you had asked: "What if I fly a plane under water, will it increase gas mileage?" Please ask yourself how you would have answered to such a question.

Last edited by a moderator:

- #18

Mark44

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The category is neither number theory nor discrete mathematics -- it's just plain old arithmetic. And no, it's not true that 0/0 = 1, for reasons already given.I could not find a proper group for number theory in this forum. I think from what I know of Discrete Mathematics, it is a truth.

Yes, and it has been answered.However, I did ask a simple thing.

Not at all, as has been amply pointed out in the responses.Is it useful?

This is post #18 -- you have received lots of good responses.Not one comment to the question.

Indeed.think you have got more answers than the question deserved

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