Is 0 divided by 0 equal to any number?

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AI Thread Summary
The discussion centers around the mathematical concepts of division by zero and the equality of repeating decimals, specifically 0.999... and 1. Participants argue that 0 divided by 0 can theoretically equal any number, as multiplying zero by any number results in zero. They also provide various proofs and manipulations to demonstrate that 0.999... is equal to 1, using limits and geometric series. However, there is contention regarding the validity of these proofs, with some participants questioning the legitimacy of dividing by zero and the implications of manipulating infinite decimals. The conversation highlights the complexities and misunderstandings surrounding these foundational mathematical concepts.
  • #51
Organic,
Please restrict your posts to the topic at hand.
 
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  • #52
Hi Integral,

My previous post fits exactly to subject of this thread.

Please read all of it and see for yourself.
 
  • #53
Organic,
We are all talking about the Real numbers, you are talking about the organic numbers, you are off topic. Please take your garbage back to theory development where it belongs.
 
  • #54
ShawnD said:
That's sort of how the fraction representation works. 1/3 x 3 = 1.
I know but organic seems to be struggling with the concept of converting decimals into fractions when they recur.


matt grime said:
In base 3 one has other problems such as .22222222... =1

Forget decimals, or any other system of representation like that. Just operate with the definitions of the real numbers. That's how mathematics works, practically.
Well convert 0.111111... to decimal to get 0.5, multiply by 2 to get 1 :-p
 
  • #55
O.K, merging what I put earlier with my work on base numbers.

Lets say we are working in base b, and let's us say that x is a number in base b and that x is a natural number. n is a digit in the decimal number x such that n = b -1.

So if:
x = 0.n = 1 - 10^{-1} = \frac{b-1}{b}

Or if:

x = 0.nnnnn = 1 - 10^{-5} = \frac{b^5-1}{b^5}

If n occurs p number of times:

x = 0.nnnnnnnn... = 1 - 10^{-p} = \frac{b^p-1}{b^p}

If n occurs an infinite number of times:

x = 0.nnnnnnn... = \lim _{p \rightarrow \infty} 1 - 10^{-p} = 1
Or x = \lim _{p \rightarrow \infty} \frac{b^p-1}{b^p} = \lim _{p \rightarrow \infty} (b^{-p})(b^{p}) - 1(b^{-p}) = \lim _{p \rightarrow \infty} 1 - b^{-p} = 1

Now your equation x - x: x - x = x(1-1) = x*0 = 0 As long as x has a numerical value regardless of how it is expressed.
 
  • #56
Don't think you're going to get any sympathy there, Organic, especially given the God-awful choice of font, colour, and spelling. You are posting off topic, something we're probably all guilty of at some point admittedly, but you are also posting utter tripe that has no place in a mathematics thread. I'm amazed that, as a moderator, Integral didn't just delete your incoherent rubbish. You aren't some innocent posting a silly question and being dismissed out of hand. You are a recidivistic poster whose answers are tantamount to vandalization and are entirely unmathematical and plain wrong, yet you keep making them.
 
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  • #57
Well, if it were me instead of integral, I certainly wouldn't have used the word "garbage"!

(The word I would have used would have gotten all "knocked off the air"!)
 
  • #58
Matt and HallsofIvy,

I invite you to show your skills and prove that my ideas have nothing to do with Math language development.

here it is again:

Let us take the circle's equation: (x-h)^2 + (y-k) = r^2
http://www.xavierhs.org/departments/Mathematics/PreCal/Conics/conics.htm

solid is a "one piece" state

r=radius

h=x center

k=y center

But the interesting variables are x and y, where x is the entire x-axis and y is the entire y-axis.

x-axis or y-axis are "actual form of infinity" as we can see in this model:
http://www.geocities.com/complementarytheory/RiemannsLimits.pdf

To construct the circle we have to break the solid states of both x-axis and y-axis and define a sequence of unique pairs of R members, which are used as x,y coordinates of the circle.

The point here is that we have no R members before we break the solid state of x-axis and y-axis, and only after we break them we get R members.

The same state is an information form of, for example, 0.9999999...

It cannot be in both states of finite and infinite sequence of non-zero values upon infinitely many scales.

Therefore there is a XOR condition between 1.0 and 0.9999... exactly as there is a XOR condition between a solid ("one piece") state and a broken state.
 
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  • #59
We only need to show that what you wrote doesn't have anything to do with the question as asked.

Item 1. Your bloody post which has nothing to do with the question "why does 0.9999..=1?"

Item 2. Your bloody post which has nothing to do with the question "why does 0.9999..=1?"

Strictly speaking they are the same, but I thought it important enough to mention twice. This is a question about the real numbers. Do you know what they are? Evidently not judging by your bilge of a repost.

Edit: deleted silly thing about bandwidth. Still think you're a moron though.
 
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  • #60
Can some moderator please lock this thread? I think it has been adequately answered as to why there is nothing reomtely controversial about 0.9999.. being the same as 1, and all mathematical issues arising therefrom seem to have been sorted.
 
  • #61
Can some moderator please lock this thread? I think it has been adequately answered as to why there is nothing reomtely controversial about 0.9999.. being the same as 1, and all mathematical issues arising therefrom seem to have been sorted.
Matt my dear,

Is this all you can do?
 
  • #62
It is very hard to explain to someone why their post has nothing to do with the question in hand if they refuse to accept the bleeding obvious as the last post on page 4 attempts to demonstrate. No one, not even someone with a first in mathematics can see the slightest bearing your ill-conceived opinion has on the original question, idiot boy.
 
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  • #63
Matt,

Well, you have a PHD title in Math so please use it, I am waiting to you.
 
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  • #64
Waiting for him to do what? The only thing a person with a dozen "PHD titles" in math could do was explain exactly what he already has.
 
  • #65
I don't have PhD in mathematics. I am doing one; come back in October.
 
  • #66
Yeah this is getting a little tiring Organic, it has been proved over and over again why 0.9999... = 1 and you have not managed to disprove it or provide a counter example in terms of real numbers.
 
  • #67
HallsofIvy,

I invite you to show your skills and prove that my ideas have nothing to do with Math language development.

here it is again:

Let us take the circle's equation: (x-h)^2 + (y-k) = r^2
http://www.xavierhs.org/departments/Mathematics/PreCal/Conics/conics.htm

solid is a "one piece" state

r=radius

h=x center

k=y center

But the interesting variables are x and y, where x is the entire x-axis and y is the entire y-axis.

x-axis or y-axis are "actual form of infinity" as we can see in this model:
http://www.geocities.com/complementarytheory/RiemannsLimits.pdf

To construct the circle we have to break the solid states of both x-axis and y-axis and define a sequence of unique pairs of R members, which are used as x,y coordinates of the circle.

The point here is that we have no R members before we break the solid state of x-axis and y-axis, and only after we break them we get R members.

The same state is an information form of, for example, 0.9999999...

It cannot be in both states of finite and infinite sequence of non-zero values upon infinitely many scales.

Therefore there is a XOR condition between 1.0 and 0.9999... exactly as there is a XOR condition between a solid ("one piece") state and a broken state.
 
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  • #68
Hi Zurtex,

Please prove that I am not talking about R members.
 
  • #69
The point is that this has nothing to do with the question that was asked. The decimals in your post could be replaced with anyting and it would still make as little sense, therefore you've not actually done anything remotely interesting or applicable. Not to mention the mistakes in the post anyway such as asserting that a variable IS the x-axis. No it isn't. It's a variable, which may take values in the set of real numbers, which isn't the same thing. 'Breaking the solid states' is a meaningless sentence, it doesn't even have a valid metaphorical interpretation, the real numbers aren't eggs. The idea of being an actual infinity is vague and fluffy and garbage that has nothing to do with the question in hand (I could rewrite it so that there were only a countably infinite number of points involved, and we know you get confused then.

Oh, and you're evidently not using any definition of the real numbers that makes sense to the rest of us. You do understand that they are, as mathematical objects in which one does analysis the completion of the rationals? In non-standard analysis they aren't, and don't even begin to think about the p-adics.
 
  • #70
I'm only really starting at mathematics, I certainly am not studying PhD in fact I am only at A level (doing maths equivalent to 1st year degree). But from my understanding of mathematics and this includes my extra research as I find the whole area fascinating you have proved nothing and you make no sense in more than one sentence.
 
  • #71
Organic said:
Hi Zurtex,

Please prove that I am not talking about R members.

He (or she) doesn't have to do anything of the sort. It is up to you to demonstrate that you are using the Real Numbers correctly, which you evidently aren't. SImple way to show you are would be to explain clearly if you think 0.99.. and 1 are the same real number. A simple, yes they are, or no they're not. It appears that you're saying they're different, but given your misuse of XOR it's hard to tell.
 
  • #72
Ok Matt,
...Not to mention the mistakes in the post anyway such as asserting that a variable IS the x-axis. No it isn't.

All you proved is you cannot go beyond the convetional point of view of Math language.

Dear Zurtex,

Please reply more to the point, prove that my point of view is an illegal one from Math languge point of view.
 
  • #73
Organic said:
Ok Matt,


All you proved is you cannot go beyond the convetional point of view of Math language.

Dear Zurtex,

Please reply more to the point, prove that my point of view is an illegal one from Math languge point of view.

Well seemingly this means you are talking in a slightly different maths language to the rest of us. Care to explain what this language is and how it works? In maths you must rigorously prove something, not write something down and wait for somebody to disprove it and if they point out a seeming mistake just say they have no idea what they are talking about.

Please by all means explain to us simpletons who do not understand your maths why exactly it is correct and how it proves that 0.999.. and 1 can be different numbers under mysterious and strange circumstances.
 
  • #74
The point is that your language is not the language in which one does mathematics if one wants to be understood, or say things that are not stupid and wrong. Remember if you go to a foreign country it might be advisable to learn to speak their language, and a very good idea not to tell them they are speaking it incorrectly and yours is the correct way of doing it. It smacks of arrogance and crass stupidity.

If any moderator wants to delete all these pointless posts please do so, I won't bat an eyelid.
 
  • #75
Matt,

Again you don't prove anything about my point of view.

misuse of XOR it's hard to tell.

Please show where is the mistake of using XOR to show that one case prevents the other?
 
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  • #76
Your mistake here is to use badly constructed sentences such as that which uses a mathematical symbol in its centre when it isn't what you ought to write . Here's a simple one: are 0.999... and 1 different real numbers (where we are using decimal expansions)?
 
  • #77
Matt,

The difference between my view and your view is this:

Matt's view: A one eye view where a number is a "quantity-only" information form.

Organics view: Two eyes view where a number is at least structural/quantitative information form.

Organic can see Matt's one eye view.

Matt cannot see Organic's two eyes view.

In one eye view 0.999... = 1
 
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  • #78
No, Organic, the point is that BY DEFINITION 1 and 0.999... (when considered as base 10 expansions) are the same real number (didn't you read the bit about non-standard analysis? not that I'd expect you to understand), as has been proven in this thread MANY times. That you cannot seem to understand this is because you are an ill-informed mathematical-illiterate who isnt' prepared to learn what is necessary to talk about mathematics. Nor are you prepared to answer simple questions. Now someone please close this thread!
 
  • #79
Matt,

I am talking about 2Iview.

Non-standard analysis of A.Robinson and standard analysis of Epsilon-Delta Definition are both 1Iview.
 
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  • #80
Organic,
As long as you have been posting to these forums you should know and understand that the place for your ideas is in the Theory Development forum. I will request once again that you please refrain from posting your non standard concepts in the Math forums. This is the place where a student can come to learn the STANDARD ACCEPTED Mathematics. Your contributions only serve to confuse those who are uncertain.

I have requested that the Math mentors lock this thread. I have no special privileges here or it would have been locked already. Preferably would be to shovel out Organics posts and let Matt and I finish the perfectly good conversation we were having.
 
  • #81
ok if

.\bar{9}= 1

then

\lim_{n\rightarrow \infty} .\bar{9}^n =1

correct?
 
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  • #82
JonF said:
ok if

.\bar{9}= 1

then

\lim_{n\rightarrow \infty} .\bar{9}^n =1

correct?

No, because .999... does not equal limn->∞0.9n
 
  • #83
doesn't
\lim_{n\rightarrow \infty} 1^n =1
 
  • #84
JonF said:
ok if

.\bar{9}= 1

then

\lim_{n\rightarrow \infty} .\bar{9}^n =1

correct?
You need an n on the RHS of the second expression for the limit to have any meaning.

it is correct that

\lim_{N \rightarrow \infty}9 \Sigma_{n=0}^N .1^{-n}=1

Edit: Opps, I some how missed your superscript n on my first go round.
 
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  • #85
I had granted Integral and Matt's request that the thread be locked, but as I was doing it people were still posting. Make up your mind, guys! :biggrin:

JonF said:
doesn't
\lim_{n\rightarrow \infty} 1^n =1

Whoops, I hadn't noticed the bar above the 9 in the limit.
 
  • #86
I’m just now about ½ way through my first semester of calculus. I have no clue what an RHS is. What I’m trying to say is:

Isn’t it true that .9999…. to the power of infinity = 1


I’m not trying to troll or bait here, it’s just that 1 = .9999… goes against all the math intuition I’ve have so far.
 
  • #87
Sorry just got home from school and have been thinking about this problem all day... Is it ok if they finish explaining it to me really quick?
 
  • #88
JonF said:
I’m just now about ½ way through my first semester of calculus. I have no clue what an RHS is.

RHS=Right Hand Side

I'll let Integral continue.
 
  • #89
Tom, and others, I started an answer to some of JonF's question in a new thread if you want to clean it up a little. Though I was doing it from memory in case this should get locked, so it might not be an accurate recollection of the question
 
  • #90
nope...

A mathematical issue about this arose when I tried to find a constructive bijection between IR^1 and IR^2 (or IR^k for that matter) (how do I get LaTeX here?). My idea is best illustrated with the following example:

f: 573491.14387469712 |--> (741.48491, 539.137672)
f inverse: (741.48491, 539.137672) |--> 573491.14387469712

The only problem is that certain (pairs of) real numbers map to the same 2-space point.

.0391949195999296959... (digits from pi interspersed with 9's)

and .1301040105090206050...

both map to (.314159265..., .1)

So we don't have a bijection at all.

BUT, we do get a surjective function from IR^1 to IR^2 which is INTERESTING, in that we can think of a different surjection from IR^2 to IR^1, and the combination of these is all we need to prove that A BIJECTION EXISTS.

This double representation of the same real actually CAN be a problem!

Any thoughts would be appreciated (such as a constructive bijection).
 
  • #91
the subject heading "nope" was in response to "all mathematical ideas have been aptly addressed concerning this phenomenon of .9repeating=1...".

I must have gotten lost navigating the messege board.
 
  • #92
The difference between .9repeated and 1 is the diameter of a point... :) can you argue with that?
 
  • #93
Also, when calculating something that involves .999999...you use 1, then apply the appropriate thing to the end. I know that sounds really dumb, but if you were to say "What's n*0.9999" you would just use 1, and say "infinitely close to n" or soemthing liek that.
 
  • #94
What a lovely thread to come home to after a miserable day.

(a) Don't hijack threads.
(b) Don't insult people.

The discussion seems to have moved to a new thread, so I'm locking this one.
 

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