Poll: Does 0.99 Recurring = 1

Does 0.99 Recurring = 1

  • Yes

    Votes: 225 42.5%

  • No

    Votes: 304 57.5%
  • Total voters
    529
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Originally posted by Shadez
when did you prove that?
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Quoting myself :
Is 0.0r1 the closest number to zero you can get?

What about (0.0r1 + 0)/2 ? The average of 0.0r1 and 0. Obviously thats between 0.0r1 and 0, but 0.0r1 is the closest to zero possible.

(0.0r1+0)/2 = 0.0r1

0.0r1 = 2*0.0r1
Take 0.0r1 from both sides
0.0r1 = 0

Satisfied? If 0.0r1 isn't the closest number to zero, what is? After all how can you get smaller than infinite zeros and then a 1?
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Of course, this is all assuming 0.0r1 exists, which it doesn't, but then many people in this thread seem to think it does.
 
Originally posted by Shadez
Ty, but i was actualy after how Lim n->inf [1/n] = 0 was proven.
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Assume 1/n does not tend to Zero. What does it tend to? It tends to the closest number to zero that isn't zero, call it "A".
Consider (A+0)/2. Thats between A and 0, but by definition, A is the closest number to 0 without being zero.
Thus
(A+0)/2 = A
A + 0 = 2A
A = 0.

So either you say 1/n goes to zero, or you show a contradiction exists, so your initial assumption that A wasn't zero was wrong.

This helps illustrate the point you can't prove anything you want in maths, you get contradictions. I defined A>0, then showed it was 0. 0>0, which is wrong. Thus assuming A>0 was wrong to start with, and I can't now use A>0. Do it wirh A<0 (though obviously false) and you get the same thing 0<0, wrong. Do it with A = 0, and you don't get the problem :) Hence A = 0.

You can do it in a much for analytic manner, but it'd require about 5 pages and a load of notation you'd not follow and VBB doesn't support. Hopefully my "rough and ready" proof is enough.
 
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Originally posted by AlphaNumeric
Assume 1/n does not tend to Zero. What does it tend to? It tends to the closest number to zero that isn't zero, call it "A".
Consider (A+0)/2. Thats between A and 0, but by definition, A is the closest number to 0 without being zero.
Thus

(A+0)/2 = A
A + 0 = 2A
A = 0.

Click to expand...

I dont really see how this is a proof of A=0 seeing is in the first equation you have already assumed it is 0...

multiplying out the brackets gives A/2 + 0/2 = A which means A/2 = A which means 1/2=0....

Sorry but i'm very confused!
 
Originally posted by AlphaNumeric
Its essentially the same proof. You can do it in a much for analytic manner, but it'd require about 5 pages and a load of notation you'd not follow and VBB doesn't support. Hopefully my "rough and ready" proof is enough.
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VBB?


hmm, so basicly its proven by proving it cant be anything else.

It was the 5 page jobbie i was after, but dont worry i dont have the time to sit down and read it.
 
Originally posted by yak.h'cir
Sorry but i'm very confused!
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Thats the point. If I say A isn't zero, you prove something confusing, like 1/2 = 0. You and I know 1/2 isn't 0, so you retrace the steps and examine each assumption you make.
I assumed A > 0. Now assume A = 0, and rerun the proof (but don't cancel through by A, you can't divide through by zero remember). You'll end up with A = 0, which is what you assumed. Since you have no contradition with assuming A = 0, but do with A > 0, that tells you to remove "your confusion", A = 0.

Therefore the limit is zero :)
 
Originally posted by Shadez
VBB?
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Vbulletin Board, the code used to run these forums. Its annoying enough to use ^2 as squared, doing greek notation would be horrible.
Originally posted by Shadez
It was the 5 page jobbie i was after, but dont worry i dont have the time to sit down and read it.
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I'd have to create the Field of Real Numbers first, then develop the concept of orderness, functions, limits, continuity, convergence and then I'd say the proof I just gave in a more "formal" manner. Basically, if you accept 1/x is a smooth line as x gets big, you accept the mod (ie the size of a number) is always bigger than or equal to zero and you accept (a+b)+c = a+(b+c), then you don't need to worry about all the stuff I just listed I'd do, because thats what are needed to show my "proof" follows on from the axioms.

Actually, it wouldn't be 5 pages, itd be more like 100, and even thats brushing over some things.
 
Originally posted by AlphaNumeric
Thats the point. If I say A isn't zero, you prove something confusing, like 1/2 = 0. You and I know 1/2 isn't 0, so you retrace the steps and examine each assumption you make.
I assumed A > 0. Now assume A = 0, and rerun the proof (but don't cancel through by A, you can't divide through by zero remember). You'll end up with A = 0, which is what you assumed. Since you have no contradition with assuming A = 0, but do with A > 0, that tells you to remove "your confusion", A = 0.

Therefore the limit is zero :)
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Ahh of course! Cheers.
 
I expected the people on this forum to be technically minded given the computer nature of the forum. Its worryin more than half dont understand or refuse to believe that 0.9r=1
 
Originally posted by sid
I expected the people on this forum to be technically minded given the computer nature of the forum. Its worryin more than half dont understand or refuse to believe that 0.9r=1
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I quite agree with you. This poll says nothing at all about whether 0.9r is or is not equal to 1. It simply displays the high level of ignorance among members here.
 
Even more worrying is that as time goes by people seem to be getting more ignorant, the level of 0.9r = 1 votes is gradually going down :(.

Just shows that not all computer experts are math literate!!!
 
It simply displays the high level of ignorance among members here.
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*Chuckles*

I think the more interesting illustration is the total unwillingness for people to accept a different opinion on a subject that is only possible to debate through perspective and semantics.

0.9r is equal to 1 only in a mathematical context. In the same way that the true number for pie is only useful in a pure mathematic environment. The rest of us are quite happy with pie being 3.14.

In practical terms, real world terms, logical thought terms, and sheer common sense terms, 0.9r is equal to 0.9r and nothing else.

The only thing that this conversation does achieve is to highlight how useless maths is at proving a point when dealing with something as flawed as the decimal system.

Edit: Thug? I've always thought of myself as more a Henry Gondorff kind tbh.
 
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Originally posted by Kyle Reece
I think the more interesting illustration is the total unwillingness for people to accept a different opinion on a subject that is only possible to debate through perspective and semantics.
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True, so since maths isn't open to semantics and perspectives, you cannot debate the nature of 0.9r within a maths context.
Originally posted by Kyle Reece
The rest of us are quite happy with pie being 3.14.
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Speak for yourself. I don't think any scientist or engineer worth their salt considers Pi as 3.14.
Originally posted by Kyle Reece
The only thing that this conversation does achieve is to highlight how useless maths is at proving a point when dealing with something as flawed as the decimal system.
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Can you please demonstate a concept whereby the "flawed" nature of the decimal system is expressed. Do you have a better suggestion for our number system. Base 2? Base 7? Base 3985472737?

Its all well and good saying "I think its wrong", but if you don't offer an alternative idea, you don't advance the concept, you just complain.
 
Originally posted by AlphaNumeric

Speak for yourself. I don't think any scientist or engineer worth their salt considers Pi as 3.14.
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I was taught engineers prefered Pi = 3.

Alpha, do you mind if I email you something mathsy, quite quick, but unrelated to this thread?
 
Sure, I'll log into MSN now.

An engineer might consider Pi = 3, but if they used that in the construction of bridges, houses, skyscrapers etc, you'd get some serious problems. Pi = 3.1416 is enough for engineers, pi = 3.14159265 is enough for most physicists.
 
Originally posted by Bodak
I was taught engineers prefered Pi = 3.
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I was actually going to say that I'm quite happy to use pi as approximately 3.14 (but I know that it doesn't equal 3.14) as from an engineering point of view we generally only work to 3 significant figures. Only where accuracy is required would we goto to the bother of a more accurate estimate.

Jokester
 
Originally posted by AlphaNumeric
True, so since maths isn't open to semantics and perspectives, you cannot debate the nature of 0.9r within a maths context.[/i]
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I don't think I was. I simply stated the opinion that certain people in this thread were not able to understand an opinion of the subject not using a mathematical context.

You illustrated my point, and have been doing so this entire thread, quite nicely thank you.

Speak for yourself. I don't think any scientist or engineer worth their salt considers Pi as 3.14.
Click to expand...

Until you survey all the scientists and engineers who are "worth their salt" (which is itself another arbitary rank I assuming you alone would presume to grant) then your opinion carries no more weight than mine, for I was indeed stating my opinion.

Can you please demonstate a concept whereby the "flawed" nature of the decimal system is expressed.
Click to expand...

Go out and get me a length of material that is exactly 0.9r long.

Edit: missed a /quote.. and a /b preview works wonders...
 
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