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 taliesyn
Forgive me for saying so, but that's hardly a real world example. Theoretically it can be done, but not practically which was exactly my point.
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Real world example alert:

I have 60 apples and I want to split them three ways. Then I will split them up into 3 groups consisting of 60*0.333.... apples.

(although why I'd be splitting up 60 apples into 3 groups I have no idea!) :confused:
 
Originally posted by taliesyn
Forgive me for saying so, but that's hardly a real world example. Theoretically it can be done, but not practically which was exactly my point.
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Ok then, substitute the cake for a CAD/CAM milling machine cutting a perfect circle from a block of wood then dividing it into exactly 3 thirds.
 
If the sample consists of 3 trillion atoms, then you'd cut it into three samples each of a trillion atoms.

You'd have a third, or 0.333 recurring of the whole lot.
 
Originally posted by Trojan
Ok then, substitute the cake for a CAD/CAM milling machine cutting a perfect circle from a block of wood then dividing it into exactly 3 thirds.
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While accurate to probably parts per million or even billion, that is not exactly 1/3.

If you were able to count in individual atoms, then it would be (provided you has a multiple of 3 atoms), but even a computer made circle is not a circle in the mathematical sense, though you'd need a hugely accurate measuring machine to notice it.
 
The three examples are good ones although 3 Trillion atoms are not equal to 1, and neither is 60 apples. Mr. Trojan, forgive my facetiousness, but the same applies to your milled circle :)

In the real world 1 is 1, not an algebraic representation of 1. It's just 1, not 1 = 60a, or 1 = 3 Trillion a.

Do the same with 1 apple, or 1 atom (without going into quarks, gluons and the like), and you cannot practically reach infinity so you cannot exactly split them into 3.

As I said, I don't disagree wth the mathematical proofs, I just don't see that the theory can be empirically proven :)
 
Why can't you split an apple into three if you can count the number of atoms, and it's a multiple of three, where's the problem?
 
If you define the apple as its atoms, and the number of atoms is a multiple of 3, then you could divide the apple into 3.

Having not read the thread I assume the point people are getting at is that perfect geometric shapes can't exist in the real world because you could always keep zooming in on it and finding tiny imperfections.
 
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Originally posted by Ace Rimmer
If you define the apple as its atoms, and the number of atoms is a multiple of 3, then you could divide the apple into 3.

Having not read the thread I assume the point people are getting at is that perfect geometric shapes can't exist in the real world because you could always keep zooming in on it and finding tiny imperfections.
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I see your respective points Mr. Rimmer and Mr. daz, but then you're defining the apple as atoms and not an apple. You find an apple which has an atomic structure which is an exact multiple of 3 and then you can split it into 3 and then we'll all count the atoms. I'll then admit defeat.

Theoretically, such an apple may exist, but no one has seen one as far as we know.

Geometric shapes can never be accurate to infinity, and so as you say, you can't prove it that way either.

So someone either show me the above apple or show me infinity and I'll be happy :)
 
OK, so now the whole notion of division is being challenged because "in the real world" we can't accurately split things into three.

It's like going back to Year 2 where we knew about division, but nothing about fractions and as such 10/3 would equal 3 remainder 1 lol...

Child 1: "How can you divide 1 into smaller pieces!!!!!"
Child 2: "It's impossible!" :eek:
Teacher: "Check this out, it's called a decimal point children."
Children (together) "ooooooohhh"

We define 3/1 as being one third, or, 0.333 recurring as a decimal.
 
Originally posted by daz
OK, so now the whole notion of division is being challenged because "in the real world" we can't accurately split things into three.

It's like going back to Year 2 where we knew about division, but nothing about fractions and as such 10/3 would equal 3 remainder 1 lol...

Child 1: "How can you divide 1 into smaller pieces!!!!!"
Child 2: "It's impossible!" :eek:
Teacher: "Check this out, it's called a decimal point children."
Children (together) "ooooooohhh"
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No, I'm not challenging division at all. I'm asking you to practically show me how you can prove the theory in the real world. As I said, I'm not disputing the mathematical proofs, just asking for real world proof without resorting to algebra.

I can't remember year 2, I'm 37 ;)
 
Originally posted by taliesyn
. You find an apple which has an atomic structure which is an exact multiple of 3 and then you can split it into 3 and then we'll all count the atoms. I'll then admit defeat.

Theoretically, such an apple may exist, but no one has seen one as far as we know.

So someone either show me the above apple or show me infinity and I'll be happy :)
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OK i might be wrong here but statistically, every 3rd apple would have an atomic stucture which is a multiple of 3??

You guys are all talking about real world examples, cutting cakes etc and pretty much everyone agrees that you cannot cut it to an infinate degree of accuracy. Agree? If in the real world we cannot go into infinate degrees of accuracy then the equation 1=0.9r does not exist in the real world. So it only exists in a mathematical world where it can be proved to be EQUAL to 1.
 
Originally posted by taliesyn
No, I'm not challenging division at all. I'm asking you to practically show me how you can prove the theory in the real world. As I said, I'm not disputing the mathematical proofs, just asking for real world proof without resorting to algebra.

I can't remember year 2, I'm 37 ;)
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Well, i'm not sure of any application in the real world where one would use recurring decimals over fractions. Infinitely recurring decimals *are* equal to their fractional counterparts, except because we don't have calculators with infinite memory space, we simply get an approximation, usually to 8 or 12 decimal places, depending on your calculator.
 
Originally posted by Drawoh Tesremos
Well spotted. It's caused a lot of heatache to many people I've shown that one to, including my old maths master when at school.:)
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Bit suprised no one had a look at the paradox I posted - as the slip is very subtle. Although, I think the first sentance will have put people off.

When I first came across it, I thought there must be a major flaw somewhere! :eek:
 
Originally posted by w11tho
Bit suprised no one had a look at the paradox I posted - as the slip is very subtle. Although, I think the first sentance will have put people off.
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How far back was it, w11tho? I missed it, and there's an awful lot to trawl through.
 
Originally posted by w11tho
If you haven't seen a Taylor series, this might not make much sense, but I'll put it up anyway. Here is another (incorrect) proof of something - this time Log(2)=0. It goes like this:

Doing the Taylor expansion of Log(1+x) and setting x=1 gives:

Log(2) = 1 - 1/2 + 1/3 - 1/4 + 1/5 - ......

And we we rearrange it as follows:

= (1 + 1/3 + 1/5 + 1/7 + ....) - (1/2 + 1/4 + 1/6 + 1/8 + ....)
= (1 + 1/3 + 1/5 + 1/7 + ....) + (1/2 + 1/4 + 1/6 + 1/8 + ....) - 2(1/2 + 1/4 + 1/6 + 1/8 + ....)
= (1 + 1/2 + 1/3 + 1/4 + ....) - (1 + 1/2 + 1/3 + 1/4 + ....)
= 0
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:)
 
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Originally posted by Drawoh Tesremos
Oh yes. A very neat one. I'll not spoil it for others ...yet. :)
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I dont think it's one that people will get, as you need to know a bit of Real Analysis - but it is very perplexing at first sight!

:)
 
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