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 hendrix
In reference to this equation:

In reference to this equation:
One of my fellow maths students is trying to disprove it using:
x = 0.9r

(times 1.5)

1.5x = 1.49r

-x

0.5x = 0.49r

x = .49r/0.5

x = 0.9r

and not 1

Somebody please help me put him right
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your friend has made a mistake half way through

when he subtracted x, he assumed it was equal to 1, and not as originally stated, x=0.9r
1.49r - 0.9r not equal to 0.49r, unless 0.9r=1,
which is what he is trying to disprove

he uses as part of his proof that which he is trying to disprove

tell him he is an amateur, and to stop playing big boys games


oh, and for my two pennies:
0.9r is for all intents and purposes 1 - I live in the real world, and as an engineer couldn't really give a, well you know
but my opinion is that to be 100.0r% precise 0.9r is not 1.0r
:D
 
Originally posted by odoliam
your friend has made a mistake half way through

when he subtracted x, he assumed it was equal to 1, and not as originally stated, x=0.9r
1.49r - 0.9r not equal to 0.49r, unless 0.9r=1,
which is what he is trying to disprove

he uses as part of his proof that which he is trying to disprove

tell him he is an amateur, and to stop playing big boys games


oh, and for my two pennies:
0.9r is for all intents and purposes 1 - I live in the real world, and as an engineer couldn't really give a, well you know
but my opinion is that to be 100.0r% precise 0.9r is not 1.0r
:D
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Thats what I was trying to say!!
 
this thread has been so fun to read :D

(obviously, i havent read the whole thing)

im going with alpha numeric on this one, as he seems to be using big complicated maths words :D (and i think he has a few certificates on the wall somewhere)

is everyone else as tooled up in the maths department as he is?
 
My opinion:

0.9r is NOT 1

My reasoning is simple, by saying 0.9r you are implying that you have an infinite number of 9s. As this number cannot be defined as a mathematical number (I view it as more of an instruction) then it is impossible to attempt to prove or disprove it's value by putting it in an equation.

Imagine a metre stick that is indeed exactly 1 metre in length. Now imagine trying to point out where 0.9r is on it. Start at the point 0.9. Then move 0.09 across to 0.99. Then 0.009 across to 0.099. etc. You are moving the point further and further to the right, ever closer to the end, but a smaller amount each time.
It's pretty obvious that, not now, not in a million years, and not in infinite years are you ever going to reach the end of the metre stick (which is 1).

Therefore, to me, 0.9r is not 1 and no amount of mathematical jiggery pokery could make me think otherwise, since imo 0.9r is a mathematically undefinable quantity.

All those 'proofs' where you say X = 0.9r so 10x = 9.9r are rubbish since there is an undefined 'number' of 9s in each rendering the equation useless.

This all seems simple and obvious to me, what am I missing?

Edit: With reference to the comment above this one. I don't believe this topic has anything to do with maths at all, for the reasons I've given above.
I did A level myself, but I don't believe that being a maths professor or failing maths gcse makes any difference to an argument that is solved by logic and has nothing whatsoever to do with maths. IMO of course:)
 
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Fact:

0.9r = 0.9 + 0.09 + 0.009 ... etc..

This is a geometric progress, for which, you are able to sum to infinity using equation a / (1 - r)

Those doing maths at A-level + will back me up on this...

using equation...

a = 0.9 (first term)
r = 0.1 (common difference)

0.9 / (1- 0.1)

= 0.9/0.9

= 1



ITS PROVED! MATHEMATICALLY!

Try and counterprove it MATHEMATICALLY i tell you:p
 
Originally posted by leeframp
All those 'proofs' where you say X = 0.9r so 10x = 9.9r are rubbish since there is an undefined 'number' of 9s in each rendering the equation useless.

This all seems simple and obvious to me, what am I missing?
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In a decimal system multiplying by 10 right shifts the decimal point so no reference of the other end is required. Thus you can multiply 0.9r x 10 to give 9.9r

Jokester
 
Originally posted by SidewinderINC
(and i think he has a few certificates on the wall somewhere)
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Nothing other than a GCSE and some A Level certificates (though if you asked me where I put them, I think I might have lost them :o), but I'm a year off a BA in Maths ;)
Originally posted by SidewinderINC
is everyone else as tooled up in the maths department as he is?
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My lecturers, and they agree with me. (or rather I do with them)
Originally posted by leeframp
As this number cannot be defined as a mathematical number (I view it as more of an instruction) then it is impossible to attempt to prove or disprove it's value by putting it in an equation.
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Of course its definable. What makes an infinite sequence undefinable? You know "sin", "cos", "exp" and literally hundreds of other functions are defined by infinite power series (as you should know from Taylors Theorum in A Level), and are perfectly acceptable. Pi is an infinite sequence of numbers, but still a perfectly defined number.
Originally posted by leeframp
All those 'proofs' where you say X = 0.9r so 10x = 9.9r are rubbish since there is an undefined 'number' of 9s in each rendering the equation useless.

This all seems simple and obvious to me, what am I missing?
Click to expand...
The fact 0.9r is a definable number.
 
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Originally posted by AlphaNumeric
I'm a year off a BA in Maths ;)
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I thought it'd be a BSc, or is there something different about your course that makes it "non science"?

Incidently, and I wasn't going to post, but since the thread came back to life...
I have a mate doing Economics/Maths, and he's in half my lectures. He came round my room before to sort some stuff out, and I asked him, if 0.9r=1. He said he didn't know, but thinking there and then, said no. I asked him to TELL me the Gauss formula, and if the average of two numbers was smaller than the larger of the two values. He accepted both these things, as he'd told me. I used the Gauss formula to show 0.9r=1, and then used the "average" to show 0.0r1=0. He was happy enough with the proofs.
 
Originally posted by AlphaNumeric
Of course its definable. What makes an infinite sequence undefinable? You know "sin", "cos", "exp" and literally hundreds of other functions are defined by infinite power series.
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I agree that numbers like these are used in maths, but I interpret your use of the word 'defined' in this way as an approximation rather than a 'definite' value.
When pi is used to calculate an area, a truncated form of the indefinable value is used to perform a calculation. So the value you have used, and therefore the answer you get, is an approximation.

3.1415926535897932384626433832795 is an approximation of pi, but it does not 'equal' pi. Nor will any answers you get from that number be the 'exact' answer. Sure, it will be near enough to be considered 'right' in practical terms, but like I said, I don't consider the 'real' pi to be definable. Same with 0.9r.

In summary, I still can't see how anything infinite can be converted from theory into mathematics.
 
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Originally posted by leeframp
3.1415926535897932384626433832795 is an approximation of pi, but it does not 'equal' pi. Nor will any answers you get from that number be the 'exact' answer. Sure, it will be near enough to be considered 'right' in practical terms, but like I said, I don't consider the 'real' pi to be definable. Same with 0.9r.
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0.9r is perfectly definable, I can tell you the value of any of the digits at any point in the number, something I can't do for pi.

Jokester
 
Originally posted by jokester
0.9r is perfectly definable, I can tell you the value of any of the digits at any point in the number, something I can't do for pi.

Jokester
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I can tell you that as well, the value of the digit at any point in the 'number' is 9.

How many 9s are there then?
 
Originally posted by leeframp
I agree that numbers like these are used in maths, but I interpret your use of the word 'defined' in this way as an approximation rather than a 'definite' value.
When pi is used to calculate an area, a truncated form of the indefinable value is used to perform a calculation. So the value you have used, and therefore the answer you get, is an approximation.

3.1415926535897932384626433832795 is an approximation of pi, but it does not 'equal' pi. Nor will any answers you get from that number be the 'exact' answer. Sure, it will be near enough to be considered 'right' in practical terms, but like I said, I don't consider the 'real' pi to be definable. Same with 0.9r.
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I'm sorry to say this - but you don't know what you're talking about. For instance, sqrt(2) has an infinite decimal expansion, and it is the only positve number that satisfies x²=2. Sin(Pi) = 0, not Sin(3.141), not Sin(3.1415926535897932384626433832795), but EXACTLY Sin(Pi).
 
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