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paulhicks



Joined: Jul 19, 2004

Post   Posted: Oct 04, 2011 - 22:04 Reply with quote Back to top

A mate of mine was round this evening and claimed something that seemed odd to me. His claim was:

"0.999 (going on for infinity) is exactly the same as 1 in all circumstances".

No i have no idea how we got onto the subject either but frankly i lack a basic understanding of maths beyond my 2 times table. Even so this seemed fundamentaly wrong to me.
I know there are penty of people on here with better maths brains than me so my question is:

Is this correct?

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phil78



Joined: Jul 29, 2004

Post   Posted: Oct 04, 2011 - 22:06 Reply with quote Back to top

I believe the answer is yes, they are the same but i agree it doesn't seem to make sense
WhatBall



Joined: Aug 21, 2008

Post   Posted: Oct 04, 2011 - 22:10 Reply with quote Back to top

"0.999 (going on for infinity) is exactly the same as 1 in all circumstances."

Tell that to the person who won the lottery, or died by being hit by a piece of falling space debris. Wink

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James_Probert



Joined: Nov 25, 2007

Post   Posted: Oct 04, 2011 - 22:11 Reply with quote Back to top

It's not (by definition).

But most purposes, it is (as you're going to round the value at some point, due to the fact that you'd run out of universe to count in/with).

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sann0638



Joined: Aug 09, 2010

Post   Posted: Oct 04, 2011 - 22:13 Reply with quote Back to top

As an example, 1/9 is 0.1 recurring.
Therefore 9/9 is 0.9 recurring.
But obviously 9/9 = 1.

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paulhicks



Joined: Jul 19, 2004

Post   Posted: Oct 04, 2011 - 22:13 Reply with quote Back to top

James_Probert wrote:
It's not (by definition).

But most purposes, it is (as you're going to round the value at some point, due to the fact that you'd run out of universe to count in/with).


See that was what i assumed he was getting at but apparently not. Confused

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Sutherlands



Joined: Aug 01, 2009

Post   Posted: Oct 04, 2011 - 22:13 Reply with quote Back to top

@WhatBall, that doesn't even make sense...

@paulhicks - Yes, those are two ways of representing the exact same number. There are a few ways to prove this.

First, by the real number theorum, between any two distinct real numbers, there is another number which is the average of the two. What is the average of 1 and .99999...? There is no number between them.

Second:
1/9 = .11111....
2/9 = .22222....
3/9 = .33333....
9/9 = .99999....
1 = .99999....

Third:
x = .9999....
10x = 9.9999....
10x - x = 9.9999.... - .9999....
9x = 9
x = 1
Sutherlands



Joined: Aug 01, 2009

Post   Posted: Oct 04, 2011 - 22:14 Reply with quote Back to top

James_Probert wrote:
It is(by definition).
FTFY
DukeTyrion



Joined: Feb 18, 2004

Post   Posted: Oct 04, 2011 - 22:16 Reply with quote Back to top

The problem is, the decimal system can never quite be exact.

Fractions were much better back in the old days.
ryanfitz



Joined: Mar 24, 2009

Post   Posted: Oct 04, 2011 - 22:16 Reply with quote Back to top

It is accepted in theoretical math, but while correct for performing mathematical calculations, are not 'exactly the same' for obvious visible reasons.

the idea is that if the .9999 bar goes on indefinitely, you will never reach the 1Mad chance as there will be infinitely more 9s
James_Probert



Joined: Nov 25, 2007

Post   Posted: Oct 04, 2011 - 22:19 Reply with quote Back to top

sann0638 wrote:
As an example, 1/9 is 0.1 recurring.

It's not.
0.1 recurring is the nearest decimal to 1/9, although the exact value is impossible to give.
sann0638 wrote:
Therefore 9/9 is 0.9 recurring.
But obviously 9/9 = 1.

the statement I've given above explains why this is a fallacy, although it is accurate for the (very) large majority (if not all currently found) cases.
WhatBall wrote:
"0.999 (going on for infinity) is exactly the same as 1 in all circumstances."

Tell that to the person who won the lottery, or died by being hit by a piece of falling space debris. Wink

ermmm, those are non-zero (and measurable) probabilities, so not a valid counter-argument.


Yes, I'm aware I've just argued both sides of the arguement Very Happy

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dode74



Joined: Aug 14, 2009

Post   Posted: Oct 04, 2011 - 22:22 Reply with quote Back to top

Good explanation from Yahoo:

Quote:
The number "0.9999..." can be "expanded" as:

0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

In other words, each term in this endless summation will have a "9" preceded by some number of zeroes. This may also be written as:

0.999... = 9/10 + (9/10)(1/10)^1 + (9/10)(1/10)^2 + (9/10)(1/10)^3 + ...

That is, this is an infinite geometric series with first term a = 9/10 and common ratio r = 1/10. Since the size of the common ratio r is less than 1, we can use the infinite-sum formula to find the value:

0.999... = (9/10)[1/(1 - 1/10)] = (9/10)(10/9) = 1

So the formula proves that 0.9999... = 1.
WhatBall



Joined: Aug 21, 2008

Post   Posted: Oct 04, 2011 - 22:23 Reply with quote Back to top

I've identified the mathematicians by highlighting their inability to laugh at a silly answer to a math related question. Very Happy

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GAZZATROT



Joined: Apr 26, 2009

Post   Posted: Oct 04, 2011 - 22:25 Reply with quote Back to top

Erm, I'm CERTAINLY not an expert but if you minus one from this number you would have a negative figure.... therefore it is less than 1.

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Sutherlands



Joined: Aug 01, 2009

Post   Posted: Oct 04, 2011 - 22:26 Reply with quote Back to top

DukeTyrion wrote:
The problem is, the decimal system can never quite be exact.
Give me a fraction that can't be represented as a decimal, please.

ryanfitz wrote:
It is accepted in theoretical math, but while correct for performing mathematical calculations, are not 'exactly the same' for obvious visible reasons.
I wasn't aware that math used sight to prove something. No, those numbers are exactly the same.
James_Probert wrote:
sann0638 wrote:
As an example, 1/9 is 0.1 recurring.

It's not.
0.1 recurring is the nearest decimal to 1/9, although the exact value is impossible to give.
It is exactly the same. The exact value is not impossible to give.
GAZZATROT wrote:
Erm, I'm CERTAINLY not an expert
Agreed
GAZZATROT wrote:
but if you minus one from this number you would have a negative figure.... therefore it is less than 1.
No, you'll have 0.
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