0.999999 recurring actually equals 1

[Bugz]

but thats still not true



0.999... REPRESENTS 1


but it doesnt equal it

I've found some nice quotes from some maths nerds:

"In fact, 0.9999... does equal 1, it can't be not quite equal to 1, and it doesn't have any properties ("interesting" or otherwise) that distinguish it from 1. It is simply an alternate representation of 1. To claim otherwise is to misunderstand the meaning of "0.9999..."."

"Firstly, rational numbers are fractions, i.e., the ration of one integer to another. When you are talking about 0.999..., you are talking about infinitely long decimal fractions, i.e., the limit of a series of finite decimal fractions, i.e., the domain of real numbers. So when you say that 0.999... = 1, you are saying that the real number expressed by 0.999... is the same as the real number 1."

""0.9999..." is definied (by mathematicians) as the limit of the sequence 0.9, 0.99, 0.999, 0.9999, ...

The word "limit" itself has a precise mathematical definition, and using this definition one can prove that the limit of the above sequence is indeed 1.

So if you're using the standard mathematical definition of 0.9999..., then the statement that 0.9999... = 1 is uncontroversial. So far as I can tell the only reason people tend to think there's something mysterious here is that they are (perhaps unintentionally) using 0.9999... to mean something slightly different (and perhaps less clearly defined) than what mathematicians use it to mean."

0.999 does represent one - an alternative reprensentation.

P.S - post 8 I stated they are the same 'real number.'

 

[Overdriven]

When ever I try and divide by 0, I get divide by 0 error encountered

EDIT: Gohan, I'm going to agree with Bugz on this one.. Give up.

 

[gohan]

I've found some nice quotes from some maths nerds:

"In fact, 0.9999... does equal 1, it can't be not quite equal to 1, and it doesn't have any properties ("interesting" or otherwise) that distinguish it from 1. It is simply an alternate representation of 1. To claim otherwise is to misunderstand the meaning of "0.9999..."."

"Firstly, rational numbers are fractions, i.e., the ration of one integer to another. When you are talking about 0.999..., you are talking about infinitely long decimal fractions, i.e., the limit of a series of finite decimal fractions, i.e., the domain of real numbers. So when you say that 0.999... = 1, you are saying that the real number expressed by 0.999... is the same as the real number 1."

""0.9999..." is definied (by mathematicians) as the limit of the sequence 0.9, 0.99, 0.999, 0.9999, ...

The word "limit" itself has a precise mathematical definition, and using this definition one can prove that the limit of the above sequence is indeed 1.

So if you're using the standard mathematical definition of 0.9999..., then the statement that 0.9999... = 1 is uncontroversial. So far as I can tell the only reason people tend to think there's something mysterious here is that they are (perhaps unintentionally) using 0.9999... to mean something slightly different (and perhaps less clearly defined) than what mathematicians use it to mean."

0.999 does represent one - an alternative reprensentation.

well thats more or less what i said in my last post, and the one beofre that were i pointed out 0.999... is the product of fractions not going into decimals and not a real number



not bad for a retarded little AS level kid then


i still disagree with the term 0.999... = 1 tho.... as it doesn't

 

[Bugz]

How Can 0.999... = 1?

As long as it is 0.9 recurring, then 0.9 recurring and 1 are the same 'real' number.

So you were arguing what I stated on the 8th post of this thread?

P.S if you wish to refer to yourself as a retard then go ahead, but no-one else here said tht :l

 

[gohan]

So you were arguing what I stated on the 8th page of this thread?

P.S if you wish to refer to yourself as a retard then go ahead, but no-one else here said tht :l

no just insinuated it in every other post, but thats ok that makes u look big on the internet

 

[Dukat]

 

[Bugz]

no just insinuated it in every other post, but thats ok that makes u look big on the internet

If you believe I insinuated it then I apologize - as it wasn't my intentions. Because you didn't make clear what you were arguing and the fact I had already stated it on the 8th post, I generally thought you failed to understand the concept of it, rather than the 'conditions,' hence my references to the many proofs by many experianced mathsmaticians. That said, next time try to formulate your posts a bit more as it was hard to follow your line of thought from my side of it all.

No hard feelings anyway - and yes, what you were arguing is an important aspect of the 'proof' and 'theory,' just you need to present things more coherently!

 

[aika]

its easily provable with limits.
limit of 0.99999... when 9 is written n times, while n reaches infinity equals to limit of the sum 9/10^n while n reaches infinity.
which in turn equals to limit of 1-1/10^n while n reaches infinity. Using limit arithmetics you can divide it into 2 limits, so it equals the limit of 1 minus the the limit of 1/10^n while n reaches to infinity.
Limit of 1/10^n while n reaches infinity is 0 and limit of 1 is 1. Which gives the result of 0.99999.. = 1-0 = 1.

Sorry, its quite hard to type this series of equations without the proper symbols

 

[Bahumat]

There's been alot of faceplanting onto high horses in this thread *BahumatLedstandt glares at you*

*arrghhhh you just got WTF eaten for 2k dmg!*

 

[Wonk]

We need master Laddey in here, to sort this math shit out.

 

[Bahumat]

We need master Laddey in here, to sort this math shit out.

ahh he's like Terry Thomas out on the rag

 

[CorNokZ]

Dont ever fucking divide by 0

 

[Huntingtons]

0.999... and 1 are just different forms of the same number.

Same reason why 0.33... and 1/3rd are the same - same 'real' value - different forms.

that is a void argument. 1 is a rational number (is that the word) 1/3 isnt a rational number (its something else). if you can find a way of saying 0.999... is a fraction and equals it to 1 you could (maybe compare them)

but.

if i add 0.000..1 to 0.999... i would by your definition get 1.000..1 would i not?

i saw you claimed it wasnt about rational (real?) numbers. so i guess its kinda null.

 

[Chronictank]

if i add 0.000..1 to 0.999... i would by your definition get 1.000..1 would i not?

It would not

You cant add 0.0000..1 because .999... by defninition never ends so where will this .1 be added?,
as soon as you define a limit it is no longer .9 re-occuring

 

[old.Tohtori]

*lifts finger*

*prepares to say something*

*sucks finger*

 

[Chronictank]

*lifts finger*

*prepares to say something*

*sucks finger*

welcome back :d

 

[Lamp]

0.999 is not 1

its infinitely smaller and infinitely missing that tiny fraction that would make it 1 and therefore cannot be 1

Only 1.0000000000000000000 etc equals one

Anything less - no matter how small - is not one

Its quite straight-forward really.

 

[old.Tohtori]

welcome back :d

Ta *bow*

 

[mooSe_]

0.999 is not 1

its infinitely smaller and infinitely missing that tiny fraction that would make it 1 and therefore cannot be 1

Only 1.0000000000000000000 etc equals one

Anything less - no matter how small - is not one

Its quite straight-forward really.

but it isn't 0.999 its 0.999... which is an infinite series of numbers.

 

[Lamp]

and is therefore infinitely smaller than 1 but not equal to 1

 

[Chronictank]

and is therefore infinitely smaller than 1 but not equal to 1

not quite, it is another valid mathematical representation of 1
You are treating it like a real number which it is not

 

[Marc]

I dont care what GCSE maths students say, 1 is not 0.999... and never will be.

 

[Chronictank]

I dont care what GCSE maths students say, 1 is not 0.999... and never will be.

It's not GCSE
The only way to know why it is the same is to know how the maths behind it works,
You are making very wrong assumptions to what the decimal representation actually means

While i take it on good faith there is a proof;

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

          = 9·0.1 + 9·0.01 + 9·0.001 + 9·0.0001 + ...

          = 9·10-1 + 9·10-2 + 9·10-3 + 9·10-4 + ...

            n=∞
          =  Σ 9·10-n
            n=1

                n=N
         := lim  Σ  9·10-n
            N→∞ n=1

          = lim ( 9·10-1 + 9·10-2 + ... + 9·10-N )
            N→∞

          = lim ( 9·0.1 + 9·0.01 + ... + 9·0.000...0001 )
            N→∞                              \________/
                                              N digits

          = lim ( 0.9 + 0.09 + ... + 0.000...0009 )
            N→∞                        \________/
                                        N digits

          = lim ( 0.999...999 )
            N→∞     \_______/
                     N nines

          = lim ( 1 - 0.000...0001 )
            N→∞         \________/
                         N digits

          = lim ( 1 - 10-N )
            N→∞

          = lim 1 - lim 10-N
            N→∞     N→∞

          = 1 - 0
          = 1

If you can provide proof that it does not equal one feel free to share

 

[old.Tohtori]

From my limited vision and enormous capacity for seeing things, i oxymoron this to be a case of "he said she means".

People are arguing that 0.999n isn't 1, which is isn't if looked at from a direct "this is a number x" point of view, but if looked at from a mathematical dryhumping point of view, it can be "proven" it is 1.

Use versus data.

...

What?!

It's not getting "into this", it's arbitrating!

 

[Bugz]

The proofs me and Chronic gave are the most basic of basic proofs and aren't really 'the proper proofs.'

If you enjoy maths and are not too bad at it - some of the proofs are really quite interesting

 

[old.Tohtori]

Just an interesting question to put forward;

If you take 1 and take away 0.000n1 and if you take 0.999n and take away 0.000n1, do you get the same result?

 

[taB]

Bugz & Chronic are correct. We did the infinite series and Bugz's simpler one as part of studying limits at uni. There are loads of different proofs on wikipedia.

Most of the confusion comes from not understanding what 0.(9) (or 0.999...) actually means.

 

[gohan]

well the thing is its not a number, its a fraction


its 0.333... x 3


but 0.333... isnt 1/3


is a failed atempt at 1/3 being decimalised



its also not a real number


so 0.999... does not eqaul 1


nor is it infinatly smaller,

its not a number,


it equals 1 in that 1/3 x 3 = 1

but its all comes about because alot of frations cannot be decimalised cleanly!


so yes 0.999... = 1 as any sum that come to 0.999... is through broken decimels and the answer that should have come about is 1



but as a statement 0.999... = 1


is wrong


u can clearly see it doesn't EQUAL 1


its taken as 1, or its a representation of 1

or it shoudl alwys be replaced with 1



but i doesnt fucking equal 1 or it would be ZERO POINT nien nien niennnnnnnnnnnn

 

[Lucius]

Although this question initiates debate, I think there are more pressing problems in Mathematics than that of whether 0.999... = 1. However, it's good that people talk about Mathematics, and as Bugz said, there are some very interesting proofs out there. Not just for this particular problem but many others .

 

[aika]

ok, integral of sin(x^2)