Is 1 = 0.9999......

[bigredguy]

Why the hell do people keep bumping this up let it die once and for all.

 

[Kyteland]

Originally posted by: bigredguy
Why the hell do people keep bumping this up let it die once and for all.

So that people like smaks10 can experience the joy that is 0.99....=1.

edit: spelling

 

[Krugger]

i wondered why this was still alive. screw it, i'm gonna go find mr. nash in the library... he'll know the answer.
-Krugger

 

[naddicott]

I read the whole damn thread! (yes I'm bored)

I'm surprised that none of the cynics hooked onto the link that luvly gave: Is 0.999... = 1? A serious question.

I liked the introductory quote there, and it sums up the debate nicely:

Few mathematical structures have undergone as many revisions or have been presented in as many guises as the real numbers. Every generation reexamines the reals in the light of its values and mathematical objectives. F. Faltin, N. Metropolis, B. Ross and G.-C. Rota, The real numbers as a wreath product

I was lucky enough to take one of G.C. Rota's classes, and he always loved unconventional thinking (and he was a far better mathematician than Nash ever was, IMO).

I'm also disappointed and yet not surprised by the disdain those who cling to the conventional school of thought showed to anyone who answered 'no', as if that answer in itself made them some elementary school idiot who couldn't get their tables straight. Obviously some of the 'no's are given on instinct and can be swayed with the simplistic 'proofs', but others clearly know quite a bit of mathematics and disagree for the fun of it or due to somewhat unconventional (but not therefore implicitly wrong) views of the nature of real numbers.

From my personal perspective, I see it as a matter of convenience. I answered 'no' here to extend an absurdly long thread, but the day to day reality I deal with makes it convenient to adopt the conventions adopted by the 'yes' proofs. Here is how I like to look at it (highly oversimplified, read luvly's link if you want to chew on a proper mathmatical argument):

0.999... = 1 - "an infinitely small number"
"an infinitely small number" is a fantastically good approximation of 0

For the purpose of this thread, I'll hold the ground that no matter how close to 0 an infinitely small number may be, it is never actually equal to 0. Yes, that means I condemn any calculations dependant on limit theory to a mathematics of approximation. (whoever tried to counter this line of thought by saying 'this one use of calculus and limits leads to an exact answer, therefore all use of calculus and limits gives exact answers' - shame on you, that type of argument is a logical fallacy).

For the purpose of engineering work, I'm more than happy to accept a definition of equality that allows an infinitely small number to be equal to zero. It's convenient and too much productive work would get held up if I didn't allow that convention.

Most importantly, I've managed to bump a hilariously long thread.

 

[silverpig]

And you also seem to have missed all of RossGr's proofs which don't use limits at all...

 

[bleeb]

If you look at RossG's proofs, you will see that he introduces some form of approximation, thereby destroying any viable evidence that 0.9999... = 1.

0.9999.... != 1.


Guys we are almost at 1000 posts! =) lets keep 'em coming.

 

[silverpig]

Originally posted by: bleeb
If you look at RossG's proofs, you will see that he introduces some form of approximation, thereby destroying any viable evidence that 0.9999... = 1.

0.9999.... != 1.


Guys we are almost at 1000 posts! =) lets keep 'em coming.

No he doesn't. He proves that 0.999... + any number is larger than 1, and that 0.999... - any number is smaller than 1.

 

[Koing]

Originally posted by: bleeb
If you look at RossG's proofs, you will see that he introduces some form of approximation, thereby destroying any viable evidence that 0.9999... = 1.

0.9999.... != 1.


Guys we are almost at 1000 posts! =) lets keep 'em coming.

crazy thread with lots of good info

 

[bleeb]

do we agree that zero is a number? then adding 0.9999... + 0 = a number less than 1. subtracting zero from 0.9999.... also produces something that is less than 1.

Therefore, 0.9999... != 1.

Where is his proof, I'd like to see it.

btw, the second part of your comment is redundant.

 

[Darien]

Originally posted by: bleeb
do we agree that zero is a number? then adding 0.9999... + 0 = a number less than 1. subtracting zero from 0.9999.... also produces something that is less than 1.

Therefore, 0.9999... != 1.

Where is his proof, I'd like to see it.

btw, the second part of your comment is redundant.

What number do you add .9999.... to get 1? There is no such number. So .999.... = 1.

Stop bumping this thread :|

 

[silverpig]

Originally posted by: bleeb
do we agree that zero is a number? then adding 0.9999... + 0 = a number less than 1. subtracting zero from 0.9999.... also produces something that is less than 1.

Therefore, 0.9999... != 1.

Where is his proof, I'd like to see it.

btw, the second part of your comment is redundant.

0.999... + 0 = 0.999... since we don't know what 0.999... equals, we can't say it's larger or smaller or the same as 1 yet. That does absolutely nothing for us.

 

[bleeb]

Originally posted by: Darien

Originally posted by: bleeb
do we agree that zero is a number? then adding 0.9999... + 0 = a number less than 1. subtracting zero from 0.9999.... also produces something that is less than 1.

Therefore, 0.9999... != 1.

Where is his proof, I'd like to see it.

btw, the second part of your comment is redundant.

What number do you add .9999.... to get 1? There is no such number. So .999.... = 1.

Stop bumping this thread :|

You simply add (IN VERY SIMPLIFIED NOTATION):

0.9999... + (1-0.9999.... ) = 1

You have to understand about sets & different levels of infinity.

 

[silverpig]

Originally posted by: bleeb

btw, the second part of your comment is redundant.

It's not redundant at all. It is required for the proof in showing that 0.999... = 1.

Let x = some number. Say we can show that x + any number is larger than 1. That does nothing for us. x could be 4, x could be 12... We have to pin x somewhere. That's where the second statement comes in.

 

[silverpig]

Originally posted by: bleeb

Originally posted by: Darien

Originally posted by: bleeb
do we agree that zero is a number? then adding 0.9999... + 0 = a number less than 1. subtracting zero from 0.9999.... also produces something that is less than 1.

Therefore, 0.9999... != 1.

Where is his proof, I'd like to see it.

btw, the second part of your comment is redundant.

What number do you add .9999.... to get 1? There is no such number. So .999.... = 1.

Stop bumping this thread :|

You simply add (IN VERY SIMPLIFIED NOTATION):

0.9999... + (1-0.9999.... ) = 1

You have to understand about sets & different levels of infinity.

Okay, now you're obviously just trying to be a pain in the ass about this whole thing. I'm out.

 

[bleeb]

Originally posted by: silverpig

Originally posted by: bleeb

btw, the second part of your comment is redundant.

It's not redundant at all. It is required for the proof in showing that 0.999... = 1.

Let x = some number. Say we can show that x + any number is larger than 1. That does nothing for us. x could be 4, x could be 12... We have to pin x somewhere. That's where the second statement comes in.

gotcha

 

[Darien]

Originally posted by: bleeb

Originally posted by: Darien

Originally posted by: bleeb
do we agree that zero is a number? then adding 0.9999... + 0 = a number less than 1. subtracting zero from 0.9999.... also produces something that is less than 1.

Therefore, 0.9999... != 1.

Where is his proof, I'd like to see it.

btw, the second part of your comment is redundant.

What number do you add .9999.... to get 1? There is no such number. So .999.... = 1.

Stop bumping this thread :|

You simply add (IN VERY SIMPLIFIED NOTATION):

0.9999... + (1-0.9999.... ) = 1

You have to understand about sets & different levels of infinity.

lim (x -> infinity) of 1 - 10/x = 1



All .9999 = 1 shows is that representing values in decimal and fraction notation can be odd

To put it simply...:
1/9 = .111...
2/9 = .222...
3/9 = .333...
...
8/9 = .888..

Since 9/9 = 1 = 1/9 + 8/9 = .111... + .888...
logically, since 1+8 = 9, you know addition of such decimals cannot exceed .999...



Edit:
I'm sure someone in this thread has mentioned this argument before. I'm not going to search 900+ posts for it though

 

[bleeb]

Originally posted by: Darien

Originally posted by: bleeb

Originally posted by: Darien

Originally posted by: bleeb
do we agree that zero is a number? then adding 0.9999... + 0 = a number less than 1. subtracting zero from 0.9999.... also produces something that is less than 1.

Therefore, 0.9999... != 1.

Where is his proof, I'd like to see it.

btw, the second part of your comment is redundant.

What number do you add .9999.... to get 1? There is no such number. So .999.... = 1.

Stop bumping this thread :|

You simply add (IN VERY SIMPLIFIED NOTATION):

0.9999... + (1-0.9999.... ) = 1

You have to understand about sets & different levels of infinity.

lim (x -> infinity) of 1 - 10/x = 1



All .9999 = 1 shows is that representing values in decimal and fraction notation can be odd

To put it simply...:
1/9 = .111...
2/9 = .222...
3/9 = .333...
...
8/9 = .888..

Since 9/9 = 1 = 1/9 + 8/9 = .111... + .888...
logically, since 1+8 = 9, you know addition of such decimals cannot exceed .999...



Edit:
I'm sure someone in this thread has mentioned this argument before. I'm not going to search 900+ posts for it though

You are introducing the discrediting approximation in your proof at 1/9 + 8/9 = .111... + .888.... which still only proves that the notion is confusing.

 

[Darien]

Originally posted by: bleeb

Originally posted by: Darien

Originally posted by: bleeb

Originally posted by: Darien

Originally posted by: bleeb
do we agree that zero is a number? then adding 0.9999... + 0 = a number less than 1. subtracting zero from 0.9999.... also produces something that is less than 1.

Therefore, 0.9999... != 1.

Where is his proof, I'd like to see it.

btw, the second part of your comment is redundant.

What number do you add .9999.... to get 1? There is no such number. So .999.... = 1.

Stop bumping this thread :|

You simply add (IN VERY SIMPLIFIED NOTATION):

0.9999... + (1-0.9999.... ) = 1

You have to understand about sets & different levels of infinity.

lim (x -> infinity) of 1 - 10/x = 1



All .9999 = 1 shows is that representing values in decimal and fraction notation can be odd

To put it simply...:
1/9 = .111...
2/9 = .222...
3/9 = .333...
...
8/9 = .888..

Since 9/9 = 1 = 1/9 + 8/9 = .111... + .888...
logically, since 1+8 = 9, you know addition of such decimals cannot exceed .999...



Edit:
I'm sure someone in this thread has mentioned this argument before. I'm not going to search 900+ posts for it though

You are introducing the discrediting approximation in your proof at 1/9 + 8/9 = .111... + .888.... which still only proves that the notion is confusing.

That was the point of why I wrote that out -- current notation we have in mathematics in representing values is flawed.



lim (x-> infinity) of 1 - 10/x = 1 is the reason why 0.999... = 1

 

[MadRat]

Originally posted by: silverpig
And you also seem to have missed all of RossGr's proofs which don't use limits at all...

Nowhere did he actually prove anything except that he can't distinguish between objective arguments and ones based on subjectives.

 

[AkumaX]

lim (x-> infinity) of 1 - 10/x = 1 is the reason why 0.999... = 1


why 10/x?

 

[hdeck]

.999... != 1

 

[ElFenix]

.9999 != 1

 

[thomsbrain]

do 999 posts equal 1000 posts?

 

[deftron]

no

 

[Darien]

Originally posted by: ElFenix
.9999 != 1

LOL

You simply add (IN VERY SIMPLIFIED NOTATION):

0.9999... + (1-0.9999.... ) = 1

You have to understand about sets & different levels of infinity.

So what you've done is x + (y - x) = y
All you've shown is 0 = 0. it does not prove anything, especially when you're trying to argue against...in this case, x != y
x + (x - x) = x