Is 1 = 0.9999......

[Kyteland]

We're having a debate at work. Is 1=0.99999..... repeating. I say that this holds but one of my coworkers claims that multiplication breaks down for an infinitely repeating number.

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

What do you think?

 

[dullard]

It depends, are you a mathematician or an engineer?

 

[VBboy]

Someone needs to take a programming class and learn about Overflow, Underflow, and Round-off errors (resulting in precision loss) when performing calculations on a machine with limited accuracy.

 

[Fausto]

Originally posted by: dullard
It depends, are you a mathematician or an engineer?

...or a philosopher?

 

[Anubis]

yup it is we proved it in math last semester. just like you did it

 

[Haircut]

Yes it is, and we discussed this ad nauseum in the HT forum a while ago.

 

[Placer14]

You're mean. I remember this...and it also made my brain explode last time. There's a proof that proves you wrong, but I doin't remember it. So, for now, you're right.

 

[notfred]

Originally posted by: VBboy
Someone needs to take a programming class and learn about Overflow, Underflow, and Round-off errors (resulting in precision loss) when performing calculations on a machine with limited accuracy.

This has nothing to do with computers.

 

[slikmunks]

i vote yes.... especially if it's 9.999.............................................................................................

 

[Czar]

1.000000000000000000000000000000000000000000000000000000000000000...... = 1
0.999999999999999999999999999999999999999999999999999999999999999...... ~= 1

just depends how you round it
its like saying that 1/3 is the same as 0.3, which it isnt

 

[Scarpozzi]

The question is moot.

Everyone knows that the only reason anyone rounds is to simplify and answer or to prove an assumption... So the answer to the question is YES....it's both yes and no...

 

[Electrode]

The flaw:

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

After the bold statement, x is considered to be the result of the bold statement, as opposed to 0.9999... as previously assumed, therefore the final statement is 1 = 1.

 

[NTB]

Ever heard the phrase "Close enough for government work"?

Nate

 

[spidey07]

Its been proven many time. Including the proofs and series to go along with it.

Check out the ad nausem post in Highly Technical from 6 months ago.

 

[FrustratedUser]

No, isn't that obvious?

 

[Kyteland]

Originally posted by: Electrode
The flaw:

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

In the bold statement, x is redefined.

How is x redefined?

 

[flood]

1/3 = 0.3333...

1/3 + 1/3 + 1/3 = 1
0.3333... + 0.3333... + 0.3333... = 0.9999...

1 = 0.9999...

 

[bleeb]

Originally posted by: Kyteland
We're having a debate at work. Is 1=0.99999..... repeating. I say that this holds but one of my coworkers claims that multiplication breaks down for an infinitely repeating number.

x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

What do you think?

This proof is WRONG... you already stated that x=0.9999.... so then, since X=0.9999
9 * (0.9999...) != 9
x != 1.

Therefore: X = 0.9999... != 1

MORON. Jus playing =) Happy Doodles!

 

[spidey07]

LOL!!

15 people voted no.

 

[Lonyo]

If 10x - x gives us 9, then 9 = 9x.
If we multiply x by 9, does it equal 9? Only if x is 1 exactly, otherwise 9x doesn't equal 9.
9 x 0.99.... = 9? I don't see how really. Surely it would be 8.9999.....
The only way I see of getting 9 useing 9 is by 9 x 1

 

[Haircut]

Originally posted by: Czar
1.000000000000000000000000000000000000000000000000000000000000000...... = 1
0.999999999999999999999999999999999999999999999999999999999999999...... ~= 1

just depends how you round it
its like saying that 1/3 is the same as 0.3, which it isnt

This has nothing to do with rounding, approximate answers or anything like that.
0.999.... is the same number as 1.

There are other ways to prove it that the one shown here, but it doesn't change the fact that they are two ways of writing the same number.

 

[Kyteland]

Originally posted by: spidey07
Its been proven many time. Including the proofs and series to go along with it.

Check out the ad nausem post in Highly Technical from 6 months ago.

Link? I couldn't find it...

 

[bleeb]

Originally posted by: flood
1/3 = 0.3333...

1/3 + 1/3 + 1/3 = 1
0.3333... + 0.3333... + 0.3333... = 0.9999...

1 = 0.9999...

You're WRONG TOO.

1/3 is an exact answer

0.3333... is an approximation

Therefore,

1 != 0.9999

 

[Orsorum]

Yes and no. For all intents and purposed, 0.999999.... is 1. (0.9999999... eventually converges to 1)

 

[flood]

Originally posted by: bleeb

Originally posted by: flood
1/3 = 0.3333...

1/3 + 1/3 + 1/3 = 1
0.3333... + 0.3333... + 0.3333... = 0.9999...

1 = 0.9999...

You're WRONG TOO.

1/3 is an exact answer

0.3333... is an approximation

Therefore,

1 != 0.9999

1/3 and 0.3333... are the same.
do the long division and you'll see.