0.9999999999.... vs 1?

[COMMUNIST FLISK]

so... are they equal? (this is a revival of the old forum thread)
lets reach a conclusion properly this time lols.

 

[Ozymandyus]

Most certainly!

 

[COMMUNIST FLISK]

Aye!

 

[Counterpoint]

so... are they equal? (this is a revival of the old forum thread)
lets reach a conclusion properly this time lols.

Thank you for reviving my old thread. I appreciate it.

Back on topic, they are equal.

 

[COMMUNIST FLISK]

post some proof for the non believers my friend!

Thank you for reviving my old thread. I appreciate it.

Back on topic, they are equal.

no problem, im suprised no one else had

 

[blinddesign]

the answer's yes... and it's "definitely".

1/3=0.3r

(0.3r)x3=0.9r

(1/3)x3=1

.'.0.9r=1

or
X=1/3
X=0.3r
3X=0.9r
3X=1

 

[Aught3]

I thought this was sorted out on the last forum, proofs were posted and explanations given. If anyone isn't sure we could just redirect them there.
http://leagueofreason.forums-free.com/does-999-repeating-equal-1-0-merged-with-1-3-t484.html

 

[COMMUNIST FLISK]

I thought this was sorted out on the last forum, proofs were posted and explanations given. If anyone isn't sure we could just redirect them there.
http://leagueofreason.forums-free.com/does-999-repeating-equal-1-0-merged-with-1-3-t484.html

-_- theres 2 reasons i restarted this thread

1) new people who have joined might want to post, and two, the discussion still wasnt over at that point, not properly anyway, dont be so lazy

 

[Master_Ghost_Knight]

Lets just recap the proofs.
1.

Let's do the following mechanism to construct .9999999"¦.., i.e. .9+.09+.009+"¦"¦. ad infinitum.
This is the same as 9x0.1+9x0.01+9x.001+"¦ ad infinitum
which is the same as 9x0.1+9x0.1^2+9x0.1^3+"¦ ad infinitum
which is the same as

2.

Take the following equation:

now replace 0.999(9) whit x

 

[nasher168]

But surely o.999 recurring is 0.00 recurring-with-a-one-perched-on-the-"end" less than 1.
That makes no sense to us humans with our brains unable to comprehend infinity, but why should that make it untrue.


DISCLAIMER: The above comment came from a person with no mathematical expertise past GCSE level and as such may be completely ignored.

 

[Whisperelmwood]

I'm with nasher168 ..

but again, I've never had any truck with math. I failed GCSE math twice >>

 

[GoodKat]

But surely o.999 recurring is 0.00 recurring-with-a-one-perched-on-the-"end" less than 1.

.0 repeating infinitely with a 1 at the end is 0

 

[PuppetXeno]

There's no way of notation:

1 - 0.999999(9) = 0.0(0)1 ?

then how much is 0.0(0)1 / 2 ?

0.0(0)05 ? errr technically would be the same as 0.0(0)5 because the 0 repeats so adding another afterwards is redundant.

and how much is 0.0(0)5 * 2 ?

0.0(0,? ? ? -1 ? ? ? ) 1 errrrrrr

It's not only pointless to discriminate an infinitely small difference... Infinitely small is non existant.

 

[Master_Ghost_Knight]

People very often make the mistake on thinking that there is such a thing as an imediatly close number. There are no emidiatly close numbers. R is a continuum, no matter what 2 diffrent numbers you can come up whit there is allways an infinite ammount of numbers that you can put in the midle.

 

[diagoras54]

Statistically speaking, 0.99999 repeating equals 1, but the probability of being wrong is the basis of scientific theory. If we could be absolutely certain of our accuracy we could call evolution and gravity "facts". Instead, "theory" implies that that our understanding is always open to new information, and that there's always a chance of being wrong. That probability is so low that we can confidently call them facts, but no matter how certain we are, no matter how close to 1 we get, we can never reach it.

 

[Aught3]

It's not just statistically speaking, there is no difference between 0.999... and 1. If there was a difference there should be some (non-zero) number that you could subtract from 1 to give 0.999... There is no such number, 1 and 0.999... have identical numerical values.

Wait seven people have voted no so far, wtf?

 

[diagoras54]

It's not just statistically speaking, there is no difference between 0.999... and 1. If there was a difference there should be some (non-zero) number that you could subtract from 1 to give 0.999... There is no such number, 1 and 0.999... have identical numerical values.

Wait seven people have voted no so far, wtf?

I agree, but you can also look at it from the perspective of limits, with 0.99999 repeating infinitely getting closer to, but never reaching, 1. From that view, 0.999999 repeating can never equal 1.

 

[Aught3]

Yes it does equal one, if you have an infinite number of nines then you are at the limit.

Let me ask you a question, what do you think the decimal form of 1/3 is?

 

[diagoras54]

Yes it does equal one, if you have an infinite number of nines then you are at the limit.

Let me ask you a question, what do you think the decimal form of 1/3 is?

Not so. You can't reach a limit; that's the point. If you draw it graphically the parabola gets infinitely closer to 1 but can never reach it. It's like dividing a number in half repeatedly: 1/2, 1/4, 1/8, 1/16, etc. You can continue dividing in half infinitely. http://en.wikipedia.org/wiki/Asymptote
Clearly it's 0.33333 repeating, but I suspect a trap...

 

[IBSpify]

Let me ask you a question, what do you think the decimal form of 1/3 is?

There is no 100% accurate way to write 1/3 in decimal form, much like there is no 100% accurate way to write pi in decimal form, so you have to round it off and stop at some point