NightCrawler
02-13-2006, 07:46 AM
I can't accept this thought: "Infinitely small quantities don't matter."

Some of you may have heard/read this.

.999~ = 1

Proof??

1} n = .999~ (tilde denoting infinite progression)
2} n * 10 = .999~ * 10
3} 10n = 9.999~
4} 10n - n = 9.999~ - n [.999~....]
5} 9n = 9.000
6} 9n / 9 = 9 / 9
7} n = 1

n = 1 AND n =.999~ ??

Even though I gave the proof, I cannot accept the conclusion.

My largest problem lies in lines 2-5. (multiplying by 10, and subtracting .999~) I cannot accept omitting quantities because we cannot compute infinite numbers.

NightCrawler
02-13-2006, 07:48 AM
By the problems I mean that when you multiply .999~ by 10, you don't get 9.999~

Then subtracting n from 9.999~...

skynes
02-13-2006, 07:57 AM
9n is in fact 8.999999999~1

yeah there's a one on the end.

Get a calculator. Multiple .9999999 by 9 and you will get

8.9999991

It will always be one short of hitting 9.

Because.

At the end of infinity, there will be a 9. Which is one short of 10 so every time you increase N by N, it's actualy
N - 0.00000000000000000000000001

so

N = .9999999999999999 ~9
2N = 1.999999999999999 ~8
3N = 2.999999999999999 ~7
4N = 3.999999999999999 ~6
~
~
9N = 8.999999999999999 ~1

therefore
10N = 9.99999999999999~0

It's that Zero at the end which blows it all over.

0-9 = negative 1

so
9N = 8.999999 ~ 1

And that is the error in the Equation.

petrameansrock
02-13-2006, 11:25 AM
....ummm okay.....

terrasin
02-13-2006, 11:57 AM
Even though I gave the proof, I cannot accept the conclusion.
Doesn't it just seem like some scientist just created all that hogwash (2-5) off the top of his head just to win a bet?

.9999~ will always be 1 step short of being 1, reguardless of the math...

CJ

aliengurl7
02-13-2006, 11:59 AM
I can't accept this thought: "Infinitely small quantities don't matter."

Some of you may have heard/read this.

.999~ = 1

Proof??

1} n = .999~ (tilde denoting infinite progression)
2} n * 10 = .999~ * 10
3} 10n = 9.999~
4} 10n - n = 9.999~ - n [.999~....]
5} 9n = 9.000
6} 9n / 9 = 9 / 9
7} n = 1

n = 1 AND n =.999~ ??

Even though I gave the proof, I cannot accept the conclusion.

My largest problem lies in lines 2-5. (multiplying by 10, and subtracting .999~) I cannot accept omitting quantities because we cannot compute infinite numbers.


Nightcrawler... get some sleep. :)

amodman
02-13-2006, 02:25 PM
It's not that they don't matter, per se. It's that, we don't care, lol. ;)

disciple
02-13-2006, 02:51 PM
Doesn't it just seem like some scientist just created all that hogwash (2-5) off the top of his head just to win a bet?
Yes. [/end response]

Nightcrawler... get some sleep. :)
I agree with her. :P

agent_c68
02-13-2006, 06:20 PM
Extremely small quantities usually don't matter. Scale is usually the reason.

For example, you are trying to figure out how long something needs to be, you get some number like 42.000000548247 inches. Would that .000000548247 really matter in a real world situation?

But if you were working on a microscopic scale, then .0005478 inches would matter.

so it depends on the situation, although I have thought that proof was kind of ackward.

korey_cooper_jr
02-13-2006, 06:23 PM
All I know is that it matters in Pre-Cal, or else we get a huge, red, bloody "Incorrected!!!!" X on our paper :(

Unregistered
02-13-2006, 06:45 PM
All I know is that it matters in Pre-Cal, or else we get a huge, red, bloody "Incorrected!!!!" X on our paper :(

In mathmatical Theory, small numbers matter unless you are suposed to round. even then, rounding is one of the last steps.

In Real world Practice, you round all the time within reasonable limits.

cloroxmartini
02-13-2006, 08:30 PM
This comes into play when you start to take the limits of equations.

NightCrawler
02-14-2006, 07:36 AM
Ah, but you guys... the people that presented the proof to me were convinced that .999~ EQUALS 1, not 'if you round it off'... because that is obvious. Not that the number didn't 'matter', they were saying that it just IS 1, because the quantity is infinitely small.

terrasin
02-14-2006, 09:26 AM
We actually got into a big discussion about this one night while bored. I still fail to see how .999~ equals 1 though some were trying to do the math, it just didn't ADD up. Har Har. :P

CJ

sky_flashings
02-14-2006, 11:20 AM
...so...dizzy...

skynes
02-15-2006, 01:36 AM
http://www.panheads.org/boards/showpost.php?p=242904&postcount=3

I believe I had the answer to it here.

NightCrawler
02-15-2006, 07:48 AM
Heh, yes, Scottie. I'll give my friends the re-proof... can't believe I didn't throw that at them.