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» The Geek Culture Forums!   » Techno-Talking   » Math-a-holics and Code Junkies   » I must find out. (Page 1)

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Author Topic: I must find out.
Tiroth
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Icon 1 posted February 05, 2008 10:52      Profile for Tiroth   Author's Homepage         Edit/Delete Post   Reply With Quote 
After much thought and experimentation, I've decided to ask those who are experts at math. This has been bothering me since I was 9. I believe .999 repeating = infinity. Here are two basic experiments I've conducted with infinity.

Lets break down .999...
You see .9 and instantly understand what is below, what is above, and what is equal.

Then you see .99 and and 9 hundreths to that length.

then you see .999 and add 9 thousanths to that length.

If this goes on forever, won't
.999 repeating > 1 eventually? In math, we're used to having one number be a specific point, but repeating numbers destroy that.

Here is another experiment I counducted when I was ~10.

I was trying to reach 0 by subtracting half of the number before it. Look here

1
.5
.25
.125
.0625
.03125
ect.

I eventually concluded that it is impossible to get to 0 that way. It will go on into infinitely smaller numbers.

What do you all think of .999 repeating being equal to or greater than 1?

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Life is neither a good nor an evil; it is simply the place where good and evil exist.

-Seneca

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Ashitaka

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Icon 1 posted February 05, 2008 11:05      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
mathhmatically 0.999999 -> infinity is not one.

I deal with this daily. If I test something, I can never say that it is completly pure(purity =1) I can only say that the purity equals the LOQ(level of quantification) of my test (purity = 0.99 or 0.999. So in that sense 0.999 never equals 1.

But in reality it doesn't matter. If I can prove that a substance is 0.999999 percent pure(or 1 ppb impure), even if that remaining percentage is something extremly dangerous, say CN, it doesn't matter and we can aprove the substance for human use. In that sense 0.9999 is close enough to be considered 1. (As normally you are not allowed to inject cyanide into humans.)

There is the age old joke about the differce between mathmatician and an engineer in which an engineer and a mathmatician are allowed to haif thier distance bewtween them and the woman of thier desire every day. The mathmatician gives up on the first day because he knows he will never reach the woman, halfing the distance between them every day. The engineer doesn't give up because while he knows he will never reach the woman, he knows at a certain point it won't matter and he'll be close enough for what he wants.

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Tiroth
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Icon 1 posted February 05, 2008 11:11      Profile for Tiroth   Author's Homepage         Edit/Delete Post   Reply With Quote 
But if you look at it one digit at a time and it gets bigger with every little digit, wouldn't it eventually surpass 1? And likewise, if something goes on forever, how can we give it a definitive point on a number line?

--------------------
Life is neither a good nor an evil; it is simply the place where good and evil exist.

-Seneca

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The Famous Druid

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Icon 1 posted February 05, 2008 11:18      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by Tiroth:
But if you look at it one digit at a time and it gets bigger with every little digit, wouldn't it eventually surpass 1? And likewise, if something goes on forever, how can we give it a definitive point on a number line?

Every successive 9 reduces its distance from 1 by a factor of 10

code:
x_________1-x
0.9 0.1
0.99 0.01
0.999 0.001
0.9999 0.0001

So, it gets closer and closer to 1, but never gets there.

--------------------
If you watch 'The History Of NASA' backwards, it's about a space agency that has no manned spaceflight capability, then does low-orbit flights, then lands on the Moon.

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Ashitaka

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Icon 1 posted February 05, 2008 11:24      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by Tiroth:
But if you look at it one digit at a time and it gets bigger with every little digit, wouldn't it eventually surpass 1? And likewise, if something goes on forever, how can we give it a definitive point on a number line?

No, because the way I see it, you are adding exponentially less every time. You may see this as adding anouther number, I see it as adding a much smaller number every time.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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Tiroth
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Icon 1 posted February 05, 2008 11:31      Profile for Tiroth   Author's Homepage         Edit/Delete Post   Reply With Quote 
Thanks for clearing this up for me a bit, I see how it being infinitely close to one could be close enough to be = in some peoples' minds.

--------------------
Life is neither a good nor an evil; it is simply the place where good and evil exist.

-Seneca

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Tiroth
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Icon 1 posted February 05, 2008 12:03      Profile for Tiroth   Author's Homepage         Edit/Delete Post   Reply With Quote 
Can someone help me win this argument now? I know .999 does not = 1.

http://forums.worldofwarcraft.com/thread.html?topicId=2288079708&pageNo=7&sid=1#120

--------------------
Life is neither a good nor an evil; it is simply the place where good and evil exist.

-Seneca

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Richard Wolf VI
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Icon 10 posted February 05, 2008 12:12      Profile for Richard Wolf VI   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
I beg to differ.

Let x = 0.999...

0.999... * (10 - 1) = x * ( 10 - 1 )
0.999... * 10 - 0.999... = 9 * x
9.999... - 0.999... = 9 * x
9 = 9 * x
1 = x

By transitive property 1 = 0.999...

Or even nicer:

1/9 = 0.111...
2/9 = 0.222...

If you get it: (1/9)*9 = 9/9 = 0.999...

But 9/9 = 1. Therefore 1 = 0.999...

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Ashitaka

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Icon 1 posted February 05, 2008 12:12      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
Sorry in advanced to anybody that has a mentally handicapped (differentially abled) relative or freind.


DO NOT READ FURTHER


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Arguing on the internet is like competing in the special olympics.

Even if you win, you are still retarded.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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Tiroth
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Icon 1 posted February 05, 2008 12:15      Profile for Tiroth   Author's Homepage         Edit/Delete Post   Reply With Quote 
This is an intelligent argument though, it is not saying

LAWL I RIGHT U WRONG NUB LOL

They are making valid arguments.

Edit: Start from page 1, these last ones aren't as good.

--------------------
Life is neither a good nor an evil; it is simply the place where good and evil exist.

-Seneca

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dragonman97

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Icon 1 posted February 05, 2008 12:19      Profile for dragonman97   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
All of the above is Zeno's Paradox.

.9[ad-infinitum] will NEVER be greater than one, but it will get very close to being one.

Halving one will never get to zero, but will get exceptionally close.

For the exceptionally lazy, I've Googled for the Wikipedia article:
http://en.wikipedia.org/wiki/Zeno's_paradoxes

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There are three things you can be sure of in life: Death, taxes, and reading about fake illnesses online...

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Ashitaka

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Icon 1 posted February 05, 2008 12:19      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by iWanToUseaMac:
I beg to differ.

Let x = 0.999...

0.999... * (10 - 1) = x * ( 10 - 1 )
0.999... * 10 - 0.999... = 9 * x
9.999... - 0.999... = 9 * x
9 = 9 * x
1 = x

By transitive property 1 = 0.999...

Or even nicer:

1/9 = 0.111...
2/9 = 0.222...

If you get it: (1/9)*9 = 9/9 = 0.999...

But 9/9 = 1. Therefore 1 = 0.999...

Both of your derivations are mathmatically flawed. In the first you perform an operation that is not allowed. In the second your logic is flawed.

These both are well know tricks of mathmatics to confuse neophytes. I have seen these tricks may times. I have never been tricked, not even when I was young and had never seen them before.


I would hope that anybody that has graduated from high school (secondary education of your state) would see through simple math tricks like these but the lottery and the american loan system is proof enough that less educated people are easily tricked when it comes to math.

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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Tiroth
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Icon 1 posted February 05, 2008 12:21      Profile for Tiroth   Author's Homepage         Edit/Delete Post   Reply With Quote 
Oh crap, I infected us with the WoW OT forums.

--------------------
Life is neither a good nor an evil; it is simply the place where good and evil exist.

-Seneca

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The Famous Druid

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Icon 1 posted February 05, 2008 12:30      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
Changed my mind, best not to get into this one.

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Richard Wolf VI
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Icon 10 posted February 05, 2008 12:31      Profile for Richard Wolf VI   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
DMan gave me a great idea: Wikipedia!

Ashitaka; is it illegal to make operations between real numbers? Not like if I were dividing by zero somewhere [Geek]

Remember: I'm the Math geek here, OK? [crazy]

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The same old iWanToUseaMac... Who am I fooling? I'm getting a Wii now, iWanToUseaMac isn't :P
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Metasquares
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Icon 1 posted February 05, 2008 12:43      Profile for Metasquares   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
There exists some infinitesimal epsilon (and I mean it in the mathematical sense of the term "infinitesimal") such that .9 repeating = 1 +- epsilon.

It starts out just "good enough", but being an infinitesimal, epsilon eventually disappears, which makes the equation exact.

If you're going to consider .3 repeating 1/3, however, I can't see how you can avoid calling .9 repeating 1. It is, after all, exactly 3 times the number you just called 1/3.

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Ashitaka

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Icon 1 posted February 05, 2008 12:54      Profile for Ashitaka     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by iWanToUseaMac:
DMan gave me a great idea: Wikipedia!

Ashitaka; is it illegal to make operations between real numbers? Not like if I were dividing by zero somewhere [Geek]

Remember: I'm the Math geek here, OK? [crazy]

quote:
0.999... * (10 - 1) = x * ( 10 - 1 )
0.999... * 10 - 0.999... = 9 * x

this is what is not allowed

--------------------
"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"

-Assif Mandvi

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Cap'n Vic

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Icon 1 posted February 05, 2008 13:51      Profile for Cap'n Vic     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by Ashitaka:

Arguing on the internet is like competing in the special olympics.

Even if you win, you are still retarded.

That line is almost as old as you mothers vagina.
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maximile

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Icon 1 posted February 05, 2008 16:25      Profile for maximile   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
If Wikipedia says it's equal to 1 (and the page is well-established), then that's good enough for me. I'd never imagined it could be anything else.
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dragonman97

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Icon 1 posted February 05, 2008 17:33      Profile for dragonman97   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by maximile:
If Wikipedia says it's equal to 1 (and the page is well-established), then that's good enough for me. I'd never imagined it could be anything else.

/me questions Wikipedia when it comes to something like that...wonder if it was edited by people who don't know better...

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MacManKrisK

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Icon 1 posted February 05, 2008 18:39      Profile for MacManKrisK     Send New Private Message       Edit/Delete Post   Reply With Quote 
My own proof that .999... = 1
------------------------------

1/3 = .333...

.333... * 3 = .999...
1/3 * 3 = 1
therefore .999... = 1

There you go, mathematics is fundamentally flawed! [crazy]

--------------------
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get rich and you still die"


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Metasquares
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Icon 1 posted February 05, 2008 19:11      Profile for Metasquares   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by MacManKrisK:
My own proof that .999... = 1
------------------------------

1/3 = .333...

.333... * 3 = .999...
1/3 * 3 = 1
therefore .999... = 1

There you go, mathematics is fundamentally flawed! [crazy]

I don't see the flaw. It's no weirder than saying 2 == -1 (mod 3).
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GrumpySteen

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Icon 1 posted February 05, 2008 19:20      Profile for GrumpySteen     Send New Private Message       Edit/Delete Post   Reply With Quote 
Here's the problem with far more people's logic than I would have expected at GC:
"0.999..." is not equal to infinity. Infinity is defined mathematically as numberless value and is sometimes treated as a property or a limit which can be approached, but -never- expressed as a number (and not even as an equation... I'm scowling at whomever is the first person that goes to type 1/0). Go look it up if you don't believe me.

... and airplanes have no problem taking off from a converyor belt [Razz]

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Metasquares
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Icon 1 posted February 05, 2008 19:47      Profile for Metasquares   Author's Homepage     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by dragonman97:
quote:
Originally posted by maximile:
If Wikipedia says it's equal to 1 (and the page is well-established), then that's good enough for me. I'd never imagined it could be anything else.

/me questions Wikipedia when it comes to something like that...wonder if it was edited by people who don't know better...
The proofs make sense. In particular, viewing it as a convergent infinite series is a very interesting (and quite rigorous) way to argue it.
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The Famous Druid

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Icon 1 posted February 05, 2008 20:07      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
Of course, the really important mathematical question is...

... what do you get when you multiply six by nine?

--------------------
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