I should add: Don’t let our use of (limited) symbols obscure their meaning and the meaning of the numbers they represent
That’s kind of a bullshit answer and I’m sure you know it. I suppose I should just post my own proof to this, which is a little more elegant than all the crap I’ve seen before:
.99999~~ = infinity / (infinity + 1) = 1
Indeed. Unusually elegant! I am humbled.
Um…you guys aren’t just being cute I hope? You actually think that .9 repeating is not another name for 1?
I don’t suppose the sci.math FAQ would help?
http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/
I didn’t think so.
I thought of that and then argued against the proof for a little while longer…
It’s questions like these that make me want to avoid analysis… oh well, I’m taking it in September anyway. My math marks were so low that I had to dredge up competition scores from high school to get into the course. You can probably tell what an arrogant bastard I am. That’s why I’m in comp sci, not math.
KarmaComa wrote
Except that 0.999999… is not a specific number.
In order to be able to place an infinite number of points between two points on a number line, those endpoints have to have a specific location. But .999999… does not have a specific location, because we can at will add more nines to it so that it will be closer to 1 than those points which you are trying to place there.
In other words, if you want to insist that
then fine, you can say it. But since it is an abritrarily infinitesimal difference, I can make it as small as I want, even small enough to exclude the numbers that you are squeezing in.
Ok, I may be in way over my head here, but explain to me why 0.000…1 is not the difference between 1 and 0.999…
Thanks.
God is my co-pilot. Blame Him.
Umm… Yes it is a specific number. That number is 1.
0.99999… is not zero followed by an arbitrary number of nines; it is zero followed by an infinite number of nines.
Also, as Gilligan pointed out, we’ve been here before.
Virtually yours,
DrMatrix
“Feynman was wrong.
I understand Quantum Physics completely.
Anybody seen my drugs?” - WallyM7
I’m with Knowitall. I think there is an expressable difference between 1.0 and 0.999…
I think it is 0.000…1, which I think is an irrational number (since it doesn’t properly terminate or repeat). The thing is, I’m trying to prove that it’s equal to zero, so maybe I’m full of baloney.
Mmmm … baloney (didn’t get lunch today).
Oops. How did you get that for 9N? The 9N comes from 10N - N, so that’s clear. The right side of the equation comes from 9.9999… minus 0.9999…
I’m sure you’d agree that you’ve made a mistake there in saying it would be equal to 9.9999…9981 – hey, that’s gotta be almost ten in anybody’s book.
So, what is 9.9999… minus 0.9999… ? Your opinion.
rocks
Isn’t this what mathematicians came up with limits for? Like 0.999999… is equal to the the limit, as x approaches 1, of x. And I seem to recall that in math, infinitely close isn’t always good enough.
The # one is just that, the # one.
the number 0.9999999… is that.
you can say that the difference between the two dosent matter, and I would say the same thing if I needed change for a $1,000 and the person only had $999.99 Is it the same…no. Is it close enough so that I dont give a damn? Yes
Kinooning it up for 20 years and counting
Yes, .999… is equal to 1. Simple, really. It’s already been proven, several times, and in several different ways, neat, eh?
Oh, and just so you know, 9.999… - .999… is not equal to 9.999…981
9.999-.999 = 9
9.9999-.9999 = 9
9.99999-.99999 = 9
.
.
.
9.999…-.999… = 9
I sold my soul to Satan for a dollar. I got it in the mail.
oops, I was addressing the wrong side of Karma’s comment, silly me. I’ll try again.
Hmm…
9 * ,9 = 8.1
9 * .99 = 8.91
9 * .999 = 8.991
.
.
.
9 * .999… = 8.999…
And you’d have the same problem as before, if you didn’t already have 9.999… - .999… = 9 to show that 8.999… = 9
I sold my soul to Satan for a dollar. I got it in the mail.
Kinoons, there’s a pretty big difference between a string of 5 numbers and an infinitely long string of numbers.
The difference between 1000 and 999.99 is .01, between 1000 and 999.999 it is .001, between 1000 and 999.9999 it is .0001, as the string gets longer, the difference gets smaller. For an infinitely long string, the difference is infinitely small. Infinitely small means zero.
The number one is the number one, the number .999… is .999… However, no one is arguing about that. What people are asking is “are the two distinct?”. The answer is no.
I sold my soul to Satan for a dollar. I got it in the mail.
I’m sorry, but infinitely small does not mean zero. It may be so small that we cannot measure it, but there is still a difference. In any pratical sense, does it matter? Not a chance. But in the most pure sense of the debate there is a difference, we just dont give a damn about it. Nothing we can produce requires the perfection of the measurement or value between 0.999… and 1.000…
Kinooning it up for 20 years and counting
In the infinite sequence 0.9…
a=.9 and r=.1
and S=[a/(1-r)]
so S=[.9/(1-.1)]=(.9/.9)=1 
If at first you don’t succeed you’re about average.
your point being…
I’m a math major! Let me through!
I’m going to put this into layman’s terms for you. There is no difference between .999999… and 1. This is because if you subtract .9 from 1, you get .1. If you subtract .99 from 1, you get .01, a one trailing behind one zero. If you subtract .999 from 1, you get a 1 trailing behind two zeros. So, if you subtract .999999… from 1, you get a 1 trailing behind an infinite number of zeros. Now, imagine a banner with this written on it, if you would. Start at the decimal place, and begin pulling on it. If it were a million zeros, or a billion zeros, or a googolplex zeros we were talking about, eventually, you would reach the one, and the end of the banner. However, with the infinite number of zeros, you could reel in those zeros until Doomsday, and that one would never show up. Thus, .000000…0001 is not close enough to zero as makes no difference, it is zero, plain and simple.
Heck is where you go when you don’t believe in Gosh.
A number of people have asked about a number they represent as 0.000…1 and wonder whether it isn’t the difference between 1.0 and 0.999…
The problem with this is that whereas 0.999… is readily definable and calculatable (just add 0.9 to 0.09 to 0.009 etc), the same can’t be said about 0.000…1 Other than saying “first write down a decimal point followed by an infinite number of 0’s then put a 1”, how else could you give me (or a machine) explicit instructions on how to define or calculate it? I think you can’t. And, if you have to state that an infinite number of 0’s come before the 1, then this “number” represented by 0.000…1 must be indistinguishible from 0 (i.e. the difference between it and 0 is infinitely small), and hence equal to 0.