# Is 0.999...=1 ? **URL:** \ **Category:** Factual Questions\ **Created:** [April 4, 2000, 2:32pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990 "2000-04-04T14:32:00Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [April 4, 2000, 7:08pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/21 "2000-04-04T19:08:00Z")
I should add: Don’t let our use of (limited) symbols obscure their meaning and the meaning of the numbers they represent ---
**Author:** ![KarmaComa](https://avatars.discourse-cdn.com/v4/letter/k/e36b37/32.png) [@KarmaComa](https://boards.straightdope.com/u/KarmaComa)\ **Post date:** [April 4, 2000, 7:09pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/22 "2000-04-04T19:09:00Z")
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 ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [April 4, 2000, 7:11pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/23 "2000-04-04T19:11:00Z")
Indeed. Unusually elegant! I am humbled. ---
**Author:** ![Perderabo](https://avatars.discourse-cdn.com/v4/letter/p/a183cd/32.png) [@Perderabo](https://boards.straightdope.com/u/Perderabo)\ **Post date:** [April 4, 2000, 7:14pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/24 "2000-04-04T19:14:00Z")
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/](http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/) I didn’t think so. ---
**Author:** ![KarmaComa](https://avatars.discourse-cdn.com/v4/letter/k/e36b37/32.png) [@KarmaComa](https://boards.straightdope.com/u/KarmaComa)\ **Post date:** [April 4, 2000, 7:17pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/25 "2000-04-04T19:17:00Z")
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. ---
**Author:** ![Keeves](https://avatars.discourse-cdn.com/v4/letter/k/f05b48/32.png) [@Keeves](https://boards.straightdope.com/u/Keeves)\ **Post date:** [April 4, 2000, 7:18pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/26 "2000-04-04T19:18:00Z")
KarmaComa wrote > [@](#): > > Peep this: there is an infinite number of rational numbers between any two other rational numbers. 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 > [@](#): > > There is an infinitesimal difference between .999999… and 1 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. ---
**Author:** ![MrKnowItAll](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrknowitall/32/87_2.png) [@MrKnowItAll](https://boards.straightdope.com/u/MrKnowItAll)\ **Post date:** [April 4, 2000, 10:02pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/27 "2000-04-04T22:02:00Z")
> [@](#): > > Originally posted by KarlGauss: > \*\*I think you’ve missed the salient point. If 0.999… differs from 1.0, then you must be able to say _by how much it differs_. In fact, there is no number, rational or irrational, that is the difference between 0.999… and 1.0. Given this fact, given that you will be unable to demonstrate by how much 0.999… differs from 1.0, they must be considered identical. > \*\* 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._ ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [April 4, 2000, 10:13pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/28 "2000-04-04T22:13:00Z")
> [@](#): > > Originally posted by Keeves: > Except that **0.999999… is not a specific number.** 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** ---
**Author:** ![Boris\_B](https://avatars.discourse-cdn.com/v4/letter/b/fbc32d/32.png) [@Boris\_B](https://boards.straightdope.com/u/Boris_B)\ **Post date:** [April 4, 2000, 10:16pm UTC](https://boards.straightdope.com/t/is-0-999-1/10990/29 "2000-04-04T22:16:00Z")
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). ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [April 5, 2000, 1:45am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/30 "2000-04-05T01:45:00Z")
> [@](#): > > Originally posted 04-04-2000 11:04 AM by KarmaComa: > You’re still dropping a decimal place. In this instance 9N should be 9.9999…9981. You’re kind of blurring infinity here.\*\* 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 ---
**Author:** ![waterj2](https://avatars.discourse-cdn.com/v4/letter/w/858c86/32.png) [@waterj2](https://boards.straightdope.com/u/waterj2)\ **Post date:** [April 5, 2000, 1:59am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/31 "2000-04-05T01:59:00Z")
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. ---
**Author:** ![kinoons](https://avatars.discourse-cdn.com/v4/letter/k/a698b9/32.png) [@kinoons](https://boards.straightdope.com/u/kinoons)\ **Post date:** [April 5, 2000, 2:08am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/32 "2000-04-05T02:08:00Z")
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 ---
**Author:** ![Surgoshan](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Surgoshan](https://boards.straightdope.com/u/Surgoshan)\ **Post date:** [April 5, 2000, 2:09am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/33 "2000-04-05T02:09:00Z")
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. ---
**Author:** ![Surgoshan](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Surgoshan](https://boards.straightdope.com/u/Surgoshan)\ **Post date:** [April 5, 2000, 2:13am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/34 "2000-04-05T02:13:00Z")
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. ---
**Author:** ![Surgoshan](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Surgoshan](https://boards.straightdope.com/u/Surgoshan)\ **Post date:** [April 5, 2000, 2:18am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/35 "2000-04-05T02:18:00Z")
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. ---
**Author:** ![kinoons](https://avatars.discourse-cdn.com/v4/letter/k/a698b9/32.png) [@kinoons](https://boards.straightdope.com/u/kinoons)\ **Post date:** [April 5, 2000, 2:29am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/36 "2000-04-05T02:29:00Z")
> [@](#): > > Originally posted by Surgoshan: > \*\*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’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 ---
**Author:** ![Silo](https://avatars.discourse-cdn.com/v4/letter/s/ac91a4/32.png) [@Silo](https://boards.straightdope.com/u/Silo)\ **Post date:** [April 5, 2000, 2:33am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/37 "2000-04-05T02:33:00Z")
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. ---
**Author:** ![David\_God\_of\_Frogs](https://avatars.discourse-cdn.com/v4/letter/d/5f9b8f/32.png) [@David\_God\_of\_Frogs](https://boards.straightdope.com/u/David_God_of_Frogs)\ **Post date:** [April 5, 2000, 3:35am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/38 "2000-04-05T03:35:00Z")
> [@](#): > > Originally posted by Silo: > \*\*In the infinite sequence 0.9… > a=.9 and r=.1 > > and S=[a/(1-r)] > > so S=[.9/(1-.1)]=(.9/.9)=1 🙂 > \*\* your point being… ---
**Author:** ![neuro-trash\_grrrl](https://avatars.discourse-cdn.com/v4/letter/n/3ab097/32.png) [@neuro-trash\_grrrl](https://boards.straightdope.com/u/neuro-trash_grrrl)\ **Post date:** [April 5, 2000, 4:10am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/39 "2000-04-05T04:10:00Z")
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. ---
**Author:** ![KarlGauss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/karlgauss/32/3713_2.png) [@KarlGauss](https://boards.straightdope.com/u/KarlGauss)\ **Post date:** [April 5, 2000, 4:19am UTC](https://boards.straightdope.com/t/is-0-999-1/10990/40 "2000-04-05T04:19:00Z")
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. [Previous page](https://boards.straightdope.com/t/is-0-999-1/10990.md?page=1) [Next page](https://boards.straightdope.com/t/is-0-999-1/10990.md?page=3)