# .99999999 equal to 1 ??? **URL:** \ **Category:** Factual Questions\ **Created:** [August 15, 2001, 11:42pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468 "2001-08-15T23:42:36Z")\ **Posts on this page:** 20\ **Page:** 6
**Author:** ![Evno](https://avatars.discourse-cdn.com/v4/letter/e/c68b51/32.png) [@Evno](https://boards.straightdope.com/u/Evno)\ **Post date:** [August 17, 2001, 3:41am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/101 "2001-08-17T03:41:17Z")
> [@](#): > > _Math Buffoonery Buffoons say, “.99999… = 1.”_ In the words of an unknown picketer’s sign from an episode of the Simpsons: ``` **You Are Making None Sense!** ``` ---
**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:** [August 17, 2001, 4:43am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/102 "2001-08-17T04:43:57Z")
> [@](#): > > _Originally posted by_\*\* Evno \* > What I would like to ask now, to the Mathematic persons here, is: > > 1. Do you consider .999999… to be infinite? > 2. Do you consider 1 to be infinite? 1. Humph. This is too easy. 0.999… is non-negative. We disagree as to whether it is equal to 1 or not, but I think we all agree that 0.999… is less than or equal to 1. Therefore, it is some number in the closed interval [0,1]. So it is finite. 2. 1 is finite by the same argument. 0.999… is _not_ infinite. It is the limit of a sum as the number of terms goes to infinity. If you look at the epsilon definition of a limit at infinity, you will see that there is no actual infinity in the definition. While there is nothing wrong with saying infinity is a number, here it is not used as a number, but rather as a formal symbol. If you use the definition to determine the value of 0.999…, you will discover (without using infinity) that the value is exactly equal to one. I’ve got two questions: 1. Does 0 = 1-1? After all the left side has one symbol - 0, while the right side has three symbols. 2. Does 1/3 = 0.333… If not, does 1/3 have a decimal representation? * * * Virtually yours, **DrMatrix** — If I’ve told you once, I’ve told you 0.999… times. ---
**Author:** ![SPOOFE](https://avatars.discourse-cdn.com/v4/letter/s/c5a1d2/32.png) [@SPOOFE](https://boards.straightdope.com/u/SPOOFE)\ **Post date:** [August 17, 2001, 5:10am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/103 "2001-08-17T05:10:13Z")
> [@](#): > > Because the mathematical proof is beside the point. On the contrary. The mathematical proof is the only way to look at this. ---
**Author:** ![Evno](https://avatars.discourse-cdn.com/v4/letter/e/c68b51/32.png) [@Evno](https://boards.straightdope.com/u/Evno)\ **Post date:** [August 17, 2001, 5:24am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/104 "2001-08-17T05:24:06Z")
says who? Math? There are many things math can’t explain: 22/7, infinity, life, why some people hold automatic doors open (thinking it’s courteous), where my keys are, my incessant uneducated posts… Can’t infinity be an abstract idea? Let’s not apply it to math, it just causes problems. ---
**Author:** ![23skidoo](https://avatars.discourse-cdn.com/v4/letter/2/f04885/32.png) [@23skidoo](https://boards.straightdope.com/u/23skidoo)\ **Post date:** [August 17, 2001, 5:47am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/105 "2001-08-17T05:47:26Z")
> [@](#): > > \*Originally posted by Evno \* > \*\*says who? Math? There are many things math can’t explain: > > 22/7, infinity, life, why some people hold automatic doors open (thinking it’s courteous), where my keys are, my incessant uneducated posts… > > Can’t infinity be an abstract idea? Let’s not apply it to math, it just causes problems. \*\* Math can’t explain 3 1/7? ---
**Author:** ![Evno](https://avatars.discourse-cdn.com/v4/letter/e/c68b51/32.png) [@Evno](https://boards.straightdope.com/u/Evno)\ **Post date:** [August 17, 2001, 6:00am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/106 "2001-08-17T06:00:03Z")
nope. ---
**Author:** ![mangeorge](https://avatars.discourse-cdn.com/v4/letter/m/d78d45/32.png) [@mangeorge](https://boards.straightdope.com/u/mangeorge)\ **Post date:** [August 17, 2001, 7:10am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/107 "2001-08-17T07:10:09Z")
> [@](#): > > \*Originally posted by Evno \* > \*\*nope. \*\* You and you’re ‘pie in the sky’ notions. 😉 Peace, mangeorge ---
**Author:** ![SPOOFE](https://avatars.discourse-cdn.com/v4/letter/s/c5a1d2/32.png) [@SPOOFE](https://boards.straightdope.com/u/SPOOFE)\ **Post date:** [August 17, 2001, 8:07am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/108 "2001-08-17T08:07:47Z")
> [@](#): > > says who? Math? There are many things math can’t explain: And .999…=1, apparently, isn’t one of those things. ---
**Author:** ![kabbes](https://avatars.discourse-cdn.com/v4/letter/k/e99b99/32.png) [@kabbes](https://boards.straightdope.com/u/kabbes)\ **Post date:** [August 17, 2001, 11:01am UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/109 "2001-08-17T11:01:48Z")
I can’t believe that this thread has reached three pages and nobody has simply suggested to **kinoons** that he expand in base 12 instead… pan ---
**Author:** ![El\_Zagna](https://avatars.discourse-cdn.com/v4/letter/e/d2c977/32.png) [@El\_Zagna](https://boards.straightdope.com/u/El_Zagna)\ **Post date:** [August 17, 2001, 1:04pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/110 "2001-08-17T13:04:01Z")
> [@](#): > > \*Originally posted by kabbes \* > **I can’t believe that this thread has reached three pages and nobody has simply suggested to kinoons that he expand in base 12 instead…** I can’t believe thst thread has reached three pages, period! Only on the SDMB would you get this much response from such an apparently simple question. Wow! ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [August 17, 2001, 1:20pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/111 "2001-08-17T13:20:41Z")
> [@](#): > > \*Originally posted by Evno \* > \*\*Can’t infinity be an abstract idea? Let’s not apply it to math, it just causes problems. \*\* Infinity is an abstract mathematical idea. It’s just not one that’s as simple as you like to think it is. Remember, there are as many even integers as there are integers. ---
**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\ **Post date:** [August 17, 2001, 1:24pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/112 "2001-08-17T13:24:54Z")
> [@](#): > > \*Originally posted by kinoons \* > Because the mathematical proof is beside the point. The only way to write 1 is 1. Good grief, **kinoons**. This is a _mathematical_ question, with a provable answer (“yes” is the answer), and the proof _is_ the point. There’s no real debate here; the question’s been answered repeatedly already. Yet, you continue to maintain that “the only way to write 1 is 1” _even though that statement has already been shown to be false!_ Look, just to be clear, is there any type of evidence at all, showing that 0.9rep = 1.0, that you would accept? ---
**Author:** ![kinoons](https://avatars.discourse-cdn.com/v4/letter/k/a698b9/32.png) [@kinoons](https://boards.straightdope.com/u/kinoons)\ **Post date:** [August 17, 2001, 6:42pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/113 "2001-08-17T18:42:59Z")
> [@](#): > > \*Originally posted by zut \* > \*\* > > > [@](#): > > > > \*Originally posted by kinoons \* > > Because the mathematical proof is beside the point. The only way to write 1 is 1. > > Good grief, **kinoons**. This is a _mathematical_ question, with a provable answer (“yes” is the answer), and the proof _is_ the point. There’s no real debate here; the question’s been answered repeatedly already. Yet, you continue to maintain that “the only way to write 1 is 1” _even though that statement has already been shown to be false!_ > > Look, just to be clear, is there any type of evidence at all, showing that 0.9rep = 1.0, that you would accept? \*\* Okay, I understand the proofs, I’ve even managed to follow through them and they make some sense to me…here is my disconnect… Just as no two particles of matter cannot occupy the same space at the same time, no two numbers can be at the same point of the numberline at the same time. Even though the math can be manipulated to show that 0.999… can equal 1, I have a logical disconnect on how any number except one can be one. It is like when (excuse me if my terminology is a little off, it has been a while since a formal math class) if you have a quadratic equation, and one of the possible values of X does not make sense, it is thrown out. Even though the proof can be manipulated to be true, does it truly make sense? How can anything equal one but one? ---
**Author:** ![JCThunder](https://avatars.discourse-cdn.com/v4/letter/j/dc4da7/32.png) [@JCThunder](https://boards.straightdope.com/u/JCThunder)\ **Post date:** [August 17, 2001, 7:05pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/114 "2001-08-17T19:05:51Z")
No, it does not equal 1. End of story. Let it die. 3 pages too long. ---
**Author:** ![mangeorge](https://avatars.discourse-cdn.com/v4/letter/m/d78d45/32.png) [@mangeorge](https://boards.straightdope.com/u/mangeorge)\ **Post date:** [August 17, 2001, 7:09pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/115 "2001-08-17T19:09:52Z")
> [@](#): > > \*Originally posted by bnorton \* > \*\* > > > [@](#): > > > > \*Originally posted by kabbes \* > > **I can’t believe that this thread has reached three pages and nobody has simply suggested to kinoons that he expand in base 12 instead…** > > I can’t believe thst thread has reached three pages, period! Only on the SDMB would you get this much response from such an apparently simple question. Wow! \*\* The problem is, **Bill** , that it’s _not_ that simple. that’s why the thread has gone so long. Kinda like argueing the existence of god. The proof is right there, in the book. Obvious to anyone who believes. But when taken outside their own proofs, both .9999… as 1 and the existence of god fall to ordinary logic. As long as you keep having 9’s, which you must, there’ll never be a 1. Except in math. 😉 Peace, mangeorge ---
**Author:** ![The\_Hamster\_King](https://avatars.discourse-cdn.com/v4/letter/t/8edcca/32.png) [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)\ **Post date:** [August 17, 2001, 7:54pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/116 "2001-08-17T19:54:29Z")
> [@](#): > > \*Originally posted by kinoons \* > Just as no two particles of matter cannot occupy the same space at the same time, no two numbers can be at the same point of the numberline at the same time. Even though the math can be manipulated to show that 0.999… can equal 1, I have a logical disconnect on how any number except one can be one. > \*\* Do you have the same problem believing that .333… = 1/3? ---
**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\ **Post date:** [August 17, 2001, 8:10pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/117 "2001-08-17T20:10:47Z")
> [@](#): > > \*Originally posted by kinoons \* > …here is my disconnect… > I have a logical disconnect on how any number except one can be one. OK, how about this: 1. Do you agree that every number on the real number line must have an exact, although possibly infinite (and possibly non-repeating!), decimal representation? 2. If your answer to number 1 is “no”, can you give an example of a number that does not have an exact decimal representation, and why you think so? 3. If your answer to number 1 is “yes”, would you agree that the decimal representation of 1/3 is 0.3rep (i.e., 1/3 = 0.3rep)? 4. If your answer to number 3 is “no”, can you tell me what _is_ the decimal representation of 1/3? 5. If your answer to number 3 is “yes”, would you agree that I can multiply both sides of the equation in question 3 to get 3/3 = 0.9rep? 6. If your answer to number 5 is “no”, then can you tell me: does 3_1/3 not equal 3/3? Does 3_0.3rep not equal 0.9rep? What is the problem? 7. If your answer to number 5 is “yes”, do you agree that 3/3 = 1? And thus 1 = 0.9rep? I’m suspecting here that you’ll agree with number 1 and disagree with number 6, but I’d like to know just _where_ the logical disconnect occurs. And, then as an additional question: 8. You keep repeating that no number except one can be one. Are you comfortable with representing 1 as (3-2)? As 12[sup]0[/sup]? As 3/3? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [August 17, 2001, 8:18pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/118 "2001-08-17T20:18:38Z")
> [@](#): > > \*Originally posted by mangeorge \* > **…both .9999… as 1 and the existence of god fall to ordinary logic.** “Ordinary logic” here seems to mean asserting that whatever you don’t like is false. That has no place in mathematics. Now, if you want to claim that, in the real world, no matter how many 9’s you put after the decimal point, you’ll never get to one, then I’ll agree with you. If there are only a finite number of 9’s (which is all you can get in the real world), then it’s not equal to 9. But as soon as you have an infinite number of 9’s, you do have 1. The take-home lesson is that strange things happen when infinities are introduced into the mix. ---
**Author:** ![kinoons](https://avatars.discourse-cdn.com/v4/letter/k/a698b9/32.png) [@kinoons](https://boards.straightdope.com/u/kinoons)\ **Post date:** [August 17, 2001, 8:20pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/119 "2001-08-17T20:20:45Z")
I am not comfortable saying that saying 3-2 is the same thing as saying one. I am comfortable saying that when you perform the operation 3-2 the result is one. It still comes down to the only thing that equals one is one. ---
**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\ **Post date:** [August 17, 2001, 8:21pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/120 "2001-08-17T20:21:47Z")
And, by the way, the [sci.math FAQ](http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/) also covers this, for anyone who’d like a more formal reference. [Previous page](https://boards.straightdope.com/t/99999999-equal-to-1/76468.md?page=5) [Next page](https://boards.straightdope.com/t/99999999-equal-to-1/76468.md?page=7)