# An infinite question: Why doesn't .999~ = 1? **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [September 24, 2016, 7:29am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711 "2016-09-24T07:29:45Z")\ **Posts on this page:** 20\ **Page:** 22
**Author:** ![The\_Great\_Unwashed](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_great_unwashed/32/4791_2.png) [@The\_Great\_Unwashed](https://boards.straightdope.com/u/The_Great_Unwashed)\ **Post date:** [November 5, 2016, 9:56am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/421 "2016-11-05T09:56:55Z")
> [@netzweltler](#): > > Can you give me the position of 0.999… on the number line? For the nth time, yes we can, it falls where 1 is. Because it is equal to 1. The notation 0.999… does not represent a process, there’s nothing “to do”. If it were a process you would have a point – it would be the same point that Zeno made, but that “paradox” has long since been resolved, so still not much of a point. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 5, 2016, 11:53am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/422 "2016-11-05T11:53:27Z")
> [@](#): > > Sure. Why not? 3.14159 is such a string. It can easily be recognized as π. Even if the string is not infinite. Wait, let me get this straight: You can recognize 3.14159 as pi, even though it only matches for six digits, but you can’t recognize 0.9 as 1, even though it matches for an infinite number of digits? ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [November 5, 2016, 3:38pm UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/423 "2016-11-05T15:38:20Z")
> [@netzweltler](#): > > Yes. Every non-ending string of digits faces the same problem as 0.999… > > t = 0: I move my pen from point 0 to point 0.9 of the number line > t = 0.9: I move my pen from point 0.9 to point 0.99 of the number line > t = 0.99: I move my pen from point 0.99 to point 0.999 of the number line > … > > We don’t reach the limit on this list of actions. The state of the pen at t = 1 and after is solely defined by the actions on the list. Achilles is at the one end of the football field; the tortoise is at the 90-yard line but moves at 1/10 the speed of Achilles. t = 0; Achilles (with pen in pocket) moves from the 0 to the 90-yard line. t = 0.9; Achilles moves from the 90-yard line to the 99-yard line. t = 0.99; Achilles moves from the 99-yard line to the 99.9 yard line … We don’t reach the tortoise (or the 100-yard line) on this list of actions. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [November 5, 2016, 4:08pm UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/424 "2016-11-05T16:08:22Z")
For the 92nd time … > [@netzweltler](#): > > [snip] … t = 0: I move my pen to get closer to the limit but not reach the limit … [snip] … Reaching the limit means disobeying the commands on this infinite list. This is true for a finite list, and it is true for an infinite list. Ahhhh … you’ve committed the logical fallacy of “moving the goalposts” here … your first 90 posts didn’t include the specification of “but not reach the limit”. In effect now, you’ve admitted you were wrong and are quickly changing your argument so it doesn’t look like you’ve been wrong all this time. Unfortunately, you’ve not defined what “but not reach the limit” means exactly. We can start by defining what the distance is between the limit and the actual value we reach after infinite iterations. Please spare no details, either tell us which branch of mathematics you’re using or give us the _Reader’s Digest_ version of this new branch of mathematics you’ve developed of this claim you’re making. _The rafters have broken loose._ > [@netzweltler](#): > > As soon as you introduce the term “infinitesimal” you are introducing another ill-defined concept. But yes, it makes some sense to say 1 - 0.999… = infinitesimal, because the size of an infinitesimal is ill-defined and therefore might perfectly define the distance between 1 and 0.999… Infinitesimal is a well defined word, look it up in any calculus textbook. I get the feeling you’ve never taken calculus and indeed it’s a two year course in college just because understanding this well established concept of the infinitesimal is kinda sorta that fucking hard. That’s why we’re all being very patient with you, you seem very bright and intuitive but just missing this little detail … _The kingstuds have snapped in the middle._ > [@netzweltler](#): > > π is perfectly defined - the ratio of a circle’s circumference to its diameter. Here we have the logical fallacy of “the strawman” … you’ve changed what I actually posted “you cannot define π on the number line using your methods” into some thing else and then argued against that something else. Once again this has the effect of admitting you are in error, it’s impossible to argue against what I said, therefore you argue against something else. _The shearwall is beginning to twist._ > [@netzweltler](#): > > Can you give me the position of 0.999… on the number line? It is coincident with 1 using the method you described in your first 90 posts … using the method in your 91st post we can only say this cannot be determined until you edify us on the definition of “not reaching the limit” of an infinite convergent series. _… and now your house has come crashing down._ ---
**Author:** ![DMC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dmc/32/18049_2.png) [@DMC](https://boards.straightdope.com/u/DMC)\ **Post date:** [November 6, 2016, 3:40am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/425 "2016-11-06T03:40:03Z")
> [@netzweltler](#): > > Can you give me the position of 0.999… on the number line? I can, but apparently you can’t. Nor can you seem to give me a number between the two, even though there would be an **infinite** number of examples if they were indeed different numbers. ---
**Author:** ![netzweltler](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@netzweltler](https://boards.straightdope.com/u/netzweltler)\ **Post date:** [November 6, 2016, 7:57am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/426 "2016-11-06T07:57:43Z")
> [@The\_Great\_Unwashed](#): > > Will you respond to these two posts, rather than regurgitating again your “t = 0: I move my pen to get closer to the limit but not reach the limit” schtick? 0.999… is NOT a point in (0, 1). It’s not a point on the number line at all. Why should I respond to a question which presupposes that 0.999… is a point on the number line? You will get strange results if you presuppose that. So, you better give a counter-example that shows how we reach the limit although infinitely many commands tell us NOT to do so. ---
**Author:** ![netzweltler](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@netzweltler](https://boards.straightdope.com/u/netzweltler)\ **Post date:** [November 6, 2016, 8:01am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/427 "2016-11-06T08:01:38Z")
> [@The\_Great\_Unwashed](#): > > For the nth time, yes we can, it falls where 1 is. Because it is equal to 1. > > The notation 0.999… does not represent a process, there’s nothing “to do”. If it were a process you would have a point – it would be the same point that Zeno made, but that “paradox” has long since been resolved, so still not much of a point. Of course, the addition of 0.9 + 0.09 + 0.009 + … can be treated as an infinite process. ---
**Author:** ![netzweltler](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@netzweltler](https://boards.straightdope.com/u/netzweltler)\ **Post date:** [November 6, 2016, 8:04am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/428 "2016-11-06T08:04:43Z")
> [@Chronos](#): > > Wait, let me get this straight: You can recognize 3.14159 as pi, even though it only matches for six digits, but you can’t recognize 0.9 as 1, even though it matches for an infinite number of digits? 3.14159 is a good approach to π for most technical purposes. 0.99999 is a good approach to 1 for most technical purposes. So what? ---
**Author:** ![netzweltler](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@netzweltler](https://boards.straightdope.com/u/netzweltler)\ **Post date:** [November 6, 2016, 8:15am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/429 "2016-11-06T08:15:59Z")
> [@septimus](#): > > Achilles is at the one end of the football field; the tortoise is at the 90-yard line but moves at 1/10 the speed of Achilles. > > t = 0; Achilles (with pen in pocket) moves from the 0 to the 90-yard line. > t = 0.9; Achilles moves from the 90-yard line to the 99-yard line. > t = 0.99; Achilles moves from the 99-yard line to the 99.9 yard line > … > We don’t reach the tortoise (or the 100-yard line) on this list of actions. Correct. This list of actions is not a complete description of what really happens. Achilles moves continuously from 0 to the 100-yard line. He arrives there by t = 1. ---
**Author:** ![netzweltler](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@netzweltler](https://boards.straightdope.com/u/netzweltler)\ **Post date:** [November 6, 2016, 8:22am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/430 "2016-11-06T08:22:45Z")
> [@watchwolf49](#): > > For the 92nd time … > > Ahhhh … you’ve committed the logical fallacy of “moving the goalposts” here … your first 90 posts didn’t include the specification of “but not reach the limit”. In effect now, you’ve admitted you were wrong and are quickly changing your argument so it doesn’t look like you’ve been wrong all this time. > > Unfortunately, you’ve not defined what “but not reach the limit” means exactly. We can start by defining what the distance is between the limit and the actual value we reach after infinite iterations. Please spare no details, either tell us which branch of mathematics you’re using or give us the _Reader’s Digest_ version of this new branch of mathematics you’ve developed of this claim you’re making. > > _The rafters have broken loose._ > > Infinitesimal is a well defined word, look it up in any calculus textbook. I get the feeling you’ve never taken calculus and indeed it’s a two year course in college just because understanding this well established concept of the infinitesimal is kinda sorta that fucking hard. That’s why we’re all being very patient with you, you seem very bright and intuitive but just missing this little detail … > > _The kingstuds have snapped in the middle._ > > Here we have the logical fallacy of “the strawman” … you’ve changed what I actually posted “you cannot define π on the number line using your methods” into some thing else and then argued against that something else. Once again this has the effect of admitting you are in error, it’s impossible to argue against what I said, therefore you argue against something else. > > _The shearwall is beginning to twist._ > > It is coincident with 1 using the method you described in your first 90 posts … using the method in your 91st post we can only say this cannot be determined until you edify us on the definition of “not reaching the limit” of an infinite convergent series. > > _… and now your house has come crashing down._ For obvious reasons every line on the list has the same property: I move my pen to get closer to the limit but not reach the limit t = 0: I move my pen from point 0 to point 0.9 of the number line t = 0.9: I move my pen from point 0.9 to point 0.99 of the number line t = 0.99: I move my pen from point 0.99 to point 0.999 of the number line … Tell me if you can find a line on the list for which this does not hold true. ---
**Author:** ![netzweltler](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@netzweltler](https://boards.straightdope.com/u/netzweltler)\ **Post date:** [November 6, 2016, 8:25am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/431 "2016-11-06T08:25:34Z")
> [@DMC](#): > > I can, but apparently you can’t. Nor can you seem to give me a number between the two, even though there would be an **infinite** number of examples if they were indeed different numbers. Yes, if they were different numbers. Two different well-defined numbers. 1 is a well-defined point on the number line, 0.999… is not. ---
**Author:** ![The\_Great\_Unwashed](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_great_unwashed/32/4791_2.png) [@The\_Great\_Unwashed](https://boards.straightdope.com/u/The_Great_Unwashed)\ **Post date:** [November 6, 2016, 10:05am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/432 "2016-11-06T10:05:56Z")
> [@netzweltler](#): > > 0.999… is NOT a point in (0, 1). It’s not a point on the number line at all. Why should I respond to a question which presupposes that 0.999… is a point on the number line? I don’t care if it is on the number line or not. I asked what its squareroot was (or rather, just what the first few digits of its square root are). Elsewhere you have accepted that 0.999… is greater than all of {0.9, 0.99, 0.999, … } : > [@netzweltler](#): > > Greater than any element of { 0.9, 0.99, 0.999, … }, yes So even if you are right and we cannot place it on the number line, you do agree that it is still a number. **WHAT ARE THE FIRST FEW DIGITS OF ITS SQUARE ROOT?** ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [November 6, 2016, 2:46pm UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/433 "2016-11-06T14:46:25Z")
98th … > [@netzweltler](#): > > For obvious reasons every line on the list has the same property: > I move my pen to get closer to the limit but not reach the limit > > t = 0: I move my pen from point 0 to point 0.9 of the number line > t = 0.9: I move my pen from point 0.9 to point 0.99 of the number line > t = 0.99: I move my pen from point 0.99 to point 0.999 of the number line > … > > Tell me if you can find a line on the list for which this does not hold true. For your claims 1 to 90 and 92 to 98, then you’ll reach the limit on the last line, the one with the ellipsis (…). That’s what the ellipsis typically means in this context, “continue this convergent series until it converges on the limit”. For your 91st claim, this is still unclear until you define the ellipsis there. Does it mean the same as above, in which case you have a serious contradiction (the theorems of calculus prohibit both converging on a limit and not reaching the limit at the same time) … or does it mean “after a very very large but finite number of steps”? I was going to suggest a new numbering system, _ **S** _, where we limit the digits to the right of the decimal place to 10[sup]100[/sup]. With this set then we are allowed to have two different elements of _ **S** _ for which there exists _no_ element of _ **S** _ in between them. This gives us the property of being able to converge on the limit yet not reach the limit. This might be useful in Quantum Mechanics, where we have an actual physical property that has this feature, there is no quantum valve between 0.000···00135 and 0.000···00136 (where ··· = 10[sup]92[/sup] zeroes and 1 = 10[sup]100[/sup] quantum units (about a half a teaspoon)). Of course there will be the technological problem of building a pen with a tip one quantum in diameter … failing this then your pen will cross over 1 on your second step … ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [November 6, 2016, 3:12pm UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/434 "2016-11-06T15:12:09Z")
I don’t know why I persist but … > [@netzweltler](#): > > Correct. This list of actions is not a complete description of what really happens. Achilles moves continuously from 0 to the 100-yard line. He arrives there by t = 1. It’s indistinguishable from yours, except mine is more sensical. > [@netzweltler](#): > > t = 0: I move my pen from point 0 to point 0.9 of the number line > t = 0.9: I move my pen from point 0.9 to point 0.99 of the number line > t = 0.99: I move my pen from point 0.99 to point 0.999 of the number line > … Why do you continue to cut-and-paste incomprehensible gibberish over and over? What pen? What is t? Even if your first nine requires 90 minutes to draw, the third will take just 0.9 minutes, the fifth a half-second, the twelfth only several nanoseconds — impossible. Yes, yes, we get that your endlessly repeated gibberish is intended to depict some analogy, but an analogy for what? It makes no sense. Spend some time, if you can, formulating your thesis into simple English with no metaphiers. Drop the pen. Drop the incorrect concept of time. Drop the number line if you don’t understand it. _ **Explain in simple English** _ (without the meaningless “t = 0.99” etc.) what your point is. ---
**Author:** ![Budget\_Player\_Cadet](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/budget_player_cadet/32/205_2.png) [@Budget\_Player\_Cadet](https://boards.straightdope.com/u/Budget_Player_Cadet)\ **Post date:** [November 6, 2016, 11:09pm UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/435 "2016-11-06T23:09:11Z")
> [@netzweltler](#): > > We are dealing with very basic logic here - even if we are dealing with infinity. Basically the process(es) discussed always mean the same: > > t = 0: I move my pen to get closer to the limit but not reach the limit > t = 0.9: I move my pen to get closer to the limit but not reach the limit > t = 0.99: I move my pen to get closer to the limit but not reach the limit > … > > It’s an endless loop. It is an infinite series of commands: > > t = 0: Get closer to the limit but do not reach the limit! > t = 0.9: Get closer to the limit but do not reach the limit! > t = 0.99: Get closer to the limit but do not reach the limit! > … > > Reaching the limit means disobeying the commands on this infinite list. This is true for a finite list, and it is true for an infinite list. Except that this is a nonsensical and meaningless way of looking at 0.99… for all the reasons previously examined. Why the hell should we defined 0.99… as “Constantly getting closer to 1 but not reaching it”? That’s not a useful or meaningful definition for the number. That’s got no basis in calculus whatsoever. You’re talking about summing a row, and _even then_ you have no idea what you’re talking about, because it’s trivial to define a row with exactly that characteristic that behaves wildly different in the limit than in any of the individual parts! And even then, it completely ignores the fact that the limit is what happens _after an infinite number of steps_! Not during the steps, _after an infinite number of them_. And the behavior of a system after infinite steps does not have such a trivially basic relationship to the behavior of the system within any given step! As I previously demonstrated with the balls in the barrel; if you look at any given step, there are countless balls in the barrel, each numbered, and with each step, we only add more… But after an infinite number of steps, it is impossible for any ball to be in the barrel, because for any ball we name, we can point to a step where we removed that ball. This is like baby’s first infinity; you don’t seem to get that infinity is not a number and that infinite sets of tasks do not behave the way finite sets of tasks do. This is stuff I learned in middle school, or which can be learned by watching [Vsauce](https://www.youtube.com/watch?v=ffUnNaQTfZE). Please, learn the basics. Or, failing that, here’s even more basic logic for you that you seem to not grasp or to be unwilling to address. After infinite steps of moving your pen closer and closer to the limit of 1, _what is the distance between your pen and 1?_ If there is no distance, then your pen is on one, and the paradox is resolved. If there is a distance, why can I then point to a step where we clearly passed the number your distance describes? > [@netzweltler](#): > > 0.999… is NOT a point in (0, 1). Credit where credit is due: this is actually accurate. Because 0.99… is _not_ included in (0,1). Because it’s equal to 1. > [@](#): > > It’s not a point on the number line at all. :smack: It clearly _corresponds_ to a point on the number line. That point is 1. > [@netzweltler](#): > > Of course, the addition of 0.9 + 0.09 + 0.009 + … can be treated as an infinite process. Of course it can. But then you run into Zeno’s paradox, and the entire set of issues you can’t seem to get past here. There are far better, far more reasonable ways to define 0.99…; yours simply seems to be the only one that allows for your particular brand of confusion. Meanwhile, you don’t understand infinity, you don’t understand limits, and you’ve got like 3 or 4 people here explaining to you, _all in different ways_, where you’ve gone wrong. I strongly recommend you heed their words. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [November 6, 2016, 11:24pm UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/436 "2016-11-06T23:24:23Z")
> [@septimus](#): > > I don’t know why I persist but … [snip] We are like the links of an anchor chain, Grasshopper, sometimes we have to lay in fish poop until the wind changes. ---
**Author:** ![The\_Great\_Unwashed](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_great_unwashed/32/4791_2.png) [@The\_Great\_Unwashed](https://boards.straightdope.com/u/The_Great_Unwashed)\ **Post date:** [November 6, 2016, 11:30pm UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/437 "2016-11-06T23:30:42Z")
> [@Budget\_Player\_Cadet](#): > > No matter what number you come up with, I can find an interval where the ball was removed. Ergo: there isn’t a ball in there to pull out. The barrel is empty. That’s a very pretty example of the weirdness of infinities. I’m not sure your conclusion is right though – surely there’s an infinite number balls left, just none of them are numbered with whatever number you care to name (can name)?! ```auto An aside: does "your" series, **10 - 1 + 20 - 1 + 30 - 1 + ...** , converge to 0 with Ramanujan summation? ``` ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [November 7, 2016, 12:29am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/438 "2016-11-07T00:29:07Z")
> [@Budget\_Player\_Cadet](#): > > . . . As I previously demonstrated with the balls in the barrel; if you look at any given step, there are countless balls in the barrel, each numbered, and with each step, we only add more… But after an infinite number of steps, it is impossible for any ball to be in the barrel, because for any ball we name, we can point to a step where we removed that ball. . . . Grin! I love that’n. Of course, it can be addressed by a change in notation… As Martin Gardner set it up, each day ten balls are put in, and one is taken out. Say on day 1 balls 1-10 go in, and ball 1 comes out. On day 2, balls 2-20 go in, and ball 2 comes out. By this notation, the barrel is empty “after infinity,” because any specific numbered ball has been taken out. So… Change the notation. On day 1, ball 1a through 1j are put in, and ball 1a is taken out. On day 2, balls 2a through 2j are put in, and ball 2a is taken out. In this notational system, ball 1b is never taken out, and so the barrel is not empty. (ETA: This is just another way of observing that “infinity minus infinity” is not defined.) If **netzweltler** could come up with a notational system that backs up his claims, he might have something worth rebutting. He tried with the moving pen deal, but it failed. Maybe he can come up with something new. ---
**Author:** ![Budget\_Player\_Cadet](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/budget_player_cadet/32/205_2.png) [@Budget\_Player\_Cadet](https://boards.straightdope.com/u/Budget_Player_Cadet)\ **Post date:** [November 7, 2016, 5:47am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/439 "2016-11-07T05:47:00Z")
> [@The\_Great\_Unwashed](#): > > That’s a very pretty example of the weirdness of infinities. > > I’m not sure your conclusion is right though – surely there’s an infinite number balls left, just none of them are numbered with whatever number you care to name (can name)?! > > ```auto > > An aside: does "your" series, **10 - 1 + 20 - 1 + 30 - 1 + ...** , converge to 0 with Ramanujan summation? > > ``` Well, each ball we put in is numbered with a natural number, and we cannot find a ball afterwards that has a natural number on it… It’s weird. 😃 Also, I don’t know what Ramanujan summation is, I’m afraid. ---
**Author:** ![netzweltler](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@netzweltler](https://boards.straightdope.com/u/netzweltler)\ **Post date:** [November 7, 2016, 7:01am UTC](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711/440 "2016-11-07T07:01:46Z")
> [@The\_Great\_Unwashed](#): > > I don’t care if it is on the number line or not. I asked what its squareroot was (or rather, just what the first few digits of its square root are). > > Elsewhere you have accepted that 0.999… is greater than all of {0.9, 0.99, 0.999, … } : > > So even if you are right and we cannot place it on the number line, you do agree that it is still a number. No. A number has a well-defined position on the number line. > [@The\_Great\_Unwashed](#): > > **WHAT ARE THE FIRST FEW DIGITS OF ITS SQUARE ROOT?** [Previous page](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711.md?page=21) [Next page](https://boards.straightdope.com/t/an-infinite-question-why-doesnt-999-1/766711.md?page=23)