# .999 = 1? **URL:** \ **Category:** Factual Questions\ **Created:** [July 31, 2000, 6:28am UTC](https://boards.straightdope.com/t/999-1/27517 "2000-07-31T06:28:03Z")\ **Posts on this page:** 20\ **Page:** 69
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [July 26, 2014, 3:09am UTC](https://boards.straightdope.com/t/999-1/27517/1366 "2014-07-26T03:09:58Z")
> [@Indistinguishable](#): > > A) Hammering **7777777** about “…999 = -1” isn’t particularly salient (or, I think, fair); Sure it is. Why wouldn’t it be? It’s not particularly interesting not related (except to **7777777** ), but it’s certainly fair - which is itself subjective. Under the context **7777777** would like to operate, it’s salient. That’s relevant and fair enough in my book. It’s not salient to you or the parts of this topic that interest you, but whether or not that’s sufficient to drop the topic is again a subjective call. > [@Indistinguishable](#): > > B) That having been said, nothing will accomplish this goal anyway. Why are people still trying arguing with **7777777**? Once things turned to weirdly aggressive witnessing, any hope this would be a non-futile endeavor was quashed. And it’s fine; what’s one more mistaken person in the world? Ignore them. Let it go. Forget it; it’s **7** town. See up top. “Fighting ignorance”. Besides, trying to argue with other posters about why they shouldn’t argue with other posters is getting a bit meta for me. Also, pot meet kettle. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [July 26, 2014, 3:21am UTC](https://boards.straightdope.com/t/999-1/27517/1367 "2014-07-26T03:21:07Z")
For what it’s worth, for all my mention of 10-adics above, those are not the only context in which “…999” would be taken to denote -1. In fact, “…999” also denotes -1 in the reals… on one natural account of how to interpret infinite decimal notation as specifying a real number. [Not the order-based one I’ve mentioned before, which would make …999 infinite; a different one which happens to agree with that one on decimals which terminate on the left] Specifically, recall that decimal notation can be taken as describing a number through the coefficients of some power series to be evaluated at 10. If these power series are finite, there’s no debate as to how to carry out this evaluation; however, in the infinitary case, there are various summation methods we may use. There is, for example, the theory of absolute convergence, as well as the less conservative textbook theory of summation in terms of arbitrarily close approximation by sums of discrete initial segments of a series. I’m going to note another summation method by which we can interpret decimal values. Specifically: given power series P and Q, let P \* Q be their product (basically, this is multiplication without carries). It may so happen that Q(10) is absolutely convergent to 1, and (P \* Q)(10) is absolutely convergent to some finite value. In that case, let us say that P(10) sums to that value [regardless of whether it is itself absolutely convergent]. This definition would appear to make the evaluation of P(10) depend on the choice of some other arbitrary power series Q, but it’s easy to check that any two such choices must give consistent answers. The notion of summation we get from this is very close to absolute convergence, and thus inherits most of its good properties, except those having to do with ordering [e.g., we lose the guarantee that a series with positive coefficients must have a positive sum]. In particular, we will find that …999 corresponds to P(x) = 9 + 9x + 9x^2 + … . Taking Q(x) = (-1 + x)/9, so that Q(10) absolutely converges to 1, we observe that (P \* Q)(x) = -1, so that (P \* Q)(10) absolutely converges to -1, and thus we have that …999 denotes -1 on this interpretation of decimal notation into real numbers. [In fact, this is just a reframing of the very proof given by **Albert** previously.] So it’s not as though this claim depends on using some wacky number system other than the reals. It’s just a matter of how you choose to interpret decimal notation into the reals. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [July 26, 2014, 3:31am UTC](https://boards.straightdope.com/t/999-1/27517/1368 "2014-07-26T03:31:58Z")
> [@Great\_Antibob](#): > > Sure it is. Why wouldn’t it be? It’s not particularly interesting not related (except to **7777777** ), but it’s certainly fair - which is itself subjective. The reason I think it’s not salient is because, as I said, I don’t imagine getting them to say “Ok, …999 is not -1. It’s infinite, or meaningless, or some such thing” will help move them to conclude “Ok, .999 = 1”. They’ll still have all their underlying “Things aren’t equal when the digits don’t match” confusion to cling to. I guess I should clarify that by “salient”, I meant “salient to the apparent goal in such hammering of getting **7777777** to accept .999 = 1”. > [@](#): > > Under the context **7777777** would like to operate, it’s salient. That’s relevant and fair enough in my book. It’s not salient to you or the parts of this topic that interest you, but whether or not that’s sufficient to drop the topic is again a subjective call. As I said, the only reason **7777777** brought “…999” up in the first place is because they accept “…999 = -1”, and see that it will make “.999 = 1” equivalent to “…999.999… = 0”. And they refuse to accept “…999.999… = 0” because the digits don’t match; therefore, they consider “.999 = 1” disproven as well. But even if you get them to abandon “…999 = -1” and thus lose their support for “…999.999… = 0”, they can still apply the digits-don’t-match-therefore-not-equal objection directly to “.999 = 1”. That’s why I say it’s not salient to attack them on these grounds if the ultimate goal is having them say “Alright, .999 does equal 1”. As for why I say it’s not fair, it’s because it seems pretty clear that **7777777** doesn’t have the conceptual language available to say “I want to work in system so-and-so, rather than system such-and-such”, so when one thing we know for sure is that they do want us to take …999 = -1 by the **Albert** argument, why not at least grant them that context, instead of slamming them for that choice? (Remarks like “No, …999 is not a number in the conventional sense! It’s a construct which cannot possibly be resolved to any real or complex number (your failed proof which does something about as viable as dividing by zero notwithstanding)” and so on) > [@](#): > > See up top. “Fighting ignorance”. > > Besides, trying to argue with other posters about why they shouldn’t argue with other posters is getting a bit meta for me. Also, pot meet kettle. Although I said “Ignore them. Let it go.”, I didn’t mean to imply I have any right to tell you what to do. You shouldn’t stop arguing with \*\*7777777[b/], if you really intrinsically enjoy it; I was just confused that people still seemed to be thinking they could actually convince **7777777** to change their mind. If your motivations are something other than accomplishing this, you may well have good reason to carry on. I definitely am a hypocrite on the topic of stepping away from arguments, though. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [July 26, 2014, 3:39am UTC](https://boards.straightdope.com/t/999-1/27517/1369 "2014-07-26T03:39:53Z")
So, yeah. I feel bad about attempting so directly to steer the conversation away from what I unfairly presumed everyone would agree was a quagmire. My apologies. (Also, even the presumption that no one can get through to **7777777** is unfair. After all, I once thought this a remote but existent possibility too, even as others knew better; the Messianic stuff was a point of no return for me, but why should I demand it be for everyone else? More apologies…) ---
**Author:** ![7777777](https://avatars.discourse-cdn.com/v4/letter/7/9de0a6/32.png) [@7777777](https://boards.straightdope.com/u/7777777)\ **Post date:** [July 26, 2014, 11:41am UTC](https://boards.straightdope.com/t/999-1/27517/1370 "2014-07-26T11:41:41Z")
> [@Great\_Antibob](#): > > That’s the crux of the failure of your arguments. It is your arguments that are failing. If you don’t see why, you must be blind: …99999 = -1 is true What do you assume will be the number 1 based on this truth? Might the number 1 be 0.999999…? Let’s see if we can calculate it: …99999 + 2 = …00001 = 1 surprise! The result is not 0.99999…:eek: What can you do now? Should you perhaps attack seven sevens, might a new attack restore everything? Or a very old trick may help, write that 1/3=0.333333333…and multiply it by 10. Or invent a new trick, multiply it by 10 and then divide it by 10. Prove a statement true by assuming it is true. Deny everything. Deny every fact, especially if it threatens your position. Seek help from your friends. Sacrifice truth. And all this at the cost of having to pay a very high price. The price whose value is so high that I can’t tell yet. Tell me why should number 1 have a decimal expansion, even though, for example, 1/5 has? Tell me why the decimal expansion of 1 should be equal to 0.9999…even though I have proved that these two numbers are never equal, the infinitesimal difference never equals to zero, no matter if you say it does. There is no infiniteth decimal place where the difference magically disappears. No, the the difference just gets smaller and smaller… What is wrong with writing 1/3=x ? Why do you insist writing that 1/3=0.3333333…even though 1/3=1/3 and 0.3333…=0.3333…? Isn’t it a way too simple just to say that these two numbers are the same. Why you think your simple way of thinking is the ultimate truth? You have not reached infinity to be able to tell what is going on there. It seems that there is a transformation when one reaches infinity. If you did not achieve it yet, you should not behave as if you did. The numbers transform into the symbol ∞ No-one knows how this happens, it is not taught anywhere, so it is also impossible you had this knowledge, that would justify your behaviour. ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [July 26, 2014, 12:28pm UTC](https://boards.straightdope.com/t/999-1/27517/1371 "2014-07-26T12:28:37Z")
Really thought you were going to address that proof that 0.333… = 1/3 there Posts #1351 and #1352 if you’ve forgotten. In what step is the error? ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [July 26, 2014, 2:11pm UTC](https://boards.straightdope.com/t/999-1/27517/1372 "2014-07-26T14:11:53Z")
**Seven sevens** , what do you want us to say? The limit as x approaches 1 of the function f(x) = x is indeed 1, using the definitions given in first year calculus. It’s not a real number or a vector, it’s a limit. We’d like for you to take your derivation of why 0.999… ≠ 1 and show how this _disproves_ the twenty or thirty other derivations that show 0.999… = 1. Please explicitly define the terms you use. Mathematics is concise, under any set of definitions, only one of these statements is true (assuming base 10). ---
**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:** [July 26, 2014, 2:50pm UTC](https://boards.straightdope.com/t/999-1/27517/1373 "2014-07-26T14:50:55Z")
> [@7777777](#): > > Why do you insist writing that 1/3=0.3333333…even though > 1/3=1/3 and 0.3333…=0.3333…? Because it’s true. Which step in this proof is flawed? 1. x = 0.333… 2. 10x = 3.333… 3. 3 + x = 3.333… 4. 10x = 3 + x 5. 9x = 3 6. x = 3/9 7. x = 1/3 8. 0.333… = 1/3 ---
**Author:** ![7777777](https://avatars.discourse-cdn.com/v4/letter/7/9de0a6/32.png) [@7777777](https://boards.straightdope.com/u/7777777)\ **Post date:** [July 26, 2014, 3:03pm UTC](https://boards.straightdope.com/t/999-1/27517/1374 "2014-07-26T15:03:28Z")
> [@watchwolf49](#): > > **Seven sevens** , what do you want us to say? The limit as x approaches 1 of the function f(x) = x is indeed 1, using the definitions given in first year calculus. It’s not a real number or a vector, it’s a limit. > > We’d like for you to take your derivation of why 0.999… ≠ 1 and show how this _disproves_ the twenty or thirty other derivations that show 0.999… = 1. Please explicitly define the terms you use. Mathematics is concise, under any set of definitions, only one of these statements is true (assuming base 10). I don’t want you to say anything if you don’t want to say anything, just waiting when your ignorance is over, unlike you who want me to force to admit that 1=0.99999… What I wonder instead, why should not someone choose truth and knowledge instead of lies and ignorance if he had a choice. It seems that many people have no such a choice. You offer no choice. You want to force people to admit you are right. I have told many times what I think about such a behavior: brainwashing. Since you offer no choice, I will do it now. Think that you have a once in a lifetime chance to choose something big. A chance of a lifetime to achieve something big, it is hard for me to tell exactly what because people already ridicule me too much. I show you two options, and you must choose only one of them as your truth. You cannot choose them both because as it is said “you cannot have your cake and eat it”. Choose only one of these as your truth, and then the other one will be false for you: …99999 = -1 1=0.99999… and that will probably determine the rest of your life. It seems I alone have chosen …99999=-1 as my truth and 1=0.99999…as false and that’s why I am fighting against the whole world. But if I have the truth, and it not mine, how can you fight against the truth even if you have the whole world on your side? I think you are wasting your time and energy in that case. “My teaching is not Mine, but His who sent Me. If anyone is willing to do His will, he will know of the teaching, whether it is of God or whether I speak from Myself.…” Yes, there are two paths you can go by, but in the long run There’s still time to change the road you’re on. And it makes me wonder. - LedZeppelin, Stariway to Heaven ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [July 26, 2014, 3:27pm UTC](https://boards.straightdope.com/t/999-1/27517/1375 "2014-07-26T15:27:15Z")
> [@7777777](#): > > I don’t want you to say anything if you don’t want to say anything, just waiting when your ignorance is over, unlike you who want me to force to admit that 1=0.99999… > What I wonder instead, why should not someone choose truth and knowledge instead of > lies and ignorance if he had a choice. It seems that many people have no such a choice. > You offer no choice. You want to force people to admit you are right. I have told many > times what I think about such a behavior: brainwashing. > > Since you offer no choice, I will do it now. > Think that you have a once in a lifetime chance to choose something big. > A chance of a lifetime to achieve something big, it is hard for me to tell exactly what > because people already ridicule me too much. > I show you two options, and you must choose only one of them as your truth. > You cannot choose them both because as it is said “you cannot have your cake and eat it”. > > Choose only one of these as your truth, and then the other one will be false for you: > …99999 = -1 > 1=0.99999… > and that will probably determine the rest of your life. It seems I alone have > chosen …99999=-1 as my truth and 1=0.99999…as false and that’s why I am fighting against the whole world. > But if I have the truth, and it not mine, how can you fight against the truth even > if you have the whole world on your side? I think you are wasting your time and energy in that case. > “My teaching is not Mine, but His who sent Me. If anyone is willing to do His will, he will know of the teaching, whether it is of God or whether I speak from Myself.…” > > Yes, there are two paths you can go by, but in the long run > There’s still time to change the road you’re on. > And it makes me wonder. > > - LedZeppelin, Stariway to Heaven I do believe that you are beginning to repeat yourself. Maybe you should try preaching from a different chapter, like telling us why the sons of Ham should be shunned or sodomites need to be stoned. Those are also golden oldies. ---
**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:** [July 26, 2014, 3:36pm UTC](https://boards.straightdope.com/t/999-1/27517/1376 "2014-07-26T15:36:49Z")
7777777, please just say which step(s) in The Hamster King’s post (#1373) you disagree with? ---
**Author:** ![x-ray\_vision](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/x-ray_vision/32/351_2.png) [@x-ray\_vision](https://boards.straightdope.com/u/x-ray_vision)\ **Post date:** [July 26, 2014, 3:48pm UTC](https://boards.straightdope.com/t/999-1/27517/1377 "2014-07-26T15:48:54Z")
> [@The\_Great\_Unwashed](#): > > 7777777, please just say which step(s) in The Hamster King’s post (#1373) you disagree with? According to the posts I’ve read by him so far, he would disagree with step 5. 9x = 3 He would say 9x = 2.99999… and not 9x = 3. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [July 26, 2014, 4:05pm UTC](https://boards.straightdope.com/t/999-1/27517/1378 "2014-07-26T16:05:33Z")
**The Hamster King** might at that point instead say “Alright, 9x = 2 + 3x. So x = 2/(9 - 3) = 1/3”. A simpler example of this same phenomenon to consider in making sense of a system distinguishing .999… from 1 is whether .999… + .999… = 1.999… = 1 + .999…, as digit-by-digit calculation might suggest. [To which one can give various responses, in accordance with various interpretations, etc., etc., as I always say] ---
**Author:** ![Colibri](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/colibri/32/1841_2.png) [@Colibri](https://boards.straightdope.com/u/Colibri)\ **Post date:** [July 26, 2014, 4:06pm UTC](https://boards.straightdope.com/t/999-1/27517/1379 "2014-07-26T16:06:57Z")
> [@7777777](#): > > I don’t want you to say anything if you don’t want to say anything, just waiting when your ignorance is over, unlike you who want me to force to admit that 1=0.99999… > What I wonder instead, why should not someone choose truth and knowledge instead of > lies and ignorance if he had a choice. It seems that many people have no such a choice. > You offer no choice. You want to force people to admit you are right. I have told many > times what I think about such a behavior: brainwashing. > [@7777777](#): > > If you don’t see why, you must be blind: **Moderator Warning** **7777777** , insults are not permitted in General Questions. This is an official warning. > [@7777777](#): > > Since you offer no choice, I will do it now. > Think that you have a once in a lifetime chance to choose something big. > A chance of a lifetime to achieve something big, it is hard for me to tell exactly what > because people already ridicule me too much. > I show you two options, and you must choose only one of them as your truth. > You cannot choose them both because as it is said “you cannot have your cake and eat it”. > > Choose only one of these as your truth, and then the other one will be false for you: > …99999 = -1 > 1=0.99999… > and that will probably determine the rest of your life. It seems I alone have > chosen …99999=-1 as my truth and 1=0.99999…as false and that’s why I am fighting against the whole world. > But if I have the truth, and it not mine, how can you fight against the truth even > if you have the whole world on your side? I think you are wasting your time and energy in that case. > [@7777777](#): > > “My teaching is not Mine, but His who sent Me. If anyone is willing to do His will, he will know of the teaching, whether it is of God or whether I speak from Myself.…” > [@7777777](#): > > You have not reached infinity to be able to tell what is going on there. > It seems that there is a transformation when one reaches infinity. > If you did not achieve it yet, you should not behave as if you did. > The numbers transform into the symbol ∞ > No-one knows how this happens, it is not taught anywhere, so it is also > impossible you had this knowledge, that would justify your behaviour. These posts are also not appropriate for General Questions. This forum is for factual information, not for personal opinions. It’s clear at this point that your position is based on your personal beliefs rather than any actual mathematical theory. In addition, religious witnessing is only permitted in our Great Debates forum. I am instructing you to drop this line of discussion. If you are unable to support your ideas mathematically (and it’s rather clear you cannot), take the discussion elsewhere. Further posts along these lines will result in a warning, and you may find your posting privileges under discussion by the staff. Colibri General Questions Moderator PS. While I’m not instructing other posters not to respond, I don’t see much point in engaging a poster who is not even attempting to argue factually. ---
**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:** [July 26, 2014, 4:09pm UTC](https://boards.straightdope.com/t/999-1/27517/1380 "2014-07-26T16:09:54Z")
> [@x-ray\_vision](#): > > According to the posts I’ve read by him so far, he would disagree with step 5. > > 9x = 3 > > He would say 9x = 2.99999… and not 9x = 3. :dubious: That’s just normal algebra given the previous step. If 10x = x + 3 then 9x = 3. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [July 26, 2014, 4:43pm UTC](https://boards.straightdope.com/t/999-1/27517/1381 "2014-07-26T16:43:12Z")
People surely tire of me providing such defenses, but if I were to want to say that 9x = 2.999… and not 3, here’s one way to do so which is slightly different from previously discussed ways of doing so, but captures an important aspect of the intuitions expressed inchoately by some: > [@The\_Great\_Unwashed](#): > > 1. x = 0.333… I’ll take this to mean x is a number at least as large as 0.3, 0.33, 0.333…, and _strictly_ less than 0.4, 0.34, 0.334, … . We have no further information about x; there may be more than one number of this sort, but we’ve picked one out and called it x. (The strictness of the upper bound here is, as we know, not the standard interpretation of decimal notation, but clearly such strictness is in mind for those who argue that 0.999… must be less than 1.000… because the first digit is smaller. So let’s understand how that would work [even though such objectors should also be made to understand how the standard use of decimal notation works]) > [@](#): > > 1. 10x = 3.333… I’ll take this to mean “10x is at least as large as 3, 3.3, 3.33, etc., and strictly less than 4, 3.4, 3.34, etc.”. And dividing through by 10, this is indeed equivalent to 1). No problem. > [@](#): > > 1. 10x - x = 3.333… - 0.333… Equation 2) - Equation 1) I’ll take this to mean “10x - x is equal to the difference of two numbers, the first of which is as described in 1), the second of which is as described in 2)”. No problem. > [@](#): > > 1. 9x = 3 I’ll disagree at this point. The argument for the right-hand side is by subtraction, but just because A falls within the intervals [3, 4), [3.3, 3.4), [3.33, 3.34) and B falls within the intervals [0.3, 0.4), [0.33, 0.34), …, doesn’t mean A - B = 3. All we can conclude are things like that A - B falls within the intervals (3.3 - 0.4, 3.4 - 0.3), (3.33 - 0.34, 3.34 - 0.33), … = (2.9, 3.1), (2.99, 3.01), (2.99, 3.001), … . A - B could be equal to 3, or larger than it, or smaller than it. The error, on this interpretation of the notation, is in presuming that knowing a decimal expansion of A and the decimal expansion of B lets one deduce the decimal expansion of A - B. It could be that more than one value falls within the same decimal expansion (so that 1/3 would not be the only value with decimal expansion 0.333…, but so could a value slightly less than 1/3, which could be our x). On this account, the problem is never that one valued might have multiple decimal notations, but rather than one decimal notation might correspond to multiple values. ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [July 26, 2014, 4:43pm UTC](https://boards.straightdope.com/t/999-1/27517/1382 "2014-07-26T16:43:42Z")
> [@x-ray\_vision](#): > > According to the posts I’ve read by him so far, he would disagree with step 5. > > 9x = 3 > > He would say 9x = 2.99999… and not 9x = 3. That would be just plain wrong. I doubt he would say that. Regardless of the value of x, if we have 10x = 3 + x then we would have to admit that if we subtract x from both sides, we have 9x = 3x That’s if we’re doing basic algebra, as taught in middle school, high school, and college pre-calc courses. ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [July 26, 2014, 4:45pm UTC](https://boards.straightdope.com/t/999-1/27517/1383 "2014-07-26T16:45:28Z")
I’m amused we’re still discussing this. Frankly, I find the tangents far more interesting. They at least have something from which I can learn. Thanks especially to **Indistinguishable**. ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [July 26, 2014, 4:48pm UTC](https://boards.straightdope.com/t/999-1/27517/1384 "2014-07-26T16:48:13Z")
> [@Indistinguishable](#): > > I’ll disagree at this point. Hah! Well, summagun. Ignorance, or something very much like it, fought. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [July 26, 2014, 4:55pm UTC](https://boards.straightdope.com/t/999-1/27517/1385 "2014-07-26T16:55:28Z")
> [@Learjeff](#): > > Hah! Well, summagun. Ignorance, or something very much like it, fought. Glad to have been of help. Keep in mind, of course, that I’m only saying that’s one nonstandard way you could imagine interpreting decimal notation. You weren’t wrong to think that **The Hamster King** ’s argument was perfectly legitimate, in the context of the standard interpretation of the notation. Please don’t think you were mistaken about the standard interpretation of things; all I hope to do is show how we can also understand other possibilities, formalizing the intuitions others of an admittedly mathematically unsophisticated sort struggle to express in their arguments. (Also, I see now that while I intended to respond to **The Hamster King** ’s illustration of the argument, I actually quoted **The Great Unwashed** ’s. But it makes no difference.) [Previous page](https://boards.straightdope.com/t/999-1/27517.md?page=68) [Next page](https://boards.straightdope.com/t/999-1/27517.md?page=70)