# .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:** 22
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [August 7, 2012, 2:02am UTC](https://boards.straightdope.com/t/999-1/27517/421 "2012-08-07T02:02:55Z")
> [@Senegoid](#): > > [sub]Oh, wait… There’s still infinitely more posts to go![/sub] That’s a lot of hard drives which Cecil will have to buy. Even if IBM goes all out, they get stuck at [10^10^80+2 bits.](http://physics.stackexchange.com/questions/8895/how-many-bits-are-needed-to-simulate-the-universe) (minus CPU, of course). ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 7, 2012, 2:04am UTC](https://boards.straightdope.com/t/999-1/27517/422 "2012-08-07T02:04:13Z")
Anyone who is ingterested in actually reading the entire sub thread here on this. I started it on post 273. My initial conclusion was that it lead to a contradiciton. But I later accepted it does not. The limit of .000…0 is the same as the limit .000…1 however, I believe I did show that you can reach the end of an infinte series of numbers. ---
**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:** [August 7, 2012, 2:06am UTC](https://boards.straightdope.com/t/999-1/27517/423 "2012-08-07T02:06:27Z")
> [@erik150x](#): > > If I travel from point A to B, have I not crossed an infinite number of half way points? No, you have by definition crossed one half-way point. > [@](#): > > Is this infinity some how smaller than the repeating decimals? One point isn’t an infinity. > [@](#): > > If so explain how? Oh, right, you’re going on again about your inability to understand the different ways of dividing a unit. How you divide one unit is meaningless. Whether you express it “1/2 + 1/2” or “1/2 + 1/4 + 1/8 …” it’s still one unit. > [@](#): > > If not, then if I move form point A to point B have I not just reach end of af infinitie decimal expansion? I’m having trouble parsing this, but I think you’re back to stating that you don’t believe in the concept of a limit. You’re wrong about this. > [@](#): > > If you want to make the same darn statement over and over and over, that there is no end, fine then tell me how I ever reach point B in Zeno’s paradox, because that is an infinite amount of points but I clearly reach the end. Yep. Limits. Still wrong. > [@](#): > > I see no one explaining the flaw. I see that in your system you’re still defining “no one” to mean “everyone.” That’s very confusing. Perhaps you should stick to standard definitions. > [@](#): > > Simply saying there is no end, does not permit me to reach poitn B in Zeno’s Paradox, so then we have another paradox? Nope. ---
**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:** [August 7, 2012, 2:08am UTC](https://boards.straightdope.com/t/999-1/27517/424 "2012-08-07T02:08:06Z")
> [@erik150x](#): > > however, I believe I did show that you can reach the end of an infinte series of numbers. Wrongo. But you can divide a unit into an infinite number of parts. Not the same thing. ---
**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:** [August 7, 2012, 2:09am UTC](https://boards.straightdope.com/t/999-1/27517/425 "2012-08-07T02:09:07Z")
> [@LinusK](#): > > No, I’d say he thinks the difference is not that you put a 1 at the end of the zeroes, but that the difference is infinitely small. You underestimate him. See the above post. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 7, 2012, 2:12am UTC](https://boards.straightdope.com/t/999-1/27517/426 "2012-08-07T02:12:03Z")
> [@Exapno\_Mapcase](#): > > Wrongo. But you can divide a unit into an infinite number of parts. Not the same thing. RE: No, you have by definition crossed one half-way point.? You clearly do not understand Zeno’s Paradox here. From any point A to point B, you must cross an infinite number of halfway points: 1/2 + 1/4 + 1/8 + … = 1 Distance traveld = 1 number of points = infinity What are YOU even talking about… 1 half way point??? ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [August 7, 2012, 2:21am UTC](https://boards.straightdope.com/t/999-1/27517/427 "2012-08-07T02:21:05Z")
> [@erik150x](#): > > RE: No, you have by definition crossed one half-way point.? > > You clearly do not understand Zeno’s Paradox here. > > From any point A to point B, you must cross an infinite number of halfway points: > > 1/2 + 1/4 + 1/8 + … = 1 > > Distance traveld = 1 > number of points = infinity > > What are YOU even talking about… 1 half way point??? Between point A and B there is exactly ONE half way point, which is at 1/2 \* distance(A,B) + location(A). What you ARE doing is passing between a half-way point, a quarter-way point, an eighth-way point… Either way, I’m not sure it was worth Exapno pointing out, it seems like semantics to me, I certainly see where you’re getting what you said and don’t think it’s wrong, per-se. You’re just defining a shifting start point for your half-way calculation. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 7, 2012, 2:24am UTC](https://boards.straightdope.com/t/999-1/27517/428 "2012-08-07T02:24:43Z")
The assumption that you can never reach the end of an infinite anything is flawed, and I think this is demonstrated by the resolutioin to Zeno’s paradox quite nicely. Let’s say Point A to Point B is 1 mile I travle 1/2 mile in 1/2 hour another 1/4 mile in 1/4 hour another 1/8 mile in 1/8 hour In 1 hour I reach the end of an INFINITE series of halfway points. So tell my why i can not map these 1 to 1 to the decimal expansion of say .999… and reach the end? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 7, 2012, 2:39am UTC](https://boards.straightdope.com/t/999-1/27517/429 "2012-08-07T02:39:33Z")
> [@Jragon](#): > > Yes, you have clearly restated Zeno’s paradox. The answer to it involves limits. You refuse to accept the concept of limits, so it’s kind of difficult to answer anything because you say “uh uh, without limits!” I am sympathetic to your frustration. However, irrelevant thought it may be to the larger point, I must re-insist that the resolution to Zeno’s paradox does not involve limits. Limits are neither necessary, nor even useful, for resolving the paradox (This post isn’t targeted at you, specifically, but at this all too common assertion) A) The theory of limits cannot be used to resolve Zeno’s paradox: After all, you can’t resolve a contradiction by just proffering another argument with a different conclusion. Then it just becomes an even greater contradiction! “The theory of limits says you can cross in finite time, but Zeno’s argument says you can’t. Ack, a contradiction!” The only way to resolve a paradox is by noting a flaw in the paradoxical argument. And once you’ve done that, there’s nothing more you have to do. B) The theory of limits is not necessary to resolve Zeno’s paradox: For example, let us suppose ourselves to live in a world of only rational distance ratios. Johnocles wants to get from milepost 1 to milepost 2. Zeno objects “Ah, but first, you must get to 3/2. And then you must get to 7/5. And then you must get to 17/12. And then you must get to 41/29.” And so on and so on, each intermediate n/d = x milestone followed by another one at (2n + d)/(n + d) = (x + 2)/(x + 1). Well, that sequence of intermediate milestones has no limit (not in this rational world). But it doesn’t matter. If Johnocles walks at a mile an hour, he’ll still get from milepost 1 to milepost 2 in a very finite hour, and cover all the infinite intermediaries in the intervening time, hitting each after the corresponding rational number of hours. Zeno was simply mistaken to think there was any contradiction between an interval having finite length and its containing infinitely many points. And you don’t need any theory of limits or infinite summation to recognize this mistake (nor do such theories play any role in banishing this mistake, formally; the only role they can play is psychological, by adding evidence to your comforting experience that you needn’t flip your shit every time you see the words “finite” and “infinite” next to each other). Zeno’s paradox is, after a moment’s thought, no paradox in the context of rationals, despite the failure of limits to exist. And it’s no paradox in the context of surreals, despite the even greater failure of limits to exist. And it’s no paradox in the context of reals, where limits do exist. But the way in which it’s no paradox is the same in all three of these. Limits don’t come into it. It’s just that, when Zeno says “How can you do infinitely many things in a finite amount of time? There can’t be infinitely many points in a finite interval!”, he’s speaking bosh. There can very clearly be such a thing. The leap from “Interval of finite length” to “Interval containing finitely many points” is fallacious, as demonstrated by the very example Zeno gives! ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [August 7, 2012, 2:47am UTC](https://boards.straightdope.com/t/999-1/27517/430 "2012-08-07T02:47:40Z")
Yeah, I jumped the gun a bit. I was going to retract that statement if I posted again. Though for the physical world at least there are a lot of **other** good explanations that we have now (such as planck lengths possibly discretizing the number space in the real world, which is much more intuitive than other explanations). ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 7, 2012, 2:48am UTC](https://boards.straightdope.com/t/999-1/27517/431 "2012-08-07T02:48:04Z")
> [@Indistinguishable](#): > > Zeno objects “Ah, but first, you must get to 3/2. And then you must get to 7/5. And then you must get to 17/12. And then you must get to 41/29.” And so on and so on, each intermediate n/d = x milestone followed by another one at (2n + d)/(n + d) = (x + 2)/(x + 1). Er, two quibbles: A) That should read (n + 2d)/(n + d) B) For the sake of having a monotonic sequence, let’s actually take every other item from this sequence. Thus, first 7/5, then 41/29, then 239/169, and so on, each n/d = x followed by (3n + 4d)/(2n + 3d) = (3x + 4)/(2x + 3). ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 7, 2012, 2:49am UTC](https://boards.straightdope.com/t/999-1/27517/432 "2012-08-07T02:49:00Z")
> [@Indistinguishable](#): > > The equation we looked at ([I shall link it again](http://imageshack.us/photo/my-images/213/capturenfo.png/)) does nothing to show that 1/10[sup]∞[/sup] is 0. It simply claims this (or rather, claims that 1 - the limit as n goes to ∞ of 1/10[sup]n[/sup] is 1) without argument. It _assumes_ this as one of its background rules. It is dependent upon those background rules. It is based on those rules. It is not a matter of external fact. > > We could work in a context of different background rules, and then the argument would no longer go through. We would have a different conclusion, relative to different rules. > [@allotrope](#): > > Yes, the background rules are basic logic. > > But since you’re the expert, which of the axioms are to blame for this travesty? I’m curious now. I’d like to remind you that you never answered my question. Are you ready to do that yet? ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 7, 2012, 2:53am UTC](https://boards.straightdope.com/t/999-1/27517/433 "2012-08-07T02:53:20Z")
> [@Indistinguishable](#): > > I am sympathetic to your frustration. However, irrelevant thought it may be to the larger point, I must re-insist that the resolution to Zeno’s paradox does not involve limits. Limits are neither necessary, nor even useful, for resolving the paradox (This post isn’t targeted at you, specifically, but at this all too common assertion) > > A) The theory of limits cannot be used to resolve Zeno’s paradox: > > After all, you can’t resolve a contradiction by just proffering another argument with a different conclusion. Then it just becomes an even greater contradiction! “The theory of limits says you can cross in finite time, but Zeno’s argument says you can’t. Ack, a contradiction!” > > The only way to resolve a paradox is by noting a flaw in the paradoxical argument. And once you’ve done that, there’s nothing more you have to do. > > B) The theory of limits is not necessary to resolve Zeno’s paradox: > > For example, let us suppose ourselves to live in a world of only rational distance ratios. > > Johnocles wants to get from milepost 1 to milepost 2. > > Zeno objects “Ah, but first, you must get to 3/2. And then you must get to 7/5. And then you must get to 17/12. And then you must get to 41/29.” And so on and so on, each intermediate n/d = x milestone followed by another one at (2n + d)/(n + d) = (x + 2)/(x + 1). > > Well, that sequence of intermediate milestones has no limit (not in this rational world). But it doesn’t matter. If Johnocles walks at a mile an hour, he’ll still get from milepost 1 to milepost 2 in a very finite hour, and cover all the infinite intermediaries in the intervening time, hitting each after the corresponding rational number of hours. Zeno was simply mistaken to think there was any contradiction between an interval having finite length and its containing infinitely many points. And you don’t need any theory of limits or infinite summation to recognize this mistake (nor do such theories play any role in banishing this mistake, formally; the only role they can play is psychological, by adding evidence to your comforting experience that you needn’t flip your shit every time you see the words “finite” and “infinite” next to each other). > > Zeno’s paradox is, after a moment’s thought, no paradox in the context of rationals, despite the failure of limits to exist. And it’s no paradox in the context of surreals, despite the even greater failure of limits to exist. And it’s no paradox in the context of reals, where limits do exist. But the way in which it’s no paradox is the same in all three of these. Limits don’t come into it. > > It’s just that, when Zeno says “How can you do infinitely many things in a finite amount of time? There can’t be infinitely many points in a finite interval!”, he’s speaking bosh. There can very clearly be such a thing. The leap from “Interval of finite length” to “Interval containing finitely many points” is fallacious, as demonstrated by the very example Zeno gives! Leave limits in the problem, take them I out. It doesn’t matter to me. Re: There can’t be infinitely many points in a finite interval!", he’s speaking bosh With all due respect what you just said seems complete bosh. How many rational numbers exits between the number 0 and 1? What is the upper bound you place on divding a lnegth of 1" or 1 mile or whatever? Bosh, to you sir. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 7, 2012, 3:00am UTC](https://boards.straightdope.com/t/999-1/27517/434 "2012-08-07T03:00:25Z")
> [@allotrope](#): > > I’d like to remind you that you never answered my question. Are you ready to do that yet? I’m not particularly interested in doing so. I doubt either you, or I, or anyone else reading this thread would enjoy the continuation of “The **Indistinguishable** and **Allotrope** Show”, or feel it was worth their time. But, if you insist, you may clarify your question for me: What do you mean by “this travesty”? If you mean “the result that 1/10[sup]∞[/sup] = 0”, this could follow from the axioms “A positive value raised to ∞ is infinite” and “The reciprocal of an infinite value is 0” (given suitable other rules as backdrop via which to manipulate these particularly salient ones; one cannot single out any one particular rule to blame). It could follow from other axioms as well. It depends on how you set up your axiom system. One natural rule system which would lead to this result would be that of the “affinely extended real number” system. If you mean “the result that 1/10[sup]∞[/sup] is positive”, this could follow from the axioms “A positive value raised to ∞ is positive” and “The reciprocal of a positive value is positive” (given suitable other rules as backdrop via which to manipulate these particularly salient ones; one cannot single out any one particular rule to blame). It could follow from other axioms as well. It depends on how you set up your axiom system. Two natural rule systems which would lead to this result would be that of the [hyperreal number](http://boards.straightdope.com/sdmb/showpost.php?p=15348503&postcount=118)" system and that of the “surreal number” system (in both cases, interpreting ∞ as either a canonical or an arbitrary positive infinite value). ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [August 7, 2012, 3:03am UTC](https://boards.straightdope.com/t/999-1/27517/435 "2012-08-07T03:03:51Z")
> [@Senegoid](#): > > Holy tamoley! Four pages of new posts, and that’s just TODAY! . . . > > This thread is rapidly overtaking the [Problems With Relativity](http://www.boards.straightdope.com/sdmb/showthread.php?t=404854) thread! . . . Holy Mother of God, NO! > [@erik150x](#): > > . . . The limit of .000…0 is the same as the limit .000…1 > . . . (Wow, that’s awkward, as ". . . " means “snip” and is not the same as “…” which means “repeated indefinitely.” But…moving on…) Neither of the two strings you just used is defined. You can’t put a digit after “…” “.000…0” has no meaning. I would like to ask you to define it, please; I’m pretty sure you cannot. This is all precedented; according to Martin Gardner, Charles Dodgson also didn’t understand limits. He complained that the infinitesimal calculus didn’t “eliminate” the difference between a limit and the actual number, but only reduced it to a very small, yet positive difference. When even a maths professor couldn’t get it, I think it is forgiveable for one of hoi polloi (the rest of us!) not to get it. Also worth quoting is Norton Juster’s quip from “The Phantom Tollbooth:” “‘Just follow that line forever,’ said the Mathemagician, ‘and when you reach the end, turn left.’” ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 7, 2012, 3:05am UTC](https://boards.straightdope.com/t/999-1/27517/436 "2012-08-07T03:05:11Z")
> [@Indistinguishable](#): > > I’m not particularly interested in doing so. I doubt either you, or I, or anyone else reading this thread would enjoy the continuation of “The **Indistinguishable** and **Allotrope** Show”, or feel it was worth their time. But, if you insist, you may clarify your question for me: What do you mean by “this travesty”? > > If you mean “the result that 1/10[sup]∞[/sup] = 0”, this could follow from the axioms “A positive value raised to ∞ is infinite” and “The reciprocal of an infinite value is 0” (given suitable other rules as backdrop via which to manipulate these particularly salient ones; one cannot single out any one particular rule to blame). It could follow from other axioms as well. It depends on how you set up your axiom system. One natural rule system which would lead to this result would be that which flows from the rules defining the “real number” system. > > If you mean “the result that 1/10[sup]∞[/sup] is positive”, this could follow from the axioms “A positive value raised to ∞ is positive” and “The reciprocal of a positive value is positive” (given suitable other rules as backdrop via which to manipulate these particularly salient ones; one cannot single out any one particular rule to blame). It could follow from other axioms as well. It depends on how you set up your axiom system. Two natural rule systems which would lead to this result would be that which flows from the rules defining the “[hyperreal number](http://boards.straightdope.com/sdmb/showpost.php?p=15348503&postcount=118)” or “surreal number” systems. I guess I have to remind you of what you said, AGAIN > [@Indistinguishable](#): > > The equation we looked at ([I shall link it again](http://imageshack.us/photo/my-images/213/capturenfo.png/)) \*\* does nothing to show that 1/10[sup]∞[/sup] is 0. It simply claims this (or rather, claims that 1 - the limit as n goes to ∞ of 1/10[sup]n[/sup] is 1) without argument. It _assumes_ this as one of its background rules. It is dependent upon those background rules. It is based on those rules. It is not a matter of external fact.\*\* > > We could work in a context of different background rules, and then the argument would no longer go through. We would have a different conclusion, relative to different rules. So where is the axiom that that says this is merely assumed rather than proved. Because you see, I seem to remember proving this in MY calc courses and NOT assuming it. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 7, 2012, 3:05am UTC](https://boards.straightdope.com/t/999-1/27517/437 "2012-08-07T03:05:14Z")
> [@Indistinguishable](#): > > Er, two quibbles: > > A) That should read (n + 2d)/(n + d) > > B) For the sake of having a monotonic sequence, let’s actually take every other item from this sequence. Thus, first 7/5, then 41/29, then 239/169, and so on, each n/d = x followed by (3n + 4d)/(2n + 3d) = (3x + 4)/(2x + 3). The sequence as I have stated and is most commonaly stated: Sum(i=1 to infinity) [1/2^i] Regardless of how you would lke to figure out that sum, these are the series points I am mapping to the infinite decimal expansion .999… There is not need to change anything, I have no clue why you are attmepting to do so? ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [August 7, 2012, 3:09am UTC](https://boards.straightdope.com/t/999-1/27517/438 "2012-08-07T03:09:06Z")
> [@Indistinguishable](#): > > I’m not particularly interested in doing so. I doubt either you, or I, or anyone else reading this thread would enjoy the continuation of “The **Indistinguishable** and **Allotrope** Show”, or feel it was worth their time. But, if you insist, you may clarify your question for me: What do you mean by “this travesty”? > > If you mean “the result that 1/10[sup]∞[/sup] = 0”, this could follow from the axioms “A positive value raised to ∞ is infinite” and “The reciprocal of an infinite value is 0” (given suitable other rules as backdrop via which to manipulate these particularly salient ones; one cannot single out any one particular rule to blame). It could follow from other axioms as well. It depends on how you set up your axiom system. One natural rule system which would lead to this result would be that which flows from the rules defining the “real number” system. > > If you mean “the result that 1/10[sup]∞[/sup] is positive”, this could follow from the axioms “A positive value raised to ∞ is positive” and “The reciprocal of a positive value is positive” (given suitable other rules as backdrop via which to manipulate these particularly salient ones; one cannot single out any one particular rule to blame). It could follow from other axioms as well. It depends on how you set up your axiom system. Two natural rule systems which would lead to this result would be that which flows from the rules defining the “[hyperreal number](http://boards.straightdope.com/sdmb/showpost.php?p=15348503&postcount=118)” or “surreal number” systems. I actually **am** curious what the exact axiomatic construction of the Reals is (whichever is simplest). As far as I can tell, the only axiom used to construct the real numbers that even involves infinity is that the set of all reals have a least upper bound/supremum of aleph-0. The other stuff is obvious (definition of addition, multiplication, etc), I’m curious if there’s a comprehensive list of all of the axioms that define the reals. All the ones I’ve found online so far omit anything about infinitesimals or infinities (aside from least upper bound). I’m not asking you to construct such a thing yourself, I just can’t find it, it HAS to exist SOMEWHERE. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 7, 2012, 3:10am UTC](https://boards.straightdope.com/t/999-1/27517/439 "2012-08-07T03:10:01Z")
> [@allotrope](#): > > I guess I have to remind you of what you said, AGAIN > > So where is the axiom that that says this is merely assumed rather than proved. Because you see, I seem to remember proving this in MY calc courses and NOT assuming it. Of course you can prove it… _from other rules_. A typical proof is along the lines of what I had written in [this post](http://boards.straightdope.com/sdmb/showpost.php?p=15355286&postcount=399), which [you dismissed](http://boards.straightdope.com/sdmb/showpost.php?p=15355319&postcount=400), but which, I assure you, is what your calculus books will expect. That argument is based on certain rules as to how limits at infinity are to be calculated. Different rules would lead to different conclusions. Every proof is relative to the rules/definitions/axioms/whatever-you-call-them being employed within that proof. ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 7, 2012, 3:11am UTC](https://boards.straightdope.com/t/999-1/27517/440 "2012-08-07T03:11:33Z")
I could be mistaken, but I’m under the impression that Indistinguishable claims to be a maths expert, so I’m sure he can help you out. [Previous page](https://boards.straightdope.com/t/999-1/27517.md?page=21) [Next page](https://boards.straightdope.com/t/999-1/27517.md?page=23)