# .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:** 15
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:25pm UTC](https://boards.straightdope.com/t/999-1/27517/281 "2012-08-06T14:25:57Z")
> [@allotrope](#): > > Your logic is flawed because you still fail to understand what infinity means. > > Let’s put a little ‘9’ at each halfway mark. There will still be an infinite number of them. As I said before, YOU NEVER GET TO POINT B EXCEPT AT INFINITY. > > It’s not my fault if you don’t read my posts now is it? Right the last point on the both line segments, the infinite point at the end of both line segment A and B? Can I not walk from one end of the line segment to the other? Do I not pass an infinite number of 0s on top and 9s on the bottom by time I reach the end of the line. Each half way point represents a number on top and bottom. 1/2 + 1/4 + 1/8 +… + 1/infinity = 1 This is the classic Limit soultion to Zeno’s paradox? Is there not an infinite number of points here? Please tell me where the logic is wrong? ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 6, 2012, 2:30pm UTC](https://boards.straightdope.com/t/999-1/27517/282 "2012-08-06T14:30:14Z")
> [@erik150x](#): > > Right the last point on the both line segments, the infinite point at the end of both line segment A and B? Can I not walk from one end of the line segment to the other? > > Do I not pass an infinite number of 0s on top and 9s on the bottom by time I reach the end of the line. > > Each half way point represents a number on top and bottom. > > 1/2 + 1/4 + 1/8 +… + 1/infinity = 1 This is the classic Limit soultion to Zeno’s paradox? Is there not an infinite number of points here? > > Please tell me where the logic is wrong? I just did, what part didn’t you understand? ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:30pm UTC](https://boards.straightdope.com/t/999-1/27517/283 "2012-08-06T14:30:41Z")
> [@allotrope](#): > > Your logic is flawed because you still fail to understand what infinity means. > > Let’s put a little ‘9’ at each halfway mark. There will still be an infinite number of them. As I said before, YOU NEVER GET TO POINT B EXCEPT AT INFINITY. > > It’s not my fault if you don’t read my posts now is it? You did not try to really understand my post. The Line segment is 1 mile (not infinite) so I can reach the end as people aften do go for walks. But we all know you must always go halfway first then half of the reaminder and so on… This is an infinite series represented by 1/2 + 1/4 + 1/8 + … + 1/infinity = 1 In both distance and time I have taveled: I have reached an infinite number of points, yes or no? ---
**Author:** ![TATG](https://avatars.discourse-cdn.com/v4/letter/t/50afbb/32.png) [@TATG](https://boards.straightdope.com/u/TATG)\ **Post date:** [August 6, 2012, 2:31pm UTC](https://boards.straightdope.com/t/999-1/27517/284 "2012-08-06T14:31:45Z")
> [@erik150x](#): > > Now we reverse the process and start subtracting line B from A. To be honest do we really need to finish the whole calculation? Because once we see the 0 at the end of line A and the 9 at the end of line B, we know what the result will be: > .000…1 There is no last numeral. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:33pm UTC](https://boards.straightdope.com/t/999-1/27517/285 "2012-08-06T14:33:22Z")
> [@allotrope](#): > > I just did, what part didn’t you understand? You said: Your logic is flawed because you still fail to understand what infinity means. – this is a useless counter, means nothing… except your opinon of my knowledge. Nothing about the actual logic I stated. Let’s put a little ‘9’ at each halfway mark. There will still be an infinite number of them. As I said before, YOU NEVER GET TO POINT B EXCEPT AT INFINITY. — How did I not reach an infinite number of points on my walk? It’s not my fault if you don’t read my posts now is it? – again usless counter statement. ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 6, 2012, 2:34pm UTC](https://boards.straightdope.com/t/999-1/27517/286 "2012-08-06T14:34:06Z")
> [@erik150x](#): > > You did not try to really understand my post. The Line segment is 1 mile (not infinite) so I can reach the end as people aften do go for walks. But we all know you must always go halfway first then half of the reaminder and so on… > This is an infinite series represented by > 1/2 + 1/4 + 1/8 + … + 1/infinity = 1 > In both distance and time I have taveled: > > I have reached an infinite number of points, yes or no? Are you going by 1/2 each time? I’ll assume yes. Are you labeling a point each time? I’ll assume yes. In that case, it will take you an infinite amount of time and you will hit an infinite number of points. You will still never reach point B except at infinity. Is that better? ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:34pm UTC](https://boards.straightdope.com/t/999-1/27517/287 "2012-08-06T14:34:37Z")
> [@TATG](#): > > There is no last numeral. But I Just told you how to find the last numeral. Please tell me how I my method is wrong? ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [August 6, 2012, 2:34pm UTC](https://boards.straightdope.com/t/999-1/27517/288 "2012-08-06T14:34:45Z")
You are solving Zeno by appealing to motion in the physical world - yet you are claiming that you physically were able to generate the labelled points - and you do have to label them all because you claim that the “last” point is the one that matters. You are thus confusing together an appeal to physical motion with an infinite process. But you need to provide a solution to Zeno in the abstract that allows your labelling to work. Placing the intervals in a one to one relationship with the fractions of time needed to label them is the usual solution - but you need to then show that time reaches the end - thus you are trying to prove something by assuming its converse. Why should the time fractions reach the end point and not the fractional distances? Either place both or neither in the physical world - you can’t place one in the physical and the other in the abstract. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:35pm UTC](https://boards.straightdope.com/t/999-1/27517/289 "2012-08-06T14:35:48Z")
> [@allotrope](#): > > Are you going by 1/2 each time? I’ll assume yes. > Are you labeling a point each time? I’ll assume yes. > > In that case, it will take you an infinite amount of time and you will hit an infinite number of points. > > You will still never reach point B except at infinity. > > Is that better? I already stated twice … once in the problem and aftwards. It is not really neccessary to label them. We already knwo what they should be. I really just need to reach the last one. ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 6, 2012, 2:36pm UTC](https://boards.straightdope.com/t/999-1/27517/290 "2012-08-06T14:36:32Z")
> [@Francis\_Vaughan](#): > > You are solving Zeno by appealing to motion in the physical world - yet you are claiming that you physically were able to generate the labelled points - and you do have to label them all because you claim that the “last” point is the one that matters. You are thus confusing together an appeal to physical motion with an infinite process. But you need to provide a solution to Zeno in the abstract that allows your labelling to work. Placing the intervals in a one to one relationship with the fractions of time needed to label them is the usual solution - but you need to then show that time reaches the end - thus you are trying to prove something by assuming its converse. Why should the time fractions reach the end point and not the fractional distances? Either place both or neither in the physical world - you can’t place one in the physical and the other in the abstract. Silly boy thinks he’s turning an example I used to try to help him back on me. He doesn’t realize whatever kind of infinity we use to map this out, it’s all the same. ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 6, 2012, 2:37pm UTC](https://boards.straightdope.com/t/999-1/27517/291 "2012-08-06T14:37:34Z")
> [@erik150x](#): > > I already stated twice … once in the problem and aftwards. It is not really neccessary to label them. We already knwo what they should be. I really just need to reach the last one. And with an infinite number of them BY DEFINITION there is no LAST ONE. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:38pm UTC](https://boards.straightdope.com/t/999-1/27517/292 "2012-08-06T14:38:21Z")
> [@Francis\_Vaughan](#): > > You are solving Zeno by appealing to motion in the physical world - yet you are claiming that you physically were able to generate the labelled points - and you do have to label them all because you claim that the “last” point is the one that matters. You are thus confusing together an appeal to physical motion with an infinite process. But you need to provide a solution to Zeno in the abstract that allows your labelling to work. Placing the intervals in a one to one relationship with the fractions of time needed to label them is the usual solution - but you need to then show that time reaches the end - thus you are trying to prove something by assuming its converse. Why should the time fractions reach the end point and not the fractional distances? Either place both or neither in the physical world - you can’t place one in the physical and the other in the abstract. I have put forth I do not need to label them, we know what they should be labeled they are the same all the way to the end. In fact the whole argument rests on simple reaching the end of an infinite series of points. which I will associate with numerals, but there is no need to physically label them, why should there be? ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:39pm UTC](https://boards.straightdope.com/t/999-1/27517/293 "2012-08-06T14:39:47Z")
> [@allotrope](#): > > And with and infinite number of them BY DEFINITION there is no LAST ONE. Again I have given you instructions on how to find it. What part of those instructions are flawed? Again, there is no need to physically label them, why should there be? ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 6, 2012, 2:41pm UTC](https://boards.straightdope.com/t/999-1/27517/294 "2012-08-06T14:41:06Z")
> [@erik150x](#): > > I have put forth I do not need to label them, we know what they should be labeled they are the same all the way to the end. In fact the whole argument rests on simple reaching the end of an infinite series of points. which I will associate with numerals, but there is no need to physically label them, why should there be? The fact that you could even say something like “reaching the end of and infinite series” with a straight face, is really . . . I don’t even know what to say. :smack: ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 6, 2012, 2:42pm UTC](https://boards.straightdope.com/t/999-1/27517/295 "2012-08-06T14:42:30Z")
> [@erik150x](#): > > Again I have given you instructions on how to find it. What part of those instructions are flawed? > > Again, there is no need to physically label them, why should there be? Your concept is flawed - there is no last one in an infinite series - that’s why they call it INFINITE. You can’t really be this thick. I don’t mean to be rude but that is just too over the top. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:43pm UTC](https://boards.straightdope.com/t/999-1/27517/296 "2012-08-06T14:43:38Z")
> [@allotrope](#): > > The fact that you could even say something like “reaching the end of and infinite series” with a straight face, is really . . . I don’t even know what to say. :smack: So tell me then how do you solve Zeno’s paradox of moving from point A to point B? Since the distince is infinitely divisible in halves, you must pass or reach an infinite number of them no? ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 6, 2012, 2:44pm UTC](https://boards.straightdope.com/t/999-1/27517/297 "2012-08-06T14:44:55Z")
> [@erik150x](#): > > So tell me then how do you solve Zeno’s paradox of moving from point A to point B? > > Since the distince is infinitely divisible in halves, you must pass or reach an infinite number of them no? I’ve told you 3 times already. After this, I’m outta here. YOU NEVER GET TO B - you only get there at infinity. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:46pm UTC](https://boards.straightdope.com/t/999-1/27517/298 "2012-08-06T14:46:09Z")
> [@allotrope](#): > > I’ve told you 3 times already. After this, I’m outta here. > > YOU NEVER GET TO B - you only get there at infinity. So you can’t move? Thats shame. I am sorry you can never get from pont A to point B? Your whole life must be an illusion? ---
**Author:** ![allotrope](https://avatars.discourse-cdn.com/v4/letter/a/edb3f5/32.png) [@allotrope](https://boards.straightdope.com/u/allotrope)\ **Post date:** [August 6, 2012, 2:49pm UTC](https://boards.straightdope.com/t/999-1/27517/299 "2012-08-06T14:49:07Z")
> [@erik150x](#): > > So you can’t move? Thats shame. I am sorry you can never get from pont A to point B? Your whole life must be an illusion? You continue to move but in every smaller increments. When the number of increments reach infinity, you arrive at point B. ---
**Author:** ![erik150x](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@erik150x](https://boards.straightdope.com/u/erik150x)\ **Post date:** [August 6, 2012, 2:50pm UTC](https://boards.straightdope.com/t/999-1/27517/300 "2012-08-06T14:50:47Z")
> [@allotrope](#): > > You continue to move but in every smaller increments. When the number of increments reach infinity, you arrive at point B. Thank you. So we agree as I moved from the start of my walk to the end, I did indeed reach an infinit number of points each 1/2 the distance of the previous? [Previous page](https://boards.straightdope.com/t/999-1/27517.md?page=14) [Next page](https://boards.straightdope.com/t/999-1/27517.md?page=16)