# Math and distance and fractions and decimal places and beer **URL:** \ **Category:** Factual Questions\ **Created:** [October 31, 2009, 9:27pm UTC](https://boards.straightdope.com/t/math-and-distance-and-fractions-and-decimal-places-and-beer/515884 "2009-10-31T21:27:43Z")\ **Posts on this page:** 6\ **Page:** 3
**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:** [November 2, 2009, 5:46am UTC](https://boards.straightdope.com/t/math-and-distance-and-fractions-and-decimal-places-and-beer/515884/41 "2009-11-02T05:46:14Z")
> [@Thudlow\_Boink](#): > > I’m not sure this is fair to say. Cantor worked out issues relating to infinite cardinalities (sizes of infinite sets). But the ideas behind the modern view of calculus (with limits) were worked out before Cantor came along, by people like Cauchy and Weierstrass. Yup. Fair comment. I was being rather loose with history, being an enthusiast for Canotr’s work, I was rather glossing over the rest tof it. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 2, 2009, 5:49am UTC](https://boards.straightdope.com/t/math-and-distance-and-fractions-and-decimal-places-and-beer/515884/42 "2009-11-02T05:49:43Z")
One could also easily imagine a number line with points on it which do not correspond to that particular system of quantities given the unfortunate name “real numbers”; e.g., one with distances greater than every integer, or with positive distances less than every positive rational. But whatever. That’s a distraction. We don’t even need the concept of “real numbers” to state or settle the problem. It still comes out to just: > [@Milossarian](#): > > Doesn’t there have to be some last fraction of a number before reaching the complete distance? No. Why would you think so? If you tell us what led you to think this, then we can show where such reasoning went wrong. Otherwise, there’s nothing more which can be said. This assumption is erroneous, and thus there is no real paradox. ---
**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:** [November 2, 2009, 5:51am UTC](https://boards.straightdope.com/t/math-and-distance-and-fractions-and-decimal-places-and-beer/515884/43 "2009-11-02T05:51:51Z")
> [@Francis\_Vaughan](#): > > Ooch, no! Bah! Now I’m correcting my correction - in so far as What I was correcting wasn’t what was written. ☹ My bad. Still true, the reals are the algebraic and the transendentals, but the original quote was correct - decimals are rationals. And if you restrict your thinking to these you don’t need to worry. I was going one further, and pointintg out that there are more numbers than these. ---
**Author:** ![Cubsfan](https://avatars.discourse-cdn.com/v4/letter/c/f4b2a3/32.png) [@Cubsfan](https://boards.straightdope.com/u/Cubsfan)\ **Post date:** [November 2, 2009, 11:20am UTC](https://boards.straightdope.com/t/math-and-distance-and-fractions-and-decimal-places-and-beer/515884/44 "2009-11-02T11:20:29Z")
This is essentially the definition of a Limit in calculus. Well, maybe not the definition, but Limits are used to represent these types of things. ---
**Author:** ![Milossarian](https://avatars.discourse-cdn.com/v4/letter/m/3ec8ea/32.png) [@Milossarian](https://boards.straightdope.com/u/Milossarian)\ **Post date:** [November 2, 2009, 5:45pm UTC](https://boards.straightdope.com/t/math-and-distance-and-fractions-and-decimal-places-and-beer/515884/45 "2009-11-02T17:45:45Z")
> [@Wendell\_Wagner](#): > > Milossarian, why don’t you read all the threads in the FAQ that CookingWithGas created related to this subject? Every objection you can come up with (yes, every one of them) and many others are discussed in those threads. The problems that you’re having with this idea aren’t new. Really, they aren’t. I did. In fact, I cited some of them in my last post. > [@Indistinguishable](#): > > You know what, let’s just keep doing this: > > No. Why would you think there did have to be? (Some last fraction of a number before reaching the complete distance?) > > We can only really resolve your confusion once you answer this. It’s difficult to put one’s head around the idea that there can be infinite points within something finite. That’s pretty much it. You are to be commended if it doesn’t boggle your mind. It boggles mine. Thanks to everybody who participated. It was very interesting to me. Continue as you please. Apologies to those who are somehow put off that a topic was discussed that’s been discussed before. ---
**Author:** ![pancakes3](https://avatars.discourse-cdn.com/v4/letter/p/ba9def/32.png) [@pancakes3](https://boards.straightdope.com/u/pancakes3)\ **Post date:** [November 2, 2009, 8:18pm UTC](https://boards.straightdope.com/t/math-and-distance-and-fractions-and-decimal-places-and-beer/515884/46 "2009-11-02T20:18:08Z")
so much for that college edumacation. [Previous page](https://boards.straightdope.com/t/math-and-distance-and-fractions-and-decimal-places-and-beer/515884.md?page=2)