# Lines, line segments, and rays **URL:** \ **Category:** Factual Questions\ **Created:** [April 19, 2018, 2:53pm UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711 "2018-04-19T14:53:13Z")\ **Posts on this page:** 9\ **Page:** 2
**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:** [April 19, 2018, 11:31pm UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/21 "2018-04-19T23:31:24Z")
Maybe it’s a hijack, but I find the negation of the Axiom of Choice much more intuitive than the Axiom of Choice itself. Mathematician: And now, I can choose one member of each of these sets. Me: OK, then do it. Choose one member of each set. Mathematician: Done! Me: So, which member did you choose for each of them? Mathematician: Oh, I don’t know which one I chose. But I can do it. Me: But if you don’t know which one you chose, what do you mean that you chose them? ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [April 20, 2018, 1:10am UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/22 "2018-04-20T01:10:57Z")
> [@Asympotically\_fat](#): > > Interestingly in quantum mechanics interestingly the term ‘ray’ is used to describe the equivalence class of vectors **v** ~ **w** iff **v** =a **w** for some non-zero scalar a. I thought about that before I saw your post, though these are not quite rays in the sense that other posters are describing, since **v** ~ - **v**. Better to picture them as lines through the origin, or, to a geometer, elements of the projective space (at least if the origin is deleted first). I’m sure the OP’s “anti-rays” show up in some construction somewhere; projective spaces commonly occur everywhere (not that that answers his question). ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [April 20, 2018, 1:18am UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/23 "2018-04-20T01:18:00Z")
How about, consider an attracting fixed point of a dynamical system. Then orbits of points in the surrounding basin of attraction will be “anti-rays” that converge to the point. ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [April 20, 2018, 1:25am UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/24 "2018-04-20T01:25:52Z")
> [@Enola\_Straight](#): > > I remember from my geometry class as a child the lesson regarding these three mathematical constructs: > > A line stretches both ways to infinity. > > A line segment is finite…a definite beginning and a definite end. > > A ray begins at a point and stretches out to infinity. > > [https://showme0-9071.kxcdn.com/files/476420/pictures/thumbs/1056882/last\_thumb1377989684.jpg](https://showme0-9071.kxcdn.com/files/476420/pictures/thumbs/1056882/last_thumb1377989684.jpg) > > Is there some kind of anti-ray? Comes in from infinity and ends at a definite point? Maybe I’m misunderstanding something, but isn’t your anti-ray exactly the same object as a ray? Just from a different perspective? ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [April 20, 2018, 1:35am UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/25 "2018-04-20T01:35:20Z")
> [@DavidwithanR](#): > > Two roads, even if both infinitely long, don’t necessarily pass through all the same places? What does this have to do with anything? > [@DavidwithanR](#): > > Paradoxes necessarily being “true statements that would appear to be mutually exclusive but in fact are not”, and optionally also fitting certain sub-categories, makes sense to me - or have I missed the point? Yes, you have. That’s not how “paradox” is defined in any context I know of. ---
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [April 20, 2018, 2:27pm UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/26 "2018-04-20T14:27:35Z")
> [@Quercus](#): > > Maybe I’m misunderstanding something, but isn’t your anti-ray exactly the same object as a ray? Just from a different perspective? Well, a ray…_radiates_…from an origin. Is it different if the “end” is a _destination?_ An object which absorbs rather than emits? ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [April 20, 2018, 3:01pm UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/27 "2018-04-20T15:01:05Z")
> [@Enola\_Straight](#): > > Well, a ray…_radiates_…from an origin. Is it different if the “end” is a _destination?_ An object which absorbs rather than emits? There are different ways to think of it. One way is that a ray (or a line, or a line segment, or whatever) is just a set of points that are all just considered as a whole, and there’s no sense of action or motion (radiating, absorbing, emitting) involved. Another way is that, to someone like Euclid, there is no “completed infinity,” so you can’t get a ray that ends at a definite point because there’s no “point at infinity” to start from. And your way is yet another way, incompatible with those above, but not therefore “wrong.” ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [April 20, 2018, 8:11pm UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/28 "2018-04-20T20:11:15Z")
> [@Enola\_Straight](#): > > Well, a ray…_radiates_…from an origin. Is it different if the “end” is a _destination?_ An object which absorbs rather than emits? See Post #23-- apparently you are thinking of dynamics, say of a point moving in the plane as a function of time, in which case there is an obvious difference between a trajectory that starts at or near a point and shoots off somewhere, and one that does the opposite. Here is a specific example I stole from Wikipedia: look at the leftmost figure in [https://upload.wikimedia.org/wikipedia/en/5/55/LinearFields.png](https://upload.wikimedia.org/wikipedia/en/5/55/LinearFields.png) ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [April 20, 2018, 11:30pm UTC](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711/29 "2018-04-20T23:30:58Z")
> [@Ignotus](#): > > Yes, they are of the same (infinite) length. You can easily (I’ll leave it to you as an exercise!) map the one onto the other. And yet there is such a thing as a _long line_ and _long ray_. They are also infinitely long. But at the same time, they are longer than the “normal” infinite line and ray. (roughly speaking, the _long line_ is composed of uncountably many unit-length segments, whereas a normal line has only countably many segments) [Previous page](https://boards.straightdope.com/t/lines-line-segments-and-rays/812711.md?page=1)