|
An endpoint of a line segment $L$ is a point that belongs to the boundary of $L$ . Note that every line segment has two distinct endpoints. For example, if $V$ is a vector space and $a,b \in V$ with $b \neq 0$ , then the endpoints of the line segment $\displaystyle L = \{ a+tb : t\in[0,1]\}$ are $a$ and $a+b$ .
Note that the endpoints of the open line segment $\displaystyle L=\{a+tb:t\in(0,1)\}$ are also $a$ and $a+b$ .
Endpoints can be defined in a similar manner for other geometric objects. These include rays, arcs, and intervals.
- Rays have one endpoint.
- Arcs have two endpoints.
- Intervals can have zero, one, or two endpoints, depending on whether they are bounded above and/or below. See the entry on intervals for more details.
|
![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
{.} \psline(0,0)(4,0) \psdots(0,0)(4,0) \rput[a](0,-0.3){$a$} \rput[a](4,-0.3){$a+b$} \end{pspicture}](http://images.planetmath.org:8080/cache/objects/8165/js/img1.png "\begin{pspicture}(0,-0.5)(4,0.1) \rput[a](0,0.06){.} \psline(0,0)(4,0) \psdots(0,0)(4,0) \rput[a](0,-0.3){$a$} \rput[a](4,-0.3){$a+b$} \end{pspicture}"){kind=small}
{.} \psline{o-o}(0,0)(4,0) \rput[a](0,-0.3){$a$} \rput[a](4,-0.3){$a+b$} \end{pspicture}](http://images.planetmath.org:8080/cache/objects/8165/js/img2.png "\begin{pspicture}(0,-0.5)(4,0.1) \rput[a](0,0.06){.} \psline{o-o}(0,0)(4,0) \rput[a](0,-0.3){$a$} \rput[a](4,-0.3){$a+b$} \end{pspicture}"){kind=small}
