# endpoint

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 manner for other geometric . These include rays, arcs (http://planetmath.org/PathConnected), and intervals (http://planetmath.org/Interval).

• Rays have one endpoint.

• have two endpoints.

• can have zero, one, or two endpoints, depending on whether they are bounded above and/or below. See the entry on intervals (http://planetmath.org/Interval) for more details.

Title endpoint Endpoint 2013-03-22 16:06:05 2013-03-22 16:06:05 Wkbj79 (1863) Wkbj79 (1863) 12 Wkbj79 (1863) Definition msc 51-00 msc 03-00 end point