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[parent] endpoint (Definition)

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$.


\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}

Note that the endpoints of the open line segment $ \displaystyle L=\{a+tb:t\in(0,1)\}$ are also $ a$ and $ a+b$.


\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}

Endpoints can be defined in a similar manner for other geometric objects. These include rays, arcs, and intervals.

  • Rays have one endpoint.

    \begin{pspicture}(0,-0.1)(4,0.1) \psline{->}(0,0)(4,0) \psdot(0,0) \end{pspicture}
  • Arcs have two endpoints.

    \begin{pspicture}(0,0)(4,2) \psarc(2,0){2}{0}{180} \psdots(0,0)(4,0) \end{pspicture}
  • 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.



"endpoint" is owned by Wkbj79.
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Other names:  end point

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Cross-references: bounded, rays, open line segment, vector space, boundary, point, line segment
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This is version 9 of endpoint, born on 2006-07-22, modified 2007-06-26.
Object id is 8165, canonical name is Endpoint.
Accessed 3098 times total.

Classification:
AMS MSC03-00 (Mathematical logic and foundations :: General reference works )
 51-00 (Geometry :: General reference works )

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