\begin{definition}[Definition:Convex Set (Vector Space)/Line Segment]
Let $V$ be a vector space over $\R$ or $\C$.
Let $x, y \in V$.
The set:
:$\set {t x + \paren {1 - t} y: t \in \closedint 0 1}$ 
is called the '''(straight) line segment joining $x$ and $y$'''.
A convex set can thus be described as a set containing all '''straight line segments''' between its elements.
\end{definition}