Closed Line Segment

Last updated Nov 1, 2022

# Definition

over

\mathbb{R}

and

x_{1}, x_{2} \in V

L \subset V

between

x_{1}

and

x_{2}

the Set

L = {\lambda x_{1} + (1 - \lambda) x_{2} : \lambda \in [0,1]}

$L$ can also be expressed as $L = {x_{2} + \lambda (x_{1} - x_{2}) : \lambda \in [0,1] }$ . This follows from the observation that $\lambda x_{1} + (1 - \lambda) x_{2} = x_{2} + \lambda x_{1} - \lambda x_{2} = x_{2} + \lambda (x_{1} - x_{2})$