Line Connecting Two Points

Let $X$ be a vector space and let $a,b\in X$. The line connecting $a$ and $b$ is

This is the smallest affine set containing $\{a,b\}$ and is the affine analogue of the line segment $[a,b]$ (where $\lambda\in[0,1]$).

Examples:

• In $\mathbb{R}^2$, $L[a,b]$ is the usual straight line through $a$ and $b$.
• If $a=b$, then $L[a,a]=\{a\}$.