Convex Subset of a Vector Space over the Real Numbers

Let $\mathbb{R}$ be the ordered field of real numbers, with the notation of that item, and let $E$ be a vector space over $\mathbb{R}$.

A subset $C\subseteq E$ is convex if for all $x,y\in C$ and every $t\in\mathbb{R}$ with $0\le t$ and $t\le 1$,

$$t\,x+(1-t)\,y\in C .$$