ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Operation
▼ N-operation
▼ Binary operation
▼ Enclosed binary operation
▼ Groupoid
▼ Ringoid
▼ Semiring
▼ Ring
▼ Left ring action
▼ Module
▼ Linear combination
▼ Linear decomposition
▼ Affine decomposition
▼ Convex combination
▼ Set of convex combinations
▼ Set of euclidean real convex combinations
Definition D5700
Euclidean real line segment
Formulation 0
Let $x, y \in \mathbb{R}^N$ each be a D4924: Euclidean real number.
The line segment in $\mathbb{R}^N$ from $x$ to $y$ is the D11: Set \begin{equation} \{ t x + (1 - t) y : t \in [0, 1] \} \end{equation}