ThmDex – An index of mathematical definitions, results, and conjectures.
Result R3618 on D2367: Formal convex combination
Subresult of R3617: Turning a finite number of unsigned real numbers into convex combination coefficients
Turning two unsigned real numbers into convex combination coefficients
Formulation 0
Let $x, y \in [0, \infty)$ each be an D4767: Unsigned real number such that
(i) $x + y \neq 0$
Then
(1) \begin{equation} \frac{x}{x + y}, \frac{y}{x + y} \in [0, 1] \end{equation}
(2) \begin{equation} \frac{x}{x + y} + \frac{y}{x + y} = 1 \end{equation}
Proofs
Proof 0
Let $x, y \in [0, \infty)$ each be an D4767: Unsigned real number such that
(i) $x + y \neq 0$