Rational independence

Real numbers ${𝜔 𝑖} 𝑛 𝑖 = 1$ are said to be rationally indendent iff the only $𝑛$ -tuple ${𝑚 𝑖} 𝑛 𝑖 = 1$ satisfying $\sum 𝑛 𝑖 = 1 𝑚 𝑖 𝜔 𝑖 = 0$ is $𝑚 𝑖 = 0$ for all $𝑖$ .¹ num