I'm reading arXiv: 1706.09666 [math-ph]. In page 33 the authors introduce the universal tensor algebra for the vector space $\mathcal{E}^{obs}(M)$ through $$\mathcal{T}^{obs}(M) = \mathbb{C} \otimes \bigoplus_{n=0}^{\infty} (\mathcal{E}^{obs}(M))^{\otimes n},$$ where $(\mathcal{E}^{obs}(M))^{\otimes 0} = \mathbb{R}$. They then go to mention that
[The elements of $\mathcal{T}^{obs}(M)$] are therefore complex linear combinations of the definitively vanishing sequences of real functions $F=(\phi^{(0)},\phi^{(1)},\ldots)$ with $\phi^{(k)} \in (\mathcal{E}^{obs}(M))^{\otimes k}$.
What does "definitively vanishing sequence" means in this context?