So I've been following Paul's Notes on Differential Equations. In Section 3-7 More on the Wronskian he says "if the functions are linearly dependent then we can write at least one of them in terms of the other functions." $$\begin{align*}{c_1}{f_1}\left( x \right) + {c_2}{f_2}\left( x \right) + \cdots + {c_n}{f_n}\left( x \right) & = 0\\ {c_1}{f_1}\left( x \right) & = - \left( {{c_2}{f_2}\left( x \right) + \cdots + {c_n}{f_n}\left( x \right)} \right)\\ {f_1}\left( x \right) & = - \frac{1}{{{c_1}}}\left( {{c_2}{f_2}\left( x \right) + \cdots + {c_n}{f_n}\left( x \right)} \right)\end{align*}$$ This seems to suggest that there must be at least two nontrivial constants, $c_1$ for realness, and $c_i$, where ${1<i\leq n}$, to avoid nontriviality. The Wikipedia page for Linear Independence along with most other sources I've found claim that any set of vectors including the zero vector $\overrightarrow0$ are necessarily linearly dependent. But this would require that $\forall c_i$ where $1<i\leq n, c_i=0$, which would involve only one nonzero constant, $c_1$. Is this by definition or is my reading of Paul's Notes incorrect?
Links for Reference: https://en.wikipedia.org/wiki/Linear_independence https://tutorial.math.lamar.edu/Classes/DE/Wronskian.aspx