hey,
I have a little linear algebra question here,
if I have understood my task correctly.
Any help is appreciated.

Let $\{f_i | f \in \mathbb{N} \}$.
$f_i \in Map(\mathbb{N}, \mathbb{Q})$ is defined as:

$f_i(n)= -n \quad\forall \quad n \geq i$

$ f_i(n)=0 \quad\forall \quad n < i$

Question: Is that linearly independent?

I think, that it is lineare dependent.

for $a \cdot f_i(n) + b \cdot f_j(n) = 0 \equiv $a \cdot 0 + b \cdot 0 = 0$ if $n < i < j \quad i,j,n \in N $
And thus not always follows that for a \cdot f_i(n) + b \cdot f_j(n) = 0 $ there must be $a=0, b=0$.