I am reading a paper which sets $V_{-1}$ := R and $V_{m+1} \subset V_m$ for all $m \ge -1$.
As I know that a vector is normally counted as $V_1, V_2,...,V_n,$ so what dose this $V_{-1}$ meaning? Why count starting from $-1$? I am sorry that this question maybe too general, but I am really confused about this.
Thanks in advance!
In general you can talk about a collection of vectors $\{V_i\}_{i\in I}$, where $I$ is some set. $I$ can be $\{1,\ldots,n\},\mathbb{N},\mathbb{Z}$ or even an uncountable set.
In your case it must be countable, because you have $V_{m+1} \subset V_m$.
Usually they start counting from $m=-1$, because $m$ is used in another calculation, or because $m=0$ is a special case.