Suppose I have a finite list of real number pairs $(\nu_k, i_k)$ with $k = 1, \ldots, K$. Then I computed $\nu_0$ and $i_0$ as some kind of average of the numbers and similarly $\Delta \nu$ and $\Delta i$ as some kind of average jumping distance between the numbers in the sequence.
Now for a positive integer $N > 0$ I shall now construct the following two finite sequences:
$$\{v_0 - N\cdot\Delta v, \ldots, v_0 - \Delta v, v_0+\Delta v,\ldots,v_0+N\cdot\Delta v\}\\ \{i_0 - N\cdot\Delta i, \ldots, i_0 - \Delta i, i_0+\Delta i,\ldots,i_0+N\cdot\Delta i\} $$
I have been told they should both be of length $2N$. I do not understand why.
The notation $$\{\nu_0 - N\cdot\Delta \nu, \ldots, \nu_0 - \Delta \nu, \nu_0+\Delta \nu,\ldots,\nu_0+N\cdot\Delta \nu\}$$
means $$\begin{align*} \{&\nu_0 - N\cdot\Delta \nu,\\ &\nu_0 - (N-1)\Delta \nu,\\ &\nu_0 - (N-2)\Delta \nu,\\ &\nu_0 - (N-3)\Delta \nu,\\ &\ldots,\\ &\nu_0 - (N-(N-1))\Delta \nu = \nu_0 - \Delta \nu,\\ &\nu_0 + \Delta \nu,\\ &\nu_0 + 2\Delta \nu,\\ &\ldots\\ &\nu_0 + (N-2)\Delta \nu\\ &\nu_0 + (N-1)\Delta \nu\\ &\nu_0 + N\Delta \nu\}. \end{align*} $$ This set should exactly contain $2N$ elements if I counted correctly.