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Is the following use of indices correct? A vector $\langle x_i, x_{i+1},...,x_{i+k}\rangle$ is given. For every such vector a function is defined through $$\mu=\frac{\sum_{j=0}^k I_A(x_{i+j})}{k+1}\,,$$ where $I_A$ is the indicator function of some set A. Is it mathematically correct notation? In particular the use of $i+j$ as sub index.

user145404
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  • Yes, it is correct. But as you're doubting, you can also choose to use: \begin{equation} \mu = \frac{\sum_{j = i}^{i+k} I_A(x_j)}{k+1} \end{equation} – Olivier May 21 '14 at 08:25
  • Perfectly correct. – Claude Leibovici May 21 '14 at 08:26
  • Thanks. Which is more correct --- to use $x_{i+j}$ or double indexing $x_{i_j}$ and again sum over $j$? – user145404 May 21 '14 at 08:28
  • Double indexing is incorrect, as the elements of the vector are 1-dimensional. – Olivier May 21 '14 at 08:32
  • $x_{i_j}$ can be used, but this if you define $i_j:=i+j$. However... why writing this complex $i_j$ instead of its definition $i+j$? Don't make things complex. Good mathematics is characterized by simplicity. – drhab May 21 '14 at 08:51
  • I was afraid to use as a sub index sum of two natural numbers --- $i+j$ --- because I have not seen it before... – user145404 May 21 '14 at 08:54
  • Well. The first step is meeting it. The next is getting accustomed and familiar to it, especially by using it and discovering its profits. Good luck. :) – drhab May 21 '14 at 09:11

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As mentioned in the comments above, the notation is correct.

JRN
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  • An upvote to this answer is needed to remove this question from the unanswered list. – JRN May 22 '14 at 02:11