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In the expression $$\sum_{k=1}^nk=\frac12n(n+1)$$ $k$ is called the index of summation. What is $j$ called in $$\prod_{j=1}^nj=n!$$ I have seen web pages like https://math.illinoisstate.edu/day/courses/old/305/contentsummationnotation.html that go into great detail about the summation notation, but haven't seen similar expositions for the product notation. Terms like 'index of product' or 'index of multiplication' or 'index of procreation' don't sound right.

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    $\begingroup$ I would use a more generic term for both., $k$ and $j$ are the indexing variables in each (or shorter, the index variables), making no reference to what sort of operation we are indexing. $\endgroup$ – JMoravitz Feb 14 '18 at 1:02
  • $\begingroup$ How about " index of multiplication"? $\endgroup$ – sirous Feb 14 '18 at 1:37

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