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Is $$\sum_{i\in I_1} a_i + \sum_{i \in I_2} b_i$$ or $$\prod_{i\in I_1} a_i \cdot \prod_{i \in I_2} b_i$$ confusing or bad math? Should I rather use $j$ for indexing the $b$'s?

Jake B.
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    I think it's better to use different summation indices, just to avoid error or confusion but it's clear what you mean in each case. – lulu Jun 13 '19 at 19:47
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    It's perfectly fine, and not confusing to anyone who understands the notation. Why would you change the index? What if you had four sums? Or ten? Or twenty-seven? – MPW Jun 13 '19 at 19:47
  • I think the product could be very confusing if $I_1$ and $I_2$ have different cardinalities. The sum is probably fine, unless you might want to combine them into one sum later on, in which case the cardinality problem crops up again. That sum might not be very well-defined. – Adrian Keister Jun 13 '19 at 19:51
  • @AdrianKeister Why are different cardinalities any more problematic with the product? In each case, we're adding or multiplying $|I_1|+|I_2|$ objects. – J.G. Jun 13 '19 at 19:52
  • @J.G. It's more of an issue if you want to combine into one product. Then it's not clear what the limits of the summation should be. – Adrian Keister Jun 13 '19 at 19:54
  • @AdrianKeister Again, the combining option when $|I_1|=|I_2|$ doesn't depend on whether we're summing or multiplying. – J.G. Jun 13 '19 at 19:59

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