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I have a big expression I want to simplify, requiring multiple steps to make it clear what's going on. For example, if I wanted to write something like this: $$ \begin{align*} (1 + 2 + 3 + 4) & (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) \\ = 10&(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) \\ = 10& \cdot 45 \\ = 45&0 \end{align*} $$

Is it acceptable to replace these equations with something like this instead? $$ \begin{align*} (1 + 2 + 3 + 4)&(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) \\ = 10&(\ldots) \\ = 10& \cdot 45 \\ = 45&0 \end{align*} $$

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    $\begingroup$ The ultimate goal of writing is to communicate clearly. Ellipses open the door to misinterpretations. So while I don't rule them out completely, I think it's better to include those details—especially since copy-and-paste is very easy. Another option (in longer computations) is to give variable names to quantities, which allows them to be considered separately, and also shortens them when they're coming along for the ride like this long expression is. $\endgroup$
    – Greg Martin
    Jan 24 at 4:57
  • $\begingroup$ Why wouldn't you just write $45$ in the line you wrote the ellipsis? I understand it's just an example, but if that's actually a representative example, I'd steer clear of ellipses. $\endgroup$
    – Brian Moehring
    Jan 24 at 5:16

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If you are concerned that your expressions are ambiguous and you would like to be very explicit, give names to quantities. For example, you could write:

With $S = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$, \begin{align} (1 + 2 + 3 &{}+ 4)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) \\ &= 10S \\ &= 10 \cdot 45 \\ &= 450 \end{align}

or better yet since the left and right factors are of the same form,

With triangle numbers $$\left\{\begin{aligned} \Delta_{4\phantom{1}} &= 1 + 2 + 3 + 4 \phantom{{}+ 5 + 6 + 7 + 8 + 9}= 10 \\ \Delta_{10} &= 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45, \end{aligned}\right. $$ we have \begin{align} (1 + 2 + 3 &{}+ 4)(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) \\ &= \Delta_4 \, \Delta_{10} \\ &= 10 \cdot 45 \\ &= 450 \end{align}

However you choose to express yourself, just be sure that it's unambiguous!

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