# Is it acceptable to replace big unchanged parts of equations with multiple equal signs with ellipsis ("$\ldots$")

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*}

• 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. Jan 24 at 4:57
• 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. Jan 24 at 5:16

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}
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}