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Let $N$ and $X$ be finite sets, and let $f:X\to\mathbb{R}^N$ be a function. I want to say that there exists some number $a>0$ such that for all $x\in X$, the sum of all elements of the $n$-tuple $f(x)$ adds up to $a$. I am currently writing this as follows: \begin{gather} (\exists a>0)((\forall x\in X)(\sum_{i\in N}f_i(x)=a)) \end{gather} However, I am wondering whether I should write this with larger parentheses to properly enclose the summation, as follows: \begin{gather} (\exists a>0)\left((\forall x\in X)\left(\sum_{i\in N}f_i(x)=a\right)\right) \end{gather} I do not know whether the use of larger parentheses is recommended / acceptable to express a sentence like this one, and I can't find any guidelines.

Can somebody please help me decide which of the two expressions is "more common" / "more readable"?

EoDmnFOr3q
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    Parentheses are needed for readibility. IMO the first one is fine. – Mauro ALLEGRANZA Dec 04 '22 at 11:24
  • Thank you for your comment. If the parentheses were used to indicate some order of computations rather than just for readibility, would you then use the larger ones? – EoDmnFOr3q Dec 04 '22 at 11:28
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    I would never ascribe any sort of priority to larger parentheses. Personally, I like my parentheses to be bigger than what they enclose, hence $\left(\frac a2+b\right)$ and not $(\frac a2+b)$. But that is an aesthetic preference only. – lulu Dec 04 '22 at 11:39
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    I'd say the first display is not fine. The little parenthesis next to the big sigma displeases me. But I don't think you should go as big as the second display. Just big enough to match the sigma will do. – Gerry Myerson Dec 04 '22 at 12:03
  • Thank you all for your comments. I have tried a few things, and I have chosen to follow Gerry Myerson's approach of getting the parentheses large enough to just enclose the $\sum$. – EoDmnFOr3q Dec 05 '22 at 10:49

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