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3:57 AM
Thanks @MartinSleziak; this is the post in question, if anyone has suggestions for the improvement of its formatting: math.stackexchange.com/a/4277300/21813
@MartinSleziak To be clear, I do not (in general) dislike parentheses; but in first-order-logic object language, the only parentheses required for a quantifier are those that indicate its scope when it extends beyond the minimum construeable. So for example, $\forall x \:x=1\to y=0$ and $\forall x \; (x=1\to y=0)$ are not logically equivalent, and strictly speaking, neither requires any parenthesis around $"\forall x".$
[The former is logically equivalent to $\exists x(x=1\to y=0).$]
Your previous message has shed light on why I frequently see on MSE parentheses around quantifiers: because in Mathjax, without them and without manually inserting spaces, the string $\forall x\in\mathbb R\exists y\in\mathbb Z$ is ugly and reader-unfriendly! I'm now considering using the parentheses as per your suggestion, in lieu of having to manually add spaces.
 
 
1 hour later…
5:16 AM
I should explicitly include disclaimer that the fact that I am used to write expressions with quantifiers like this (with parentheses) definitely does not mean that it is universally considered the recommended way to write them.
 
5:58 AM
I have mentioned this in some other chatrooms, maybe users from there might have some advice: chat.stackexchange.com/transcript/19138/2021/10/16 and chat.stackexchange.com/transcript/41/2021/10/16
And I have also see this post on TeX - LaTeX: Best practice for typesetting quantifiers?
44
Q: Best practice for typesetting quantifiers?

Gaston BurrullWhen I work with quantifiers I noted that are very close to the other symbols and the result does not look good, for example $\exists a\in\mathbb{R}\exists b\in\mathbb{R}\forall c\in\mathbb{R}\forall d\in\mathbb{R}$ Which is the proper form to write quantifiers?

Although the focus there seems a bit different - I do not see adding spaces around \in in the answer posted tehre.
 
6:53 AM
in TeX, LaTeX and Friends, 5 mins ago, by David Carlisle
@MartinSleziak i'd never use outer parenthesis around the quantifier, you can compress \in as {\in}
 
 
8 hours later…
2:41 PM
Test with \in: $\forall\varepsilon>0 \exists\delta>0 \forall x\in D \left(0<|x-c|<\delta \implies |f(x)|-l<\varepsilon\right)$
Test with {\in}: $\forall\varepsilon>0 \exists\delta>0 \forall x{\in} D \left(0<|x-c|<\delta \implies |f(x)|-l<\varepsilon\right)$
There seems to be quite a difference between $\forall x\in D$ and $\forall x{\in}D$; $\forall x\in D$ and $\forall x{\in}D$.
 
3:33 PM
in TeX, LaTeX and Friends, 1 min ago, by Ryan G
@DavidCarlisle MANY THANKS for the {\in} suggestion (compressing the spaces around the element symbol)!
 
@MartinSleziak YES, the braces around \in is the solution that I never knew existed. MANY THANKS to David and to yourself!! (P.S. i won't see any responses unless pinged, as I don't check rooms and never get any notification otherwise.)
 

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