Math spacing when using quantifiers
1,436
Don't put a space before the comma, Also I would not use \forall
with an informal iterator displayed as dots.
Assuming x_i
is some boolean valued expression indexed by i
then either
\begin{equation*}
x_i \quad \text{for all $i=1,\dots,n$}
\end{equation*}
or more formally
\begin{equation*}
\forall i \in \{1,\dots,n\}\mathbin{.}x_i
\end{equation*}
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Author by
user2653422
Updated on August 01, 2022Comments

user2653422 about 4 hours
I'm often writing equations with quantifiers like these:
\begin{equation*} x_i \quad \forall i = 1, \dotsc, n \end{equation*}
I've read this answer, but I'm not sure if my case is an example for a situation where one uses EM quad.
So my first question is, would you put a
\quad
space at that position?The second question is, would you separate the first part from the quantifier with a comma like:
\begin{equation*} x_i \quad , \forall i = 1, \dotsc, n \end{equation*}

egreg over 6 yearsPersonally, I'd avoid the
\forall
:x_{i},\qquad i=1,2,\dots,n
I think that the quantifier is even mathematically wrong (at least in several cases I see). Note that you don't need\dotsc
, because\dots
is able to figure out what follows.\dotsc
is needed only if you have an open ended enumeration, such asi=1,2,\dotsc

daleif over 6 years(1) I'd never leave a floating comma. (2) in most of what I edit I use a qquad for this leaving the single quad for "f quad and quad g qquad for all..."

cfr over 6 yearsLogically,
\forall
seems wrong. I don't know if mathematicians use it differently. Or don't remember well enough to be sure. But logically, it doesn't make sense. 
David Carlisle over 6 years@cfr assuming
x_i
is a boolean valued predicate, then it makes sense although would more normally be written with the quantifier first,\forall i \in \{1,\dots\n\} . x_i

cfr over 6 years@DavidCarlisle It was more the
=
combined with the\forall
which didn't make sense. (Although, logically, I'm inclined to see thei
inx_i
as unbound.)\forall i \in \{...
for\text{for } i=1,\dots
. It's the combination which doesn't look wfflike to me.
