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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user2653422
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Updated on August 01, 2022

Comments

  • user2653422
    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
      egreg over 6 years
      Personally, 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 as i=1,2,\dotsc
    • daleif
      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
      cfr over 6 years
      Logically, \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
      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
      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 the i in x_i as unbound.) \forall i \in \{... for \text{for } i=1,\dots. It's the combination which doesn't look wff-like to me.