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This question already has an answer here:

The Chicago Manual of Style (sec. 12.16) suggests medium space (a ¼ em) before and after

  • signs for binary operations (i.e., conjunctions);
  • symbols of integration, summation, or union; and
  • signs for binary relations (i.e., verbs)

except in exponents; also medium space after commas between "coordinate points" or between elements in a list; and "no space after a binary operation or relation sign when it is modifying a symbol (i.e., used as an adjective)".

I don't know whether LaTeX follows these guidelines, but anyway I would like to know the (generally accepted) "right" amount of space in the following situations (that is, do I need to add/remove space, and if so how much?)

  • after logarithm: \log x
  • before factorial symbol: y!
  • in an implicit multiplication: x y
  • before and after "for all" symbol: x > 0 \forall x
  • between equations separated by a comma: x = 1, y = 2
  • between equations separated by text: x = 1 \text{ and } y = 2
  • after a comma separating elements of a set: \{0, 1\}
  • after a comma separating arguments of a function: f(x, y)

marked as duplicate by Joseph Wright Dec 5 '16 at 17:53

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • 1
    All this is managed by (La)TeX and rarely has to be modified. For quantifiers, note you should write them after the relation, but before. – Bernard Dec 5 '16 at 1:21
  • I always put a \quad before and after \text{} in \displaystyle. Also before \forall. – John Kormylo Dec 5 '16 at 1:30
  • This, in my opinion, may solicit "primarily opinion-based answers". – Werner Dec 5 '16 at 4:29
  • I've closed here as a dupe (rather than opinion based) as we do have question on this topic, as pointed out by @ErnestA! – Joseph Wright Dec 5 '16 at 17:54
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Partial answers (please remember that some rules may vary from country to country):

after logarithm: $\log x$ -- exactly this space
before factorial symbol: y! -- before no, after rather \,
in an implicit multiplication: x y -- in doubt you can use \,
before and after "for all" symbol: x > 0 \forall x
between equations separated by a comma: $x = 1$,  $y = 2$ -- two different equations, separated by a space
between equations separated by text: x = 1 \text{ and } y = 2 -- at least space, rather \quad
after a comma separating elements of a set: \{0, 1\} -- it depends, some people want to have spaces after commas (e.g. `,\ `).
after a comma separating arguments of a function: f(x, y) -- OK, TeX adds a proper space

In most cases TeX knows, what the spacing should be.

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