Conventions regarding the use of space in mathematical expressions

Question

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)

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 05 '16 at 01:21
I always put a \quad before and after \text{} in \displaystyle. Also before \forall. — John Kormylo, Dec 05 '16 at 01:30
This, in my opinion, may solicit "primarily opinion-based answers". — Werner, Dec 05 '16 at 04:29
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 05 '16 at 17:54

score 1 · Answer 1 · answered Dec 05 '16 at 01:47

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.

Conventions regarding the use of space in mathematical expressions

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