Behavior of \, in both text and math mode

Question

The command \, can be used in both text and math mode, where it has the same behavior. Well, this is not strictly true, of which I can give a wonderful proof, but comments are too short to contain it. --- @egreg

The above remark was given by @egreg in an answer that I posted. Since it is too long for a comment, could someone elaborate on this?

Answer 1

Let's look at the definition of \, in the kernel:

% latex.ltx, line 1304:
\DeclareRobustCommand{\,}{%
   \relax\ifmmode\mskip\thinmuskip\else\thinspace\fi
}

Now we look at \thinspace:

% latex.ltx, line 1315:
\def\thinspace{\kern .16667em }

So in text mode a kern is used; a kern is almost like glue, but is never used as a line break point unless it's followed by glue (TeXbook, page 75, end of first dangerous bend), besides not being able to stretch or shrink. So A\,B will never be broken across lines, but A\, B can be.

Note that .16667em is 1/6 of an em (in the current font). Usually \thinmuskip is set to 3mu, so it is 1/6 of an em in the symbol font, which may be the same as the em in the current text font, but not necessarily. Of course, if the value of \thinmuskip is changed, the command will give really different results in text and in math mode.

The construction \mskip\thinmuskip is primitive. A \thinmuskip is used between an operator and an ordinary symbol and in some other cases.