Spacing in math mode
In mathematical mode characters are spaced as if they were part of a single word, regardless of the actual space you insert. This article explains how to insert spaces of different lengths in mathematical mode.
Introduction
Spacing in maths mode is useful in several situations, let's see an example:
Assume we have the next sets
\[
S = \{ z \in \mathbb{C}\, \, z < 1 \} \quad \textrm{and} \quad S_2=\partial{S}
\]
As you see in this example, a mathematical text can be explicitly spaced by means of some special commands
Spaces
The spacing depends on the command you insert, the example below contains a complete list of spaces and how they look like.
Spaces in mathematical mode.
\begin{align*}
f(x) =& x^2\! +3x\! +2 \\
f(x) =& x^2+3x+2 \\
f(x) =& x^2\, +3x\, +2 \\
f(x) =& x^2\: +3x\: +2 \\
f(x) =& x^2\; +3x\; +2 \\
f(x) =& x^2\ +3x\ +2 \\
f(x) =& x^2\quad +3x\quad +2 \\
f(x) =& x^2\qquad +3x\qquad +2
\end{align*}
Check the reference guide for a description of the commands.
Note: to see a description of the align*
environment see Aligning equations with amsmath
Operators spacing
Spacing around operators and relations in math mode are governed by specific skip lengths:
\thinmuskip
(by default it is equal to 3 mu)\medmuskip
(by default it is equal to 4 mu)\thickmuskip
(by default it is equal to 5 mu)
For relationnal operators, such as < , > and =, LaTeX establishes \thickmuskip
space. But for binary operators such as +,  and x, the \medmuskip
space is set. The difference is almost unnoticeable.
Userdefined binary and relational operators
You can force the spacing used in binary or relational operators, so you can define your own.
The previous example sets a particular spacing before and after #
by using \mathrel
(relational) and \mathbin
(binary) commands.
Reference guide
Description of spacing commands
LaTeX code  Description 

\quad 
space equal to the current font size (= 18 mu) 
\, 
3/18 of \quad (= 3 mu)

\: 
4/18 of \quad (= 4 mu)

\; 
5/18 of \quad (= 5 mu)

\! 
3/18 of \quad (= 3 mu)

\ (space after backslash!) 
equivalent of space in normal text 
\qquad 
twice of \quad (= 36 mu)

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