Spaces, or white space, are rendered using some shorthand symbols, or more generally using the \mspace command.

Simple symbols (class 0) are rendered without any space between them. Operators (class 1) are rendered with spaces. Spacing symbols change the amount of spacing, either by adding more space or taking spaces away. Space is measured in math units, or mu. 18mu equals 1em.

NOTE: commands \thinspace, \medspace, \thickspace, \negthinspace, \negmedspace, \negthickspace, \mspace, and \: are not impemented here at wikia.org!

LaTeX markup... ...results in: ...is used for:
a b c d Simple symbols (class 0) have no spaces around them
\sin b \cos d Operators (class 1) have thin spaces around them
a \, b \mspace{3mu} c \thinspace d thin 3mu space
a \: b \mspace{4mu} c \medspace d medium 4mu space
a \; b \mspace{5mu} c \thickspace d thick 5mu space
a \ b \ c \ d thicker 6mu space provided by backslash followed by blank
a \quad b \mspace{18mu} c \quad d 18mu or 1em space
a \qquad b \mspace{36mu} c \qquad d 36mu or 2em space
a \! b \mspace{-3mu} c \negthinspace d negative thin -3mu space. See \int for a suggested use.
a \negmedspace b \mspace{-4mu} c \negmedspace d negative medium -4mu space
a \negthickspace b \mspace{-5mu} c \negthickspace d negative thick -5mu space

Spaces of exactly the size of some rendered text can be obtained using the \phantom, command, and its cousins, \hphantom and \vphantom. They are not implemented here at wikia.org!

LaTeX markup... ...results in: ...is used for:
a \phantom{\int XXX} b space as wide and high as integral and three X’s
a \hphantom{\int XXX} b space as wide and high as integral and three X’s;
height 0
a \hphantom{\int XXX} b space of width 0,
as high as integral and three X’s

## Using spaces in formulas

The Integral article gives suggestions on using negative space immediately following the integral sign(\!), and then some positive space (\,) before the "dx" to distinguish it as a special operator.