> For the complete documentation index, see [llms.txt](https://overleaf-pro.ayaka.space/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://overleaf-pro.ayaka.space/latex/mathematics/08-spacing-in-math-mode.md). # Spacing in math mode This article explains how to insert spaces of different widths in math mode. ## Introduction Adjusting (La)TeX's default math mode spacing can be useful in certain situations; let's see an example: ```latex \documentclass{article} \usepackage{amssymb} \begin{document} Assume we have the next sets \[ S = \{ z \in \mathbb{C}\, |\, |z| < 1 \} \quad \textrm{and} \quad S_2=\partial{S} \] \end{document} ``` [Open this example in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Math+mode+spacing+example\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamssymb%7D%0A%5Cbegin%7Bdocument%7D%0AAssume+we+have+the+next+sets%0A%5C%5B%0AS+%3D+%5C%7B+z+%5Cin+%5Cmathbb%7BC%7D%5C%2C+%7C%5C%2C+%7Cz%7C+%3C+1+%5C%7D+%5Cquad+%5Ctextrm%7Band%7D+%5Cquad+S_2%3D%5Cpartial%7BS%7D%0A%5C%5D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![Example showing adjustments to math spacing](/files/G0ToXN692yGsnBzZTHLI) As you see in this example, a mathematical text can be explicitly spaced by means of some special commands. ## Spaces The example below contains a complete list of spaces inserted using various commands and demonstrates their effect on the typeset math. ```latex \documentclass{article} \usepackage{amsmath} \begin{document} 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*} \end{document} ``` [Open this example in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Math+mode+spacing+example\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0ASpaces+in+mathematical+mode.%0A%0A%5Cbegin%7Balign%2A%7D%0Af%28x%29+%26%3D+x%5E2%5C%21+%2B3x%5C%21+%2B2+%5C%5C%0Af%28x%29+%26%3D+x%5E2%2B3x%2B2+%5C%5C%0Af%28x%29+%26%3D+x%5E2%5C%2C+%2B3x%5C%2C+%2B2+%5C%5C%0Af%28x%29+%26%3D+x%5E2%5C%3A+%2B3x%5C%3A+%2B2+%5C%5C%0Af%28x%29+%26%3D+x%5E2%5C%3B+%2B3x%5C%3B+%2B2+%5C%5C%0Af%28x%29+%26%3D+x%5E2%5C+%2B3x%5C+%2B2+%5C%5C%0Af%28x%29+%26%3D+x%5E2%5Cquad+%2B3x%5Cquad+%2B2+%5C%5C%0Af%28x%29+%26%3D+x%5E2%5Cqquad+%2B3x%5Cqquad+%2B2%0A%5Cend%7Balign%2A%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![More examples of adjusing spacing in math mode](/files/vaFgMlErIoujv503M2LF) Check the [reference guide](#reference-guide) for a description of the commands. **Note**: to see a description of the `align*` environment see [Aligning equations with amsmath](/latex/mathematics/06-aligning-equations-with-amsmath.md) ## Operators spacing Spacing around operators and relations in math mode are governed by specific skip widths: * `\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) ```latex \begin{align*} 3ax+4by=5cz\\ 3ax<4by+5cz \end{align*} ``` [Open this example in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Math+mode+operator+spacing+example\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Balign%2A%7D%0A3ax%2B4by%3D5cz%5C%5C%0A3ax%3C4by%2B5cz%0A%5Cend%7Balign%2A%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![Operator spacing in LaTeX](/files/r0LfcHtgyCERMjjUUEpQ) For relational operators, such as $$<$$, $$>$$ and $$=$$, LaTeX establishes `\thickmuskip` space. But for binary operators such as $$+$$, $$-$$ and $$\times$$, the `\medmuskip` space is set. The difference is almost unnoticeable. ## User-defined binary and relational operators You can force the spacing used in binary or relational operators, so you can [define your own](/latex/commands/01-commands.md). ```latex \begin{align*} 34x^2a \mathbin{\#} 13bc \\ 34x^2a \mathrel{\#} 13bc \end{align*} ``` [Open this example in Overleaf](https://www.overleaf.com/docs?engine=pdflatex\&snip_name=Defining+your+own+math+operators\&snip=%5Cdocumentclass%7Barticle%7D%0A%5Cusepackage%7Bamsmath%7D%0A%5Cbegin%7Bdocument%7D%0A%5Cbegin%7Balign%2A%7D%0A34x%5E2a+%5Cmathbin%7B%5C%23%7D+13bc+%5C%5C%0A34x%5E2a+%5Cmathrel%7B%5C%23%7D+13bc%0A%5Cend%7Balign%2A%7D%0A%5Cend%7Bdocument%7D) This example produces the following output: ![Defining your own binary or relational operators](/files/RI0xxoWrKwXXZjsuU4Pj) 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](/latex/formatting/01-lengths-in-latex.md)) | | `\,` | 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) | ## Further reading For more information see * [Mathematical expressions](/latex/mathematics/01-mathematical-expressions.md) * [Brackets and Parentheses](/latex/mathematics/03-brackets-and-parentheses.md) * [Aligning equations with amsmath](/latex/mathematics/06-aligning-equations-with-amsmath.md) * [Display style in math mode](/latex/mathematics/10-display-style-in-math-mode.md) * [List of Greek letters and math symbols](/latex/mathematics/11-list-of-greek-letters-and-math-symbols.md) * [Mathematical fonts](/latex/mathematics/12-mathematical-fonts.md) * [The not so short introduction to LaTeX2ε](http://www.ctan.org/tex-archive/info/lshort/) --- # Agent Instructions This documentation is published with GitBook. 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