Number sets (prime, natural, integer, rational, real and complex) in LaTeX

42 Comments

Number sets such as natural numbers (\mathbb{N}) or complex numbers (\mathbb{C}) are not provided by default by LaTeX. It doesn’t mean that LaTeX doesn’t know those sets, or more importantly their symbols…

There are two packages which provide the same set of symbols. You can choose to load either of them:

\usepackage{amsfonts} 
% or 
\usepackage{amssymb}

Now, you have access to the different set symbols through this command in math mode:

$\mathbb{set}$

Examples:

\mathbb{P} for prime numbers using \mathbb{P},
\mathbb{W} for whole numbers using \mathbb{W},
\mathbb{N} for natural numbers using \mathbb{N},
\mathbb{Z} for integers using \mathbb{Z},
\mathbb{I} for irrational numbers using \mathbb{I},
\mathbb{Q} for rational numbers using \mathbb{Q},
\mathbb{R} for real numbers using \mathbb{R} and
\mathbb{C} for complex numbers using \mathbb{C}.

\mathbb{H} for quaternions using \mathbb{H},
\mathbb{O} for octonions using \mathbb{O} and
\mathbb{S} for sedenions using \mathbb{S}

Positive and non-negative real numbers, \mathbb{R}_{>0} and \mathbb{R}_{\geq0}, can now be typeset using:

$\mathbb{R}_{>0}$ 
$\mathbb{R}_{\geq 0}$

42 Comments

  7. Enrique Argones Rúa

    Why don’t you choose the more traditional notation \mathds{R}, \mathds{N}, etc.?

    For using this you would have to include the package dsfont.

    Cheers,

    Enrique

    Reply

  9. Joe

    ..I should have been more specific: thanks Enrique! The mathbb font is pretty well known, but the font for the more traditional number systems is hard to find.

    Reply

    • Hi,

      Not sure if a number set symbol is commonly used for binary numbers. But try the following with any letter:

      \usepackage{amssymb}
...
$\mathbb{B}$

      Best, Tom.

      Reply

    • Hey Heni,

      Thanks for your question. Is this what you were looking for?

      \documentclass[11pt]{article}
\usepackage{amssymb}
\begin{document}
$\mathbb{R}^n$
\end{document}
      Reply

      • Joan

        Though a minor difference, $\mathbb{R}^n$ produces a BOLD n as the dimension of R. Is there any way to make this n slimmer?

        Thanks a lot.

      • tom

        Hi Joan,

        How you perceive it might depend on the font used. In Computer Modern, the n doesn’t look bold in my opinion. Here’s what a bold n would look like, as compared to the normal font style in math mode:

        \documentclass[11pt]{article}
\usepackage{amsfonts, amsmath, graphicx}
\begin{document}
$\mathbb{R}^{\boldsymbol n} \text{ vs. } \mathbb{R}^{n}$
\end{document}

        Maybe you want to change the font size to make the letter n slimmer, and smaller obviously?

        Also, I’d be curious to learn what configuration you used that made the letter thicker than what you would expect.

        Cheers, Tom

  15. Courtney

    Hi! In the last line, the set of positive reals should be strictly R_>0, not R_≥0, which represents the nonnegative reals. The difference is subtle, but important 🙂

    Reply

  20. Petra 

    \documentclass{beamer}
\usepackage{amsfonts}
\begin{document}
\begin{frame}
\mathbb{Q}
\end{frame}
\end{document}

    This isn’t working. Can you help me? It sais “\mathbb allowed only in math mode”

    Reply

    • tom

      Hi Petra,

      Thanks for the minimal working example. The command only works in math mode. So this should do the trick:

      $\mathbb{Q}$

      It wasn’t clear from the post and I’m going to change that. Thanks for bringing this up.

      Best, Tom

      Reply

  22. Thomas Pierre Nicolas Jean Brouard

    hi it does not work for me for P. What can be wrong? I use the two packages

    Reply

    • tom

      Hi Thomas,

      Consider the example below. If this doesn’t help solving you problem, please provide a minimal working example to illustrate the issue.

      \documentclass{article}
\usepackage{amssymb}
\begin{document}
$\mathbb{P}$
\end{document}

      Best,
      Tom

      Reply

  23. Andrew

    How do I define my own sets so that they do not collide with the conventional ones? eg. P for a set of particles (not to mean a set of Primes) in Latex.

    Reply

    • tom

      Hi Andrew,

      I’m not sure I understand the question. Would you like to generate the same symbol with a different command or a similar, but different symbol?

      Reply

  24. Lisel

    Hey Tom, thanks for your great work. I have an additional issue to solve. How can I represent this problem in a better way:

    $\mathbb{R}^{m x n}$

    as the output of the power term looks like: mxn when it would be great to have some space in between the symbols to show that its m x n and not a term mxn.

    Thank you in advance.

    Reply

    • tom

      Hi Lisel,

      Thanks for your question. I’d use the \times macro instead of “x”, as regular text gets printed in italics in math mode. The macro has some extra space left and right. If you need more, use can use the math spacing commands (\, or \: or \; — in increasing order).

      HTH, Tom

      \documentclass[11pt]{article}
\usepackage{amsfonts}
\begin{document}
$\mathbb{R}^{m\times{}n}$

$\mathbb{R}^{m\;\times\;n}$
\end{document}
      Reply

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