I noticed that in many documents you encounter $f: X \to Y$ instead of $f \colon X \to Y$. Another example are quantified expressions: $\forall x: P (x)$ versus $\forall x \colon P(x)$. I find the \colon visually more pleasing, however I sometimes think I seem to be the only one, given the overwhelming amount of documents that seem to use :. Is there a rule of thumb to decide where you should use either \colon or :?
2 Answers
Both : and \colon typeset a colon, but \colon is a punctuation symbol, while : is considered as a relation symbol as regards to spacing.
The main use of : is in set descriptions
\{\, x : x \notin x \,\}
(somebody uses \mid for this, where a simple | would be wrong; thin spaces after \{ and before \} are recommended by Knuth, be consistent in using them or not).
Conversely, \colon should be used for mappings
f\colon A \to B
but unfortunately many writers don't make this distinction and use :, getting a wrong spacing.
The rule to follow is just the same: use \colon when it's a "punctuation colon", use : when it represents a relation between what's at its left and at its right. In something like "for all x:" I would consider the colon as punctuation, so \forall x\colon
Note that the amsmath package changes the definition of \colon so that it's not exactly the same as a punctuation symbol:
\renewcommand{\colon}{\nobreak\mskip2mu\mathpunct{}\nonscript
\mkern-\thinmuskip{:}\mskip6muplus1mu\relax}
This adds a bit of space before the colon, which seems more right than with a simple \mathpunct.
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9
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11@LeoLiu Alternatively,
\mathbin{:}could be used. Which one is a matter of personal taste. Most important is consistency across the document.– egregDec 10, 2011 at 11:32 -
29How does one distinguish between "punctuation" and "relation"? The notation
f\colon A\to Bdoes denote a relation betweenfandA\to B, namely the relation "has type". And I don't see in what sense the colon in\{\, x : x\notin x \,\}denotes a "relation" betweenxandx\notin x. Apr 11, 2012 at 10:29 -
4@MikeShulman It's a matter of conventions; usually the colon for maps is considered as punctuation, the one in set descriptions as a relation symbol. Be coherent in your document.– egregApr 11, 2012 at 12:30
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11Just for clarity, the usual recommendation to use
\,after\{and before the matching\}is only in case the set involves a set descriptor (with the colon). By contrast, use\{a, b, c\}without the thin spaces in case of an explicit enumeration of elements.– murrayJun 27, 2012 at 21:00
If you're trying to typeset a variable-has-type colon in type theory, you want {:} or \mathord{:} (they display the same). For example, you'll get a nice looking STLC identity function with $\lambda x {:} A . x$.
See this page for a more general discussion.
f\colon a \to b(rather thanf : a \to b) and a general discussion of relation symbols.