# Colon between “that is” and formal definition

Is it appropriate to use "that is" followed by a colon when defining something formally? I have the following example:

Let γ be the set of groups that hold variables accessed by C, that is:

γ = {g : ∃v accessed by C, such that v ∈ g}.

Would that be appropriate in terms of punctuation and style?

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I don't think so. The mathematical example is just an illustration of a formal definition. It could be applied to any other formal text. The question is solely about how to write properly such a definition in the English language. – Eduardo Bezerra Nov 28 '12 at 13:51
In mathematical writing, the ideal is that mathematics should be punctuated in the same way as if it were ordinary text. You can bend the rules if the ordinary use of punctuation makes things confusing. But I don't see why a comma is any more confusing than a colon in the above example. If it were a long definition that wasn't set off as a centered equation, this might be another matter (but in this case, I'd recommend not using "that is" to introduce it). – Peter Shor Nov 28 '12 at 17:13
I like what @PeterShor said. I found this rule for use of colons: Use a colon to separate an explanation, rule, or example from a preceding independent clause. I'm no expert in the matter, but, it seems like, when you add the "that is", the preceding clause loses its independence. – J.R. Nov 28 '12 at 19:02
Or could you maybe use "in other words:"? – J.R. Nov 29 '12 at 13:49
After thinking about it, I don't think there's anything wrong with a colon after "that is". If you had a long list after "that is" in ordinary prose, you could definitely use a colon. And similarly, I think if you had a complicated prose definition after "that is" in a math paper, you could also use a colon. I don't think you need one in OP's example, though. – Peter Shor Nov 29 '12 at 15:43