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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
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1 Answer

up vote 4 down vote accepted

With regard to punctuating that is, we follow Jane Straus's Blue Book of Grammar and Punctuation. It is preferable to use a semicolon before that is and a comma after that.

XXX; that is, XXX.

With regard to the best way to define something formally, that is not in the scope of this site.

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I meant to ask if it was alright to use this kind of punctuation when defining something formally. I edited the question accordingly. –  Eduardo Bezerra Nov 28 '12 at 14:31
-1 You did not say if the OP's version was wrong, which is what, I think is the question. –  Kris Nov 28 '12 at 15:28
@Kris: Is everything necessarily wrong if it's not right ? Of course it's understandeable, and it's not the preferred way. I don't see how it could be called wrong per se. FTR, it's tagged [style]. –  Nikana Reklawyks Nov 29 '12 at 14:39
@NikanaReklawyks How did understandeable make it thru' the spell check? :) –  Kris Nov 29 '12 at 14:48
I think this answer is incomplete. If you had a long list after "that is" in ordinary prose, you should put a colon after it. Similarly, if you have a long definition after "that is" in a math paper, you should put a colon after it. But for the OP's example, my feeling is that a comma works fine. –  Peter Shor Nov 29 '12 at 15:41
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