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Does one put a comma after linking phrases such as "To this end, we denote ...", "For the purpose of the proof, we introduce an alternative notation ..." etc. in formal (scientific, mathematical) writing?

I suppose the question is more complicated than a simple yes–no and there may be cases where the comma is expected and when it's unexpected, so I'm probably looking for some rule of thumb. I prefer British rules if that matters.

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    It's entirely a stylistic choice. You could get a feel for how often writers include a comma there by looking at some written instances of to this end we and similar text strings in Google Books. But note that the trend over at least the past century has been to use less commas (in fact, less punctuation marks in general), so if you want to reflect current usage you should note that many older instances that include a comma probably wouldn't have done if they were written today. – FumbleFingers Jun 5 '17 at 12:45
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I think it is needed that you put a comma after it unless it has come at the end of the sentence. I don't see any difference between this and a phrase like "in my opinion", which a comma certainly comes after it.

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