Comma after introductory phrases


I am no native speaker and always confused about the comma in introductory phrases, in particular in prepositional phrases. Is there any hard rule when a comma must be set? If I make a google search for certain phrases, I often find both variants. Typical examples where I am not sure whether a comma must be set are:




  • In this case[,] we must...

  • For simple problems[,] the algorithm...

  • From Lemma 1.2[,] we obtain...

  • For a typical user[,] the algorithm...

  • In our theory[,] we...




Answer



Larry Trask’s advice in cases like this is to see what happens if you remove from the sentence the words marked off by the comma. If you are left with a meaningful sentence, then the comma is appropriate. If no meaningful sentence remains, you don’t need the comma.


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