2

For the x systems, we usually have harder constraints, such as ...

Note that for the x systems, we usually have harder constraints, such as ...
Note that for the x systems we usually have harder constraints, such as ...

I suppose that the first comma is needed in the first sentence (?).
As for the second sentence, I am a bit confused. should I still use the (first) comma or not ?

  • I wouldn't place a comma. There's no need for it. – SovereignSun Mar 29 '17 at 10:44
  • @SovereignSun Could you please tell me why ? – tam Mar 29 '17 at 12:37
  • Commas are largely a matter of style and taste (although there are a few places where you absolutely need them). In this case no comma is needed. Neither part of the sentence is an independent clause, it's not a list of items or adjectives, it's not a free modifier, it's not a quotation. – stangdon Mar 29 '17 at 14:50
  • @stangdon Let us suppose that I want to use a comma. Could you please tell me if the following usage is correct: "Note that for the x systems, we usually have harder constraints, such as..", or I am obliged to use two commas, i.e. "Note that, for the x systems, we usually have harder constraints, such as..", ? Thank you! – tam Mar 29 '17 at 15:08
  • @tam - All of the extra commas are unnecessary. You don't need any commas there. – stangdon Mar 29 '17 at 15:12
2

To paraphrase, the use of commas in your case is a matter of style, not grammar. Use commas (or not) if you want to.

AFAIK there is not a hard and fast rule forcing you to use commas in either case as "for the x systems" is not a subclause, but is instead an adjunct. Adding or removing commas does not change the meaning in either case, which would be the only thing forcing you to use commas (or not). If you are interested, this article has a nice list of "proper" comma usage, and this answer gives a very good explanation of adjunct use and commas.

As "we usually have harder constraints" and "note that we usually have harder constraints" could both be sentences on their own, and "for the x systems" can either go before or after "we usually have harder constraints" (because it is an adjunct), you can use commas if you want to.

The use of commas may help to add emphasis if necessary. Phrasing it like so:

Note that, for the x systems, we usually have harder constraints, such as ...

emphasises that you are talking specifically about "the x systems". This makes the sentence sound cumbersome though, because of the abundance of commas.

It may be better to move "for the x systems" later in the sentence so you don't need to worry about it:

Note that we usually have harder constraints for the x systems, such as ...

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