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I found this sentence in the previous answered questions:

People in this class have a good knowledge in mathematics.

My question is why there is no "The" before "people."

Please tell me if my understanding is correct.

If it is a small class and only regular members attend the class, "The" will be added as follows:

The people in this class have a good knowledge in mathematics. or The students in this class have a good knowledge in mathematics.

If it is rather a big class and regular members as well as other students can attend on an occasional basis, "The" will be left out.

Am I correct?

One more thing; Can I say, "People in this class have a good knowledge of mathematics" instead of "...in mathematics."?
Comments  
Hi Snappy,
I omit "the" in this sentence when I mean "in general;" not every person in the class without any exceptions. I might be able to point out one person in the class that does not. Or maybe I just don't know about everyone's knowledge, but I have not seen an exception in my experience with this class.
If all of the people in the class have a good knowledge of mathematics, then I would use "the".
I prefer "of" rather than "in".
Thank you for your replay. It was very helpful.

I found the following sentence on a British music school's website.

People in this class are also encouraged to take part in the Cabaret Ensemble.

In this case, doesn't "people" refer to people in general who will join the class in future as well as those who are currently studying in class?
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Hi Snappy
SnappyIn this case, doesn't "people" refer to people in general who will join the class in future as well as those who are currently studying in the class?
You do need the word "the" in your question.
SnappyPeople in this class are also encouraged to take part in the Cabaret Ensemble.
That sentence makes a general statement about "this class". Since the sentence was found on a school's website, it is probably a class that takes place with some regularity (e.g. every year or every semester).

So, it basically refers to what people taking the class are generally encouraged to do whenever "this class" takes place.
The fact that the statement refers to any session of "this class" (current or future) has no bearing on whether or not you should use "people" or "the people". What AlpheccaStars described above is also applicable here.
Thank you for your replay. Definite and indefinite articles are difficult to us, because our language (Japanese) does not have grammatical articles.
SnappyThank you for your replay.
reply, not replay.
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You are right.