First of all. This is a corresponding relationship, which should be for some people, not for some people. Similarly, any one should correspond to one rather than some. (although a little far-fetched)

Second. As you said, there are some negatives and some negatives, but when you really use them, can you express the meaning of both in one word? Therefore, it is more appropriate to refer to the correspondence before and after. Any one is the same.

Third. Although it is math, it is expressed in Chinese. Language is mainly context, which is why some people can understand it and others can't. Let me make sure that your understanding is correct. Your question is to get to the bottom of it. I'm glad you understand. The negation of "all" is expressed by "some". As for one or some, you must know it according to the meaning of the topic or the process of doing it, but when expressed, it becomes a unified "some".

There are really too many such problems in the learning process. You should learn how to make yourself understand what others mean. Don't be too rigid and learn freely.

But I can see that your scholarship is still very rigorous!