Is it appropriate to compare myself with other students in my statement of purpose for U.S. graduate school application?
This would be a bad idea and will likely have the opposite effect you want it to have.  Especially in mathematics, people are turned off by bullshit.

Let me relate an actual exchange I heard a few years ago between two rather famous mathematicians:

Person 1: "I have an amazing theorem to tell you about!"

Person 2: "Slow down.  You tell me the theorem, and I'll tell you if it's amazing."

This illustrates I think an important principal of social interactions in academia (and probably elsewhere too, though I gather that eg in politics and business this is not true).  Namely, people are very unimpressed and skeptical when someone comes out and says how great they are.  What you have to do is tell them factual things that force them to draw the conclusion for themselves that you are great.

In other words, the old adage about writing holds: show, don't tell.