| 释义 |
Dirichlet's approximation theorem Let α be a real number and Q > 1 be an integer. Then there are integers p,q with 0 < q < Q such that |qα −p|≤1/Q. Consequenctly, there are infinitely many p,q satisfying |α −p/q|≤1/q2. This is a significant result in Diophantine approximation, the study of approximating real numbers by rational numbers. Compare Roth's theorem.
|