prove | x- p/q| <= 1/(q^2) ??

kensai

怎样用·pigeon hole principle prove

| x- p/q| <= 1/(q^2)

given p and q are integers with p<q

kensai

问题不完整

For any real number x , there exists p/q such that

| x- p/q| <= 1/(q^2)

hamilan911

题目应该有问题

x is any real number
假设x是一个大过2的real number
p,q都是integer且p < q, 所以p/q < 1
那么LHS的|x - p/q|肯定大过1，但是RHS的1/(q^2)小过1

屮O_O屮

eh?問題不對路哦