The question is:
A certain real number $\theta$ has the following property: There exist infinitely many rational numbers $\frac{a}{b}$(in reduced form) such that: $\mid\theta-\frac{a}{b}\mid< \frac{1}{b^{1.0000001}}$ Prove that $\theta$ is irrational.
I just don't know how I could somehow relate $b^{1.0000001}$ to $b^2$ or $2b^2$ so that the dirichlet theorem can be applied. Or is there other ways to approach the problem?
Thank you in advance for your help!