This problem is asking about the relationship between a positive integer $x$ and its reciprocal, $x^{-1}$. I know that the reciprocal of a positive integer is always between $0$ and $1$, so it is smaller than the original integer. Therefore, the inequality $x^{-1}>x$ can never be true for any positive integer $x$. That means the answer is zero. 
For how many positive integer values of $x$ is $x^{-1}>x$?