I'm beginning to study the singularities in the minimal model program on Matsuki's "Introduction to the Mori Program". Can someone tell me why the definition of terminal singularities (for instance) is well posed?
More precisely, if X is a normal projective variety s.t. $K_{X}$ is $\mathbb{Q}$-Cartier, we say that it has terminal singularities if there exists a projective birational morphism $f:V \longrightarrow X$, with $V$ nonsingular, s.t. in the ramification formula $$K_{V}=f^{\star}K_{X}+\sum a_{i}E_{i}$$ all the coefficients $a_{i}$ are strictly positive. How can I show that this is independent from the $(f,V)$ chosen? Thank you!