How can the set $N$ of natural numbers be defined from the point of view of the ZF axiomatic set theory provided the concept of inductive set? Hrbacek-Jech (page 41) says that $N=\{x\in A:\forall(I)(x\in I)\}$ where $I$ varies over inductive sets and $A$ is any given inductive set, but in my opinion this definition fails in that in such a way $N$ depends on $A$, which is not an already defined constant but a variable. Thanks.