definition of $\mathbb{N}:=\bigcap Ind$

definition of $\mathbb{N}:=\bigcap Ind$

--- let $A$ a set, $A^+=A \cup \{A\}$
--- let $B$ a set, B is inductive if $\emptyset \in B \wedge \forall A \in
B(A^+ \in B )$
--- let $Ind:=\{C|C \text{ is inductive }\}$
is correct this definition:
$\mathbb{N}:=\bigcap Ind $, with $\bigcap Ind=\{x|\forall C \in Ind (x \in
C) \}$
????
Thanks in advance!!