Prove intersection of all inductive sets is inductive How to prove that the intersection of all inductive sets is inductive?
Subset A of ordered field F is inductive, when:
1) $1 \in A$
2) if $a \in A$ then $a+1 \in A$
Prove that $$\mathbb{I} = \bigcap \left\{A\in F\ {\large|} \ A \text{ is inductive }\right\}$$ is inductive.

HINT: Recall that $x\in\bigcap\cal A$ if and only if for every $A\in\cal A$, $x\in A$.
