Natural Numbers form Inductive Set/Proof 2

Theorem
Let $\N$ denote the natural numbers as subset of the real numbers $\R$.

Then $\N$ is an inductive set.

Proof
By the given definition of the natural numbers:


 * $\N = \displaystyle \bigcap \mathcal I$

where $\mathcal I$ is the collection of all inductive sets.

The result is a direct application of Intersection of Inductive Sets is Inductive Set.