Definition:Natural Numbers/Inductive Sets in Real Numbers

Definition
Let $\R$ be the set of real numbers.

Let $\mathcal I$ be the collection of all inductive sets in $\R$.

Then the natural numbers $\N$ are defined as:


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

where $\displaystyle \bigcap$ denotes intersection.

It follows from the definition of inductive set that according to this definition, $0 \notin \N$.