\begin{definition}[Definition:Natural Numbers/Inductive Sets in Real Numbers]
Let $\R$ be the set of real numbers.
Let $\II$ be the set of all inductive sets defined as subsets of $\R$.
Then the '''natural numbers''' $\N$ are defined as:
:$\N := \ds \bigcap \II$
where $\ds \bigcap$ denotes intersection.
It follows from the definition of inductive set that according to this definition, $0 \notin \N$.
\end{definition}