Definition:Natural Numbers/Natural Numbers in Real Numbers

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

Let $\mathcal I$ be the set 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, $0 \notin \N$.

Also see

  • Results about the natural numbers in $\R$ can be found here.