Natural Numbers form Inductive Set/Proof 2

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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:

$\N = \bigcap \II$

where $\II$ is the collection of all inductive sets.


The result is a direct application of Intersection of Inductive Set as Subset of Real Numbers is Inductive Set.

$\blacksquare$


Sources