Definition:Natural Numbers/Inductive Sets in Real Numbers
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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, $0 \notin \N$.
- Results about the natural numbers in $\R$ can be found here.
- 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 4$: The Integers and the Real Numbers