Definition:Inductive Set/Subset of Real Numbers
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Definition
Let $I$ be a subset of the real numbers $\R$.
Then $I$ is an inductive set if and only if:
- $1 \in I$
and
- $x \in I \implies \paren {x + 1} \in I$
Also see
- Results about inductive sets can be found here.
Sources
- 1981: Karl R. Stromberg: An Introduction to Classical Real Analysis: $\S 1$
- 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 4$: The Integers and the Real Numbers