Definition:Inductive Set/Subset of Real Numbers

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