# Inductive Set/Examples/Subset of Real Numbers

## Example of Inductive Set

### Inductive Set as Subset of Real Numbers

A specific instance of such an inductive set is defined by some authors as follows:

Let $I$ be a subset of the real numbers $\R$.

Then $I$ is an inductive set if and only if:

$1 \in I$

and

$x \in I \implies \paren {x + 1} \in I$