inductive set InductiveSet 2001-10-19 11:16:18 2003-11-05 17:38:14 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} An {\em inductive set} is a set $X$ with the property that, for every $x \in X$, the successor $x'$ of $x$ is also an element of $X$. One major example of an inductive set is the set of natural numbers $\mathbb{N}$.