Dickey–Fuller test

In mathematics, $\in$-induction (epsilon-induction) is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P[x]. If the truth of the property for x follows from its truth for all elements of x, for every set x, then the property is true of all sets. In symbols:

$\mathrm{\forall }x(\mathrm{\forall }y(y\in x\to P[y])\to P[x])\to \mathrm{\forall }xP[x]$

This principle, sometimes called the axiom of induction (in set theory), is equivalent to the axiom of regularity given the other ZF axioms. $\in$-induction is a special case of well-founded induction.

The name is most often pronounced "epsilon-induction", because the set membership symbol $\in$ historically developed from the Greek letter $ϵ$.