Nonreduced double point
= Nonreduced double point
{title2=$\operatorname{Spec}k[\epsilon]/(\epsilon^2)$}
The spectrum of the <dual number> ring $k[\epsilon]/(\epsilon^2)$ is a <nonreduced scheme> of length two supported at one point. Its nonzero nilpotent $\epsilon$ retains first-order information that the underlying singleton topological space forgets. It differs from the disjoint union of two reduced $k$-points.