In my discrete mathematics class, we came across the definition of well-ordered for sets:
A set is well-ordered with respect to an ordering function if, $\forall $of its nonempty subsets, $\exists$ a minimum element.
My thought was that the empty set, $\emptyset$, would fulfill this definition, albeit "vacuously" since it has no nonempty subsets. However, I was told that this is incorrect and am not sure why. Could someone please elucidate whether or not this is true and how I can determine if a definition is fulfilled "vacuously?"