Span of an empty set is the zero vector

Depending on how you define the span, this is either a definition or it follows from the definition of span (and judging by the wording it is probably the former). What's Nering's definition of span?

(One definition of span is the following: the span of a collection of vectors is the intersection of all subspaces containing them. The span of no vectors is therefore the intersection of all subspaces, which is $\{ 0 \}$.)

The span of a set D is the smallest subspace containing the elements of D. Now, every subspace contains 0. Thus if D is a null set the span of D can only be the subspace containing 0.