Suppose that we have a real valued function $f(x)$ that has local support, i.e. it's non-zero just for some values of $x$. If you are familiar with B-splines, this function $f$ can be interpreted as a B-spline of order $n$ "that is non-zero in the interval spanned by $(n+1)$ knots".The Elements of Statistical Learning (Hastie, et.at.,p.188)
My question is, isn't all the real line spanned by two points? I've always seen "span" as something related to vectors, not to merely scalars.
So what's wrong with the "local support" condition of the B-splines? Is this a improper use of the term "span"?