(v,w) is defined just for one particular graph. It’s the first edge in that graph such that f(v)<0<f(w). (So it could have been called (vn,wn)). Then for the next graph, it’s a different v. Basically, x1 looks at where the first graph skips over the zero mark, then picks the last vertex before that point, then x2 looks at the next larger graph, and if that graph skips later, it updates to the last vertex before that point in that graph, etc. I think the reason I didn’t add indices to (v,w) was just that there ar ealready the v with two indices, but I see how it can be confusing since having no index makes it sound like it’s the same value all throughout.
On your Ex. 2:
Is there something I’m missing? It seems to me that xn=v for all n>1.
(v,w) is defined just for one particular graph. It’s the first edge in that graph such that f(v)<0<f(w). (So it could have been called (vn,wn)). Then for the next graph, it’s a different v. Basically, x1 looks at where the first graph skips over the zero mark, then picks the last vertex before that point, then x2 looks at the next larger graph, and if that graph skips later, it updates to the last vertex before that point in that graph, etc. I think the reason I didn’t add indices to (v,w) was just that there ar ealready the v with two indices, but I see how it can be confusing since having no index makes it sound like it’s the same value all throughout.