http://www.mathcs.org/analysis/reals/cont/proofs/monodisc.htmlFrom last paragraph.

"Since the sum of jumps must be smaller than f(b) - f(a), the set J(n) is finite for all n".

I can uderststand that the sum of jumps must be samller than f(b)-f(a), but why the Set J(n) is finite then?

Thanks.