I'm tying to use the false position method to find the root r of f(x)=0, between 2 points a0 and b0. I have [a(i),b(i)] enclose in it f(x)=0. There is something I don't get, if the number of iteration i goes to infinity, why the length of [a(i),b(i)] doesn't unnecessary goes to 0 ? I understand that this have to do with the f(a0) et f(b0) the first 2 points chosen. can somebody explain this ?