Subject: Calculus Proof
Mark Spilker
I have a proof that I cannot do here it goes. I look forward to hearing back from you Hi Mark,
To prove the integrability of F(x) from 0 to 1 you need to consider the limit
where P is the norm of the partition and w_{i} is a point in the interval from x_{i1} to x_{i}. This limit must exist and its value must NOT depend on the choice of w_{i}. With the function that you have, no matter how small P, you can always find a rational and an irrational in each interval from x_{i1} to x_{i}. If you always choose w_{i} to be rational then the limit is 1, and if you always choose w_{i} to be irrational then the limit is 0. Thus the value of the limit depends on the choice of w_{i} and hence the integral does not exist. I hope this helps,Harley
