Explore BrainMass
Share

# Ruler function proof

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Define Ruler Function g:(0,1)-> R (it is the usual ruler function available online)

as g(x) = { 1/q if x = p/q, p and q are relatively prime
{ 0 if x is irrational.

Show (without using Riemann-Lebesgue Theorem) that g is Riemann integrable.

The hint says that since L (lower sum) is zero, it remains to show that U (Upper sum) is less than epsilon for some partition p. I'm trying to do that, but to me the answer is elusive.

https://brainmass.com/math/computing-values-of-functions/ruler-function-proof-214560

#### Solution Preview

Hello

Please find the solution in the attached files.

Proving Ruler Function is Riemann Integrable without using Riemann-Lebesgue Theorem
Define Ruler Function g:(0,1)-> R (it is the usual ruler function available online)

as g(x) = { 1/q if x = p/q, p and q are relatively ...

#### Solution Summary

This provides an example of proving the Ruler Function is Riemann Integrable without using Riemann-Lebesgue Theorem.

\$2.19