Thread: Dirichlet function upper and lower sum

Question:

Suppose that f(x)=7 if x is rational and f(x)=3 if x is irrational on the interval [1,3]. Let P be a partition of [1,3].

What is the lower sum: I have that the lower sum is 0.

What is the upper sum: I have that the upper sum is 4.

What is sup L(f,P) over all partitions: 7

What is inf U(f,P) over all partitions: 3

And that the function is integrable over [1,3]

Am I on the right track with this?

Originally Posted by CountingPenguins

And that the function is integrable over [1,3]

Lebesgue-integrable, but not Riemann-integrable.

Originally Posted by CountingPenguins

Question:

Suppose that f(x)=7 if x is rational and f(x)=3 if x is irrational on the interval [1,3]. Let P be a partition of [1,3].

What is the lower sum: I have that the lower sum is 0.

What is the upper sum: I have that the upper sum is 4.

What is sup L(f,P) over all partitions: 7

What is inf U(f,P) over all partitions: 3

And that the function is integrable over [1,3]

Am I on the right track with this?

Look here:


http://www.mathhelpforum.com/math-he...tml#post664645