   Chapter 4.3, Problem 73E

Chapter
Section
Textbook Problem

Think About It Determine whether the Dirichlet function f ( x ) = { 1 , x       is   rational 0 , x       is   rational   is integrable on the interval [0, 1]. Explain.

To determine
If the Dirichlet function

f(x)={1, x is rational0, x is irrational is integrable on the interval [0,1] or not.

Explanation

Given:

Dirichlet function:

f(x)={1, x is rational0, x is irrational

Explanation:

For the given function f, x can either be a rational number or an irrational one. As a result, there can be infinite values of x in the interval [0,1] however small it might be

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