Dirichlet Function Quiz

Who is the Dirichlet function named after?

• Gauss

• Riemann

• Euler

• Dirichlet

Answer explanation

The Dirichlet function is named after Dirichlet himself, so the correct choice is Dirichlet.

What is the Dirichlet function's value for rational numbers?

• 2

• 3

• 1

• 0

Answer explanation

The Dirichlet function's value for rational numbers is 1. It takes the value 1 for rational numbers and 0 for irrational numbers.

In which branch of mathematics is the Dirichlet function commonly used?

• Algebra

• Calculus

• Geometry

• Number Theory

Answer explanation

In Number Theory, the Dirichlet function is commonly used, making it the correct branch of mathematics for this function.

What is the periodicity property of the Dirichlet function?

• It is constant

• It is exponential

• It is linear

• It is periodic

Answer explanation

The periodicity property of the Dirichlet function is that it is periodic, meaning it repeats at regular intervals.

Why is the Dirichlet function not Riemann-integrable on any segment of R?

• It is unbounded

• It is discontinuous

• It is not continuous

• It is not defined

Answer explanation

The Dirichlet function is not Riemann-integrable on any segment of R because it is discontinuous, which violates the conditions required for Riemann integrability.