f(x) is 1 when x is rational, and f(x) is 0 is irrational. what is the name of this function?

Question

i know the name begins with a d. is it derelicht?

Answer 1

This, the indicator function of the set of rational numbers, *is* often called Dirichlet's Function. It is everywhere discontinuous.

A modification of it gives an example of a fctn discontinuous at the rational points only.

Answer 2

I like the idea of a derelict function!:

This one not only doesn't know whether it lives at x = 0 or 1, but, as set in the answer page, it's not even sure whether its name is F(x) or f(x).

Answer 3

I believe you're thinking of Dirichlets' Function which is continuous, but nowhere differentiable.


Doug

Answer 4

This is a function différential.