Name of Function

1. Jan 31, 2004

Lonewolf

The function defined over the real numbers as

Code (Text):

f(x) = {0, x rational
{1, x irrational

appears quite a lot in mathematics textbooks. Does anybody know if this function has a commonly accepted name?

2. Jan 31, 2004

Staff Emeritus
Well, it's the characteristc function of the set of irrationals, $$\chi (R - Q)$$.

3. Jan 31, 2004

Hurkyl

Staff Emeritus
I've heard it called the "salt and pepper" function.

4. Jan 31, 2004

Lonewolf

5. Jan 31, 2004

phoenixthoth

i've got a simple name and a mnemoic to remember it's name.

name: the 0 if rational and 1 if irrational function.
simple mnemoic: tziraoiif

6. Feb 2, 2004

vepore2

that doesn't sound simple

7. Feb 3, 2004

Lonewolf

What do you mean? I think it rolls right off the tounge.

8. Feb 3, 2004

himanshu121

Probably Dirchlet Function(Check Spelling)

9. Feb 3, 2004

Kalimaa23

Sure about that? The name Dirichlet has popped quite a number of time in my textbooks. I've never heard of Dirchlet.