Name of Function

[Lonewolf]

The function defined over the real numbers as


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?

[selfAdjoint]

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

[Hurkyl]

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

[Lonewolf]

Apparently, it's a special case of the Dirichlet function

http://mathworld.wolfram.com/DirichletFunction.html

That's good. I've got something less vulgar to call it now [6)]

[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

[vepore2]

Originally posted by 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

that doesn't sound simple

[Lonewolf]

What do you mean? I think it rolls right off the tounge. [6)]

[himanshu121]

Probably Dirchlet Function(Check Spelling)

[Dimitri Terryn]

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