Function f(x): Rationals = 0, Irrationals = 1

[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

 

[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.

 

[himanshu121]

Probably Dirchlet Function(Check Spelling)

 

[Kalimaa23]

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