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

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Discussion Overview

The discussion revolves around the function defined as f(x) = 0 for rational x and f(x) = 1 for irrational x. Participants explore its naming conventions and relationships to other mathematical functions, including its classification and potential common names.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant identifies the function as the characteristic function of the set of irrationals, \chi (R - Q).
  • Another participant refers to it as the "salt and pepper" function.
  • A different participant suggests it is a special case of the Dirichlet function, providing a link for reference.
  • One participant proposes a mnemonic for remembering the function's name, calling it the "0 if rational and 1 if irrational function."
  • Another participant questions the simplicity of the proposed mnemonic.
  • There is a suggestion that the function might be called the Dirchlet function, prompting a spelling check.
  • A participant expresses uncertainty about the spelling, noting that "Dirichlet" has been more commonly encountered in textbooks.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a commonly accepted name for the function, with multiple competing names and interpretations presented.

Contextual Notes

Some participants express uncertainty regarding the naming conventions and spelling of related functions, indicating a lack of clarity in the terminology used in different contexts.

Lonewolf
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The function defined over the real numbers as

Code:
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?
 
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Well, it's the characteristc function of the set of irrationals, [tex]\chi (R - Q)[/tex].
 
I've heard it called the "salt and pepper" function.
 
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
 
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
 
What do you mean? I think it rolls right off the tounge.
 
Probably Dirchlet Function(Check Spelling)
 
Sure about that? The name Dirichlet has popped quite a number of time in my textbooks. I've never heard of Dirchlet.
 

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