Talk:Indicator function
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wow -- great article -- this helped a lot.
[edit] Characteristic function
Who says "characteristic function" is "much less frequent now"? It's actually the only term I know for this (I had to guess what an "indicator function" might be, when it showed up in Talk:Boolean algebra). Also the notation I know is χA for the characteristic function of A. --Trovatore 15:26, 6 September 2005 (UTC)
I agree strongly. I had never hear of "indicator function" before I read the ergodic theory article and linked to this page from there. I propose that this page be renamed to "characteristic function". --Mosher 22:03, 23 September 2005 (UTC)
- You would have to make it a disambiguation page. Characteristic function already refers to the Fourier transform of a distribution of a random variable, which is a standard usage.--CSTAR 22:20, 23 September 2005 (UTC)
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- I assume the name indicator function or characteristic function is geographic so I don't think it wise to rule one out or another. As it is called indicator function and not characteristic function where I am. Also, perhaps you should put into the article multiplying two indicator functions. I[a, b] * I[c, d] = I[ max(a,c), min(c, d)] This property is crucial for calculating convolution.
I don't think it's geographic. I think it's more a matter of which research area you work in. Michael Hardy 18:44, 3 August 2006 (UTC)
- Maybe, I'm not sure. However, I also notice the notification is completely different as well as how the indicator function is described. Lectures never needed to speak about mapping, the explanation of course was made to be more simplistic and considering the caliber of people that might need to come here, it would better if the article were described in a manner more suitable to teaching the concept rather than stating it in the most obtuse format possible. Perhaps something where it starts off for the possible motivations for using the indicator function, for instance in circuit analysis to perform convolution... possibly different notations, like using the 1 with subscript versus a capital I with a subscript or followed by brackets to indicate the set it describes. A simple layman explanation, for instance, I [0, 1], means a function that is 1 from 0 to 1 and zero otherwise. Show that you might use it to multiply against an existing function to extract a piece of it, like f(x) * I[0,1] gives you the function from [0,1]. I'm personally wary of editing the article myself.
Perhaps the term indicator function is a shorthand for set indicator function, because the function f specifies or indicates the set { x | f(x) = 1 }. Bo Jacoby 23:09, 25 December 2006 (UTC).
[edit] Is this really true?
- a function φ of a predicate P that takes on values 0 if the predicate has a truth value of "true" and 1 if the predicate has a truth value of "false";
Everybody else translates true to 1 and false to 0. Here it is stated to be the opposite. Is it a typo?
Bo Jacoby 22:39, 25 December 2006 (UTC).
- Yes it's true, there is an intentional logic-reversal here. The logic is "negative/inverted" such that a logical AND will occur if, in a string of them multiplied together, any one representing function is 0:
- φ1*φ2*φ3*φ4 = 0 if any of the φ are 0.
- The notion of a representing function as 0 when "true" is used to "terminate" a mu-operator (causes it to become 0 forever after the first 0 is encountered). Kleene's number-theoretic defintion of a "representing function of a predicate":
- "The function of this type which correlates 0 to t and 1 to f enters into the defintion of 'representing function' given below." (Kleene (1952) p. 226, also cf p. 227).
- and his set-theoretic definition of earlier in his text:
- "We can represent a set of natural numbers by a representing function, which takes the value 0 for a natural number belonging to the set and the value 1 for a number not belonging to the set." (Kleene p. 8)
- wvbaileyWvbailey 21:07, 26 December 2006 (UTC)
