Re: A new proof of the superiority of set oriented approaches: numerical/time serie linear interpolation

Gene Wirchenko wrote:

> Bob Badour <bbadour_at_pei.sympatico.ca> wrote:
>
>

>>Gene Wirchenko wrote:
>>
>>
>>>Bob Badour <bbadour_at_pei.sympatico.ca> wrote:
>>>
>>>
>>>
>>>>Gene Wirchenko wrote:
>>>>
>>>>
>>>>
>>>>>Bob Badour <bbadour_at_pei.sympatico.ca> wrote:
>>>>>
>>>>>[snip]
>>>
>>>
>>>>>>Interpolation has a number of other traps. Suppose one evaluates:
>>>>>>f(x) = (x-1)/(x-1) at x=0 and x=2. One will reach a vastly wrong 
>>>>>>conclusion if one even tries to interpolate f(1).
>>>>>
>>>>>    What about if we limit it to functions?  Your f is not a


> 

>          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

>>>>>function, because 1 is not in the domain.  (I am assuming a general
>>>>>(for lack of a better word) domain, such as N, Z, Q, or R.)
>>>>
>>>>If 1 were not in the domain, one would have no desire to interpolate to 
>>>>it in the first place. That sounds like ignoring the problem by defining 
>>>>it out of existence.
>>>
>>>     If 1 is in the domain, then f(x) does not have a defined value
>>>for 1, and is, thus, not a function.
>>
>>I don't recall claiming that f(x) was a function. I recall claiming it 
>>was a trap for interpolation.

Ohhhh, I see! Nooow, I get it. D'Oh! Um, is the unit impulse function a function? What about the unit step function? Received on Thu May 03 2007 - 21:24:56 CEST