Re: Real world issue:- OT recreational interval

> Thanks for the feedback. As to your point 1, I freely admit the
> failing. It is an area I am currently working on, and still need

I think instead that people who hide behind insults do that because are scared to do an open confrontation with scientific arguments.

I am always ready to confront and admit my errors because I have a sincere love for what is right and I have no problem if this is stated by another person.

Ok I found this reference:

http://www.latrobe.edu.au/philosophy/phimvt/joy/j04alg.html

"Idempotency, zero elements and arities"

A binary function f(x,y) is called idempotent if for all x

        f(x,x) = x

According to the above definition:

  countDistinct (5,6) = 2
  countDistinct is "not idempotent" (1 counterexample is enough)

  max(x,x) = x for any x
  max is "idempotent"

 (1) Your statement is: "Duplication Sensitive" <=> Non Idempotent

 if we negate both sides, we obtain an equivalent statement:

 (2) "Not Duplication Sensitive" <=> Idempotent

Now observe that CountDistinct is "Not Duplication Sensitive function" example: CountDistinct (2,2) = 1.

At the same time CountDistinct is "not idempotent" (see above).

 Therefore we have found 1 case where:

 (3) "Not Duplication Sensitive function" => "idempotent"

is false. Therefore (2), (1) are false.

(The inverse implication of (3) is clearly true)

Do you see errors in the above argument?

-P Received on Sun Sep 17 2006 - 16:59:41 CDT