Re: Real world issue:- OT recreational interval

pamelafluente_at_libero.it wrote:
>
> Could you please provide me with the formal (I want a rigorous symbolic
> expression)
> definition of "binary idempotent function" ?
>
> I want to convince myself that was the right term. But I cannot find
> the "binary" version.

It's in the wikipedia entry you mentioned earlier, under "Formal definitions / Binary operation"

http://en.wikipedia.org/wiki/Idempotent

"If S is a set with a binary operation * on it, then an element s of S is said to be idempotent (with respect to *) if

    s * s = s.

In particular, any identity element is idempotent. If every element of S is idempotent, then the binary operation * is said to be idempotent. For example, the operations of set union and set intersection are both idempotent."

Consider * as binary min:

  forall s, min(s, s) = s

So min meets the definition. (Likewise max.)

However, it is not the case for sum or count.

  not forall s, s + s = s

So + is not idempotent. Since + is not idempotent, sum() isn't either.

Etc.

Marshall Received on Sun Sep 17 2006 - 16:54:11 CDT