Re: Real world issue:- OT recreational interval
Date: 17 Sep 2006 14:54:11 -0700
Message-ID: <1158530051.753622.160590_at_e3g2000cwe.googlegroups.com>
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 - 23:54:11 CEST