Re: Interpretation of Relations

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 20 Jan 2007 15:46:38 GMT
Message-ID: <yPqsh.3134$1x.54087@ursa-nb00s0.nbnet.nb.ca>

Marshall wrote:

> On Jan 20, 6:17 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>

>>Exactly! DEE is the relational equivalent of 'True' and is the identity
>>element for JOIN while DUM is the relational equivalent of 'False'.

>
>
> Terminology question:
>
> We use the term "identity" to describe a value id relative to a
> binary operator op that has the property:
>
>
> forall x. x op id = x
>
>
> Is there a term used to describe the value v in the below?
>
> forall x. x op v = v
>
> Ex.: 0 for multiply, false for AND, etc.

Fixed point. Contrast with idempotent element:

some v. v op v = v

Any fixed point for a binary op must also be an idempotent element for the op.

Addition has no fixed points and only 0 as an idempotent element.

What to call something that always results in the same value but not itself? Consider exponentiation:

for all x != 0. x ^ 0 = 1

It has two left fixed points:

for all x. 1 ^ x = 1
for all x != 0. 0 ^ x = 0 Received on Sat Jan 20 2007 - 09:46:38 CST