Re: Semigroup problem

On May 12, 1:43 am, marc...@xxxxxxxxx wrote:
On May 12, 12:28 am, magi...@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:





In article <873d683f-5f4a-4be9-8ce3-5fd6d79ff...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
 <marc...@xxxxxxxxx> wrote:
On May 12, 12:02 am, magi...@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
In article <08bc16eb-a3e7-4a11-94cb-6c5fa12fa...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

 <marc...@xxxxxxxxx> wrote:
On May 11, 6:23 pm, Jos=E9 Carlos Santos <jcsan...@xxxxxxxx> wrote:
On 11-05-2008 15:41, marc...@xxxxxxxxx wrote:

Let * be a semigroup operation that satisfies the following
properties:

all z exists x exists y (x * y =3D z).
all x all y (F(x) * G(y) =3D y * x).

The problem is: prove that * is commutative or find a counterexample
(finite if it is possible) to this claim.

What are F and G?

Capital letters from the English alphabet.

Is that a joke?

Yes. You don't like jokes?

I think they are a waste of time when you are trying to get help with
a problem, especially if you don't follow-up with the information
being requested.

They are function symbols.

And... ? This is insufficient to explain your symbology.

Fromhttp://en.wikipedia.org/wiki/Function_symbol: "the symbol F in a
formal language is a functional symbol if, given any symbol X
representing an object in the language, F(X) is again a symbol
representing an object in that language."

Do you mean:

There exists F:S->S and G:S->S (set-theoretic functions/semigroup
funtions/ what?) such that for all x and all y in S, F(x)*F(y) = y*x?

That is correct set-theoretic interpretation, with the exception that
the second F is G. If F = G then * is commutative.

Do you mean, for all x and all y, there exist elements z and w such
that w*z = y*x ?

That way z and w will depend on both x and y. This is not logically
equivalently to the original statement.

Do you actually want help, or just to waste everyone's time?

I'm just curious. If you are interested in the problem then perhaps
you can post interesting reply.
Anyway no one forces you to do that and perhaps you know better than
me that Usenet is a waste of time for the most part.

Marc-


*****************************************************************

I think it is obvious now we're dealing here with an idiot the size of
Tommy or something like that.
He ill-posts a question, he's politely asked to explain his own
symbols, he then answers with a joke and don't even bother to explain
anything, and when he's told so he gives the reply an ass would.

No more waste of time with trolls like this.

Regards
Tonio
.

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