Re: Functions and Relations

NENASHI, Tegiri wrote:
> "Aloha Kakuikanu" <aloha.kakuikanu_at_yahoo.com> wrote in
> news:1164073723.190203.250710_at_k70g2000cwa.googlegroups.com:
>
> >
> > NENASHI, Tegiri wrote:
> >> "Aloha Kakuikanu" <aloha.kakuikanu_at_yahoo.com> wrote in
> >> news:1164051960.913651.234880_at_m73g2000cwd.googlegroups.com:
> >> > But then, both composition and join are
> >> > associative. Is it merely a coincidence?
> >>
> >> There are relation compositions that are not associative:
> >>
> >> 3 -2 - 1: let const3 = 3; m2:x ->x-2; m1:x->x-1;
> >>
> >> 'const3 o m2 o m1' is not associative.
> >
> > Relation composition or function composition?
>
> What is the difference ? pretend that the composition of relations is
> followed by a projection.
>
>
> > In your example, both
> > ways seems to produce const3.
>
> Please read it from left to right like lambda application ';'. I had to
> have it written with ';'' not with 'o': const3 ; m2; m1. The correct way:
>
> m1 o m2 o const3
>
> But I think that you understood ;)
>
> >
> > Proof by googling: "function composition associative"
>
> Google is wrong: now you know that not all the time ;) The division is
> another example, Lie groups, et cetera.

Function composition is *always* associative at least for the function as defined in the set theory. You are perhaps under influence of the "dark side" of the category theory, hein mon ami ? There, there is a weird notion of noncommutative category, but for "normal" categories, associativity is one of the axioms of the c.t. So, this time, google is right. Received on Tue Nov 21 2006 - 14:38:00 CET