From: Ben Goertzel (ben@goertzel.org)
Date: Sun Oct 09 2005 - 07:14:00 MDT
Hi,
While we're digging into the details of that email of mine, note that while
I typed
> > > Consider also a set F of function mapping E into E. Elements
> > of E may be
> > > mapped into elements of F via considering them as “constant
> functions.”
> > > Define an operation * on F as function composition. Of course,
> > * is neither
> > > commutative nor associative.
in fact if * is function composition then * is associative though not
commutative.
F endowed with (+,*) would seem to be an algebraic structure called
a "near-ring"
http://planetmath.org/encyclopedia/NearRing.html
which is an observation that so far as I can tell doesn't do much
good. It is right-distributive (as required by the near-ring
axioms) but not left-distributive.
-- Ben
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