**From:** Ben Goertzel (*ben@goertzel.org*)

**Date:** Sun Oct 09 2005 - 07:14:00 MDT

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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
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*> > of E may be
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*> > > mapped into elements of F via considering them as “constant
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*> functions.”
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*> > > Define an operation * on F as function composition. Of course,
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*> > * is neither
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*> > > commutative nor associative.
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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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