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C00002 00002	Proposed revision: June 2 Draft, page 44, 6 lines up from the bottom:
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Proposed revision: June 2 Draft, page 44, 6 lines up from the bottom:

(because it has knowledge...etc)  --->

because	(i) The Suggestion facet of the Relation concept contains, as one of its
many pieces of code, the hint that "if a relation is interesting, then its inverse
is worth investigating". 
	(ii) The Fillin facet of the strategic concept for dealing with Examples
is able to find several instances of TIMES↑-↑1. For each n, TIMES↑-↑1(n) is a set
of mulisets.
	(iii) To see if TIMES↑-↑1 has any interesting properties, AM will follow
the procedures listed under the Interestingness facet of the concept named Relation.
One of these says to examine the images of the specific examples found already, and
see if they, viewed as sets, are interesting in some way. 
	(iv) The Set concept knows that it is very interesting if each element
satsfies the same mildly interesting property. But each element of each TIMES↑-↑1
image satisfies Bigger-than-doubleton, one of the primitive concepts known to AM.
	(v) The Suggestion facet of the Relation concept contains an entry to the
effect that if a relation is known to satisfy "for all xεX, at least P(x)", then
the following set is probably worth examining: "those xεX for which precisely P(x)".
In the above example, this means consider those numbers which map precisely into
doubletons, under TIMES↑-↑1. But this set is just the set of prime numbers.
	(vi) Now AM initializes a new structure, PRIMES, and a new predicate, 
IS-PRIME. AM continues looking for interesting properties satisfied by TIMES↑-↑1.
One thing that Relation looks for is whether, (∀n)(∃xεTIMES↑-↑1(n)).P(x), for
some very unusual property P. Here P is a predicate which is applied to a multiset.
Multiset knows it is interesting if each member satisfies some interesting property.
The final piece of knowledge that links all these is that IS-PRIME is temporarily
being considered interesting. So AM asks whether each TIMES↑-↑1 image contains
a multiset of primes, and the answer appears to be affirmative. AM is thus led
to propose "for all n, TIMES↑-↑1(n) contains at least one multiset of primes".
	(vii) The same piece of knowledge as in (v), leads AM to consider the
subset of numbers n which satisfy "TIMES↑-↑1(n) contains precisely one multiset
of primes". But empirically, this seems to be all the numbers it tries! So AM
proposes the following conjecture:
"For all numbers n, TIMES↑-↑1(n) contains precisely one multiset of primes".
But this is just the Unique Factorization Theorem.


Each facet will have several separate entries (facts, hints, procedures);
recall that ach concept has 25 facets, and that
there will be about 150 concepts initially. So the number of these tiny programs
(the number of pieces of knowledge)
is initially about 10↑5. AM's basic ↓_activity_↓ is to write more of them, and
its basic ↓_goal_↓ is to maintain the quality and usefulness of each new piece of
each facet. Notice how, now that PRIMES has been distinguished as a new concept,
AM has about 20 facets to fill in, dealing just with the set of prime numbers.
Similarly, one particular facet of the newly-created concept
Unique-factorization-conjecture is that of Justification. So one of the many
activities open to AM is to fill in that facet: that is, find a proof for the UFT.