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FIGURE 4.
letters' has thirty-one letters.” Note that, for instance, the proposition: “this
sentence consists of...letters” has only one eigenvalue (thirty-nine); while
the proposition: “This sentence is composed of...letters” has none!
Appendix B
B1. Proof of Expression (11):
COORD(Obs
1
*
Obs
2
) = COORD(Obs
3
)
= Obs
3
= Obs
1
*
Obs
2
= COORD(Obs
1
)
*
COORD(Obs
2
)
Q.E.D.
The apparent distributivity of the operator COORD over the composition
“*” should not be misconstrued as “*” being a linear composition. For
instance, the fixed points u
i
= exp(2pli), (for i = 0, 1, 2, 3 . . .) that comple-
ment the operator Op(u):
p
1
Ê
Ë
ˆ
¯
()
=
Op u
u
tan
±
l
l
n u
,
4
with l an arbitrary constant, compose multiplicatively:
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