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22.5 Summary & Conclusions

In summary this Notebook deals with the foundation of numbers themselves. It examines a family of series whose limits includes all rational roots of the rational numbers. This number system of iterative series includes both rationals and irrationals within its family.

System based upon iterative functions

There are a number of interesting features to this number system. While our most familiar number systems are either integer or fraction based, this number system is based upon iterative functions. Because of its iterative nature, zero is the only number that is exact, while all of the rest are approximations.

Generation Patterns independent of 'seed' or 'starting point'

Another intriguing feature is that the generation patterns of our iterative functions are independent of 'seed' or 'starting point'. This means that no matter where we start, we always end up the same place. A corollary to this feature is that the generation patterns are self-correcting. (This aspect is explored more thoroughly in the next Notebook.are Sur (4) SS: Trans Progressive? The Swerve (4) Citronelle I (7) Journal Death (4) SS: HistProg Trans (2) Citronelle I&II (4) Citronelle 2&3 (5) Citronelle 3 (4) L/China 18 (5) SS: Medicare Trans (2) SS: K/Prog Taxes (2) Citronelle 3 (7)  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C2.3 1.3 0.9 5.8 1.1 4.6 14.2 3.1 2.9 8.2 10.3 8.5 4.2 1.8 3.3 14.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0AID ID SS SS SS ID Citro J SS Citro Citro Citro China SS SS Citro @0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0%1144.7(3.136)22.0ÿËp@CARDËÓ®õ¬î%Oct 14 Nov 14 Dec 14 0 0 0799.3 93.6 93.0 2.5 1.3 1.0 0.0 -.4 2.5 0.0 0.0 0.0 0.0Jan15 Feb15 Mar15105.2 103.3 102.4!Apr 15 May 15 Jun 15"76.1 100.3 92.9#Jul15 Aug15 Sep14$42.5 87.4 112.6CDXXI August 2015b€M 31 M 31 Th 27 Sep 1>4 2>5 1&2 M 7 Su 6 8>10 6>15 11>16 9>13 8>10 18>23 24&25 20>22 SS: Myths Trans SEA2: Global Edit L/China 19 SEA2: (5) Lulu+Trans L/China 19 (3) SS: K/Prog Taxes (2) SS: Tribe/Emp Trans Journal Death Breakdown (5) L/China 20 (4) Breakdown (6) Journal Death (5) SS: K/Prog Taxes (2) Breakdown (6) Breakdown (2) Journal Daemonic (5) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 B2.5 1.2 0.6 8.4 3.5 3.5 2.4 1.1 6.9 3.5 12.1 6.3 3.4 11.6 2.3 3.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 05SS SEA Chin SEA Chin SS SS J BD Chin BD J SS BD BD J @0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0%1108.6(3.037)21.3õNð õ| ÿÿÿÿÿÿ€CARDÌc®õ¬.%Oct 15 Nov 14 Dec 14 0 0 0782.6 93.6 93.0 2.5 1.3 1.0 0.0 -.4 2.5 0.0 0.0 0.0 0.0Jan15 Feb15 Mar15105.2 103.3 102.4!Apr 15 May 15 Jun 15"76.1 100.3 92.9#Jul15 Aug15 Sep15$42.5 87.4 92.6CDXXISeptember 2015m€19>30 15>29 25>26 25>30 Oct 1>11 Oct 1>5 6>11 1>13 W 14 12>20 16>22 12>22 2>7 28>31 21>30 27&29(Journal Death (7) L/China 21 (6) SS: K/Prog Taxes (2) B2>4: Delete spaces (6) B2: Edit (10) Journal +Tran Death (6) Journal +Tran Death (5) L/China 22 (4) L/China 23 (2) B2: Edit (5) Breakdown (4) Lulu Journal Death (8) HW SS: K/Prog Taxes (3) Toddler Lorrie 18 mo(5) B3: Edit (6) L/China 24 (2) 0 0 0 0 0 0 0 0 0 0