Science > Physics > Nonrenormalization vs Renormalization 14.5: Generalization of PI To Integers Mod c
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
16 Apr 2006 11:13:40 PM |
| Object: |
Nonrenormalization vs Renormalization 14.5: Generalization of PI To Integers Mod c |
From Osher Doctorow
Probable Influence/Causation (PI) arguably has generalizations to
domains other than [0, 1] or [0, 1] X [0, 1] or its n-dimensional
version, n integer > = 1. I've discussed some of these in various
past threads.
A new generalization to Integers Mod c is relevant to Number Theory.
Suppose that:
1) a CONGRUENT b (mod c) (this is usually denoted by = with a third
bar above it)
2) b CONGRUENT d (mod c)
Then we have from Integers Mod c laws:
3) a CONFRUENT d (mod c)
In other words, if a - b = k1c and b - d = k2c, then a - d = (a - b) +
(b - d) = (k1 + k2)c so it follows that a - d = k3c where k3 = (k1 +
k2). The quantities a, b, c, d, k1, k2 are integers here.
But (1) can be rewritten:
4) a - b = k1c
and therefore:
5) a - b + 1 = 1 + k1c
We recognize in a - b + 1 the Probable Influence/Causation (b --> a) in
Fuzzy Multivalued Logic (FML) notation (or y - x + 1 in ordinary PI
notation). So regarding FML as generalizing to all integers (FML
implication ordinarily is limited to [0, 1], like usual PI) and
likewise for a - b + 1 = (b --> a) generalizing PI, we get in FML
notation from (5):
6) (b --> a) = 1 + k1c
which says:
7) (b --> a) CONGRUENT 1 (mod c)
Similarly we get from (2):
8) (d --> b) CONGRUENT 1 (mod c)
Then from (3) we get:
9) (d --> a) CONGRUENT 1 (mod c)
Therefore, the transitive law for integers a, b mod c results in the
transitive law for (b --> a), (d --> b), and (d --> a) mod c with all
parenthesis expressions congruent to 1 (mod c) or "congruents of
unity".
Osher Doctorow
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| User: "Abas, Physics" |
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| Title: Re: Nonrenormalization vs Renormalization 14.5: Generalization of PI To Integers Mod c |
17 Apr 2006 01:55:52 PM |
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"OsherD" <> wrote in message
news:1145247220.438411.163450@i40g2000cwc.googlegroups.com...
From Osher Doctorow
<snip crap>
Therefore, the transitive law for integers a, b mod c results in the
transitive law for (b --> a), (d --> b), and (d --> a) mod c with all
parenthesis expressions congruent to 1 (mod c) or "congruents of
unity".
Osher Doctorow
trivial. Why post items from a beginners textbook?
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| User: "OsherD" |
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| Title: Re: Nonrenormalization vs Renormalization 14.5: Generalization of PI To Integers Mod c |
18 Apr 2006 02:42:50 AM |
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From Osher Doctorow
Abas of abouliasnet.com typed (after <snip crap> in his "words"):
trivial. Why post items from a beginners textbook?
Between Abas, abouliasnet, "snip crap", "trivial", and "beginners
textbook," your reply reads like a "downer". Do you roll uphill too
:>) You are right about the transitive law not being
earth-shattering to say the least, but I can't always maintain my usual
level of brilliance to which you are undoubtedly used to in reading my
posts. Oops! I notice that this is your first post to sci.physics
from the "profile" button near your name and the "options" button.
Well, you're off to a rather curious start if I may say so. You might
try deleting "snip crap" in future, and "beginner" too for that matter,
though the word "trivial" suggests someone familiar with logic - great
scott, a lawyer? Maybe a politician? O.K., leave the word "trivial"
in since there's no way for you to do without it :>)
Osher
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