Science > Physics > sqrt(1 - v^2/c^2) Relates to "Real" Laurent Series and Probable Influence 3: How Probability Patches Up Laurent Chaos
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Science > Physics |
| User: |
"OsherD" |
| Date: |
06 Feb 2006 05:55:35 PM |
| Object: |
sqrt(1 - v^2/c^2) Relates to "Real" Laurent Series and Probable Influence 3: How Probability Patches Up Laurent Chaos |
From Osher Doctorow
Let's look at the following from the previous parts of this thread:
1) f(x) = 1 + x + x^2 + ... + 1/x + 1/x^2 + ...
Readers can verify for themselves that if x is a probability or in fact
any real normalized quantity between 0 and 1 (not taken equal to 0),
then terms like x + 1/x, x^2 + 1/x^2, etc., or even such pairs in the
following function:
2) g(x) = 1 + x + x^2 + ... - 1/x - 1/x^2 - ...
do not remain tractable in the sense of for example 0 < = x - 1/x < = 1
or similarly with x and 1/x interchanged.
However, by replacing 1/x by y/x which is conditional probability with
y < = x and both x, y in [0, 1] (except that x is not 0), the above
type of terms become tractable. For example:
3) 0 < = y/x - x = (y - x^2)/x < = 1 iff y > = x^2
Notice that y < = x is always assumed in Probable Influence/Causation,
so:
4) (y - x^2)/x < = 1 iff y - x^2 < = x iff x - y > = -x^2
and the latter (x - y > = -x^2) follows from y < = x.
Osher Doctorow
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| User: "Uter Hamelton" |
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| Title: Re: sqrt(1 - v^2/c^2) Relates to "Real" Laurent Series and Probable Influence 3: How Probability Patches Up Laurent Chaos |
06 Feb 2006 07:13:10 PM |
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"OsherD" <> wrote in message
news:1139270135.491000.80550@f14g2000cwb.googlegroups.com...
From Osher Doctorow
Let's look at the following from the previous parts of this thread:
1) f(x) = 1 + x + x^2 + ... + 1/x + 1/x^2 + ...
Readers can verify for themselves that if x is a probability or in fact
any real normalized quantity between 0 and 1
This is complete nonsence.
(not taken equal to 0),
then terms like x + 1/x, x^2 + 1/x^2, etc., or even such pairs in the
following function:
2) g(x) = 1 + x + x^2 + ... - 1/x - 1/x^2 - ...
do not remain tractable in the sense of for example 0 < = x - 1/x < = 1
or similarly with x and 1/x interchanged.
that is not allowed with series.
<snip rest of crap>
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| User: "OsherD" |
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| Title: Re: sqrt(1 - v^2/c^2) Relates to "Real" Laurent Series and Probable Influence 3: How Probability Patches Up Laurent Chaos |
06 Feb 2006 11:12:11 PM |
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From Osher Doctorow
Uter Hamelton of spamnot.com (location of a variety of Ingenious
Imitators who plague scientific forums with hostility) descends to
Mediocrity by his claim:
that is not allowed with series
snip rest of crap
The first line of his "un-gem" refers to a quotation from me which has
nothing to do with "what is or is not allowed with series". The
second line of his "un-gem" is a self-referential description from him.
Don't cry if I don't reply to you in future, Uter. Put it down to my
not replying to spam. Do be careful not to descend into your
"invalid.com" Mediocre personality, though.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: sqrt(1 - v^2/c^2) Relates to "Real" Laurent Series and Probable Influence 3: How Probability Patches Up Laurent Chaos |
06 Feb 2006 06:04:16 PM |
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From Osher Doctorow
In (4), I'm assuming that (y - x^2)/x is not negative from (3).
Osher Doctorow
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