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Re: Primes Are Fundamentally Additive/Subtractive, Not Multiplicative/Divisive
Posted:
Mar 8, 2009 8:30 PM
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On Sun, 8 Mar 2009, Osher Doctorow Ph.D. wrote:
> Date: Sun, 8 Mar 2009 19:11:14 -0400
> From: Osher Doctorow Ph.D. <mdoctorow@ca.rr.com>
> To: MATH-HISTORY-LIST@ENTERPRISE.MAA.ORG
> Subject: Re: Primes Are Fundamentally Additive/Subtractive,
> Not Multiplicative/Divisive
>
> To understand what is actually happening, arguably, recall that the natural logarithm is the integral from 1 to x of dt/t:
>
> 1) ln(x) = I[1/t)]dt, where I...dt is the integral from 1 to x with respect to t.
>
> Since t > 1, the argument of this integral is a number between 0 (noninclusive) and 1, quite similar and in a sense isomorphic to y/x in Conditional Probability where y is P(AB) and x is P(A) not equal to 0, or in its variant y = P(B) and x = P(A) with y < = x. So we have division fundamentally involved from an integral viewpoint in the natural logarithm and thus in all logarithms on the real numbers.
Eh? That definition for ln(x) is also valid if 0 < x <= 1 if you're
restricting yourself to real variables, and x having any finite
complex value except 0 is OK if not. Of course the infinitely many
possibilities for the path of integration lead to the infinitely many
values of the complex logarithm.
-- John Harper, School of Mathematics Statistics and Operations Research
Victoria University, PO Box 600, Wellington 6140, New Zealand
e-mail john.harper@vuw.ac.nz phone (+64)(4)463 6780 fax (+64)(4)463 5045
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