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Topic: the probability theory has holes!
Replies: 31   Last Post: Dec 3, 2009 7:55 PM

 Messages: [ Previous | Next ]
 Jim Burns Posts: 1,200 Registered: 12/6/04
Re: the probability theory has holes!
Posted: Dec 1, 2009 2:39 PM

eestath wrote:
> What i had in mind is Eratosthenes Sieve:
>
> for 2: we exlude the first 1/2
>
> for 3:then we exclude 1/3 but half of them
> have factor 2 so we actually exclude 1/2*3
>
> for 5:then we exclude 1/5 but half of them
> have factor 2 and 1/3 have factor 3 so we
> actually exclude 1/2*3*5

Right here is the problem: "1/3 have factor 3".
What you want is "2/3 DO NOT have factor 3".
The 1/3 with factor 3 have already been excluded.
Another 1/5 of the fraction ( 1 - 1/2 )*( 1 - 1/3 )
that do not have either 2 or 3 as a factor is
what you want to exclude for the next step.

And ( 1 - 1/2 )*( 1 - 1/3 )*1/5 = 1/15.

> So the Series is 1=1/2 + 1/(2*3) + 1/(2*3*5)+....

Another way to look at this:

(fraction not div by 2)*(fraction not div by 3)*
(fraction not div by 5)* ...
= (fraction not div by any prime)

which means

( 1 - 1/2 )*( 1 - 1/3 )*( 1 - 1/5 )* ... = 0

If you are not already familiar with the Riemann
zeta function, then I think you would find this
very interesting:
http://en.wikipedia.org/wiki/Riemann_zeta_function#Euler_product_formula

> You answer but you are actually wrong!!!!!!!!!!

One of the more pleasant surprises on the Internet
is finding someone who will admit that they were wrong
(when they finally understand that they were wrong).

I wonder, are you going to surprise us?

Jim Burns

Date Subject Author
12/1/09 eestath
12/1/09 Kook Spotter
12/1/09 Bart Goddard
12/1/09 eestath
12/1/09 Bart Goddard
12/1/09 eestath
12/1/09 Jim Burns
12/1/09 Bart Goddard
12/1/09 Pubkeybreaker
12/1/09 Bart Goddard
12/1/09 Gerry Myerson
12/1/09 Bart Goddard
12/1/09 eestath
12/2/09 Dik T. Winter
12/2/09 Bart Goddard
12/2/09 eestath
12/2/09 Bart Goddard
12/2/09 eestath
12/3/09 Bart Goddard
12/2/09 eestath
12/1/09 Nick
12/2/09 Dik T. Winter
12/3/09 ostap_bender_1900@hotmail.com
12/3/09 Jim Burns
12/3/09 FredJeffries@gmail.com
12/2/09 Dik T. Winter
12/1/09 Henry
12/1/09 eestath
12/1/09 eestath
12/2/09 Richard Tobin
12/1/09 eestath
12/3/09 ostap_bender_1900@hotmail.com