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

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Jim Burns

Posts: 1,200
Registered: 12/6/04
Re: the probability theory has holes!
Posted: Dec 1, 2009 2:39 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
Read the probability theory has holes!
eestath
12/1/09
Read Re: the probability theory has holes!
Kook Spotter
12/1/09
Read Re: the probability theory has holes!
Bart Goddard
12/1/09
Read Re: the probability theory has holes!
eestath
12/1/09
Read Re: the probability theory has holes!
Bart Goddard
12/1/09
Read Re: the probability theory has holes!
eestath
12/1/09
Read Re: the probability theory has holes!
Jim Burns
12/1/09
Read Re: the probability theory has holes!
Bart Goddard
12/1/09
Read Re: the probability theory has holes!
Pubkeybreaker
12/1/09
Read Re: the probability theory has holes!
Bart Goddard
12/1/09
Read Re: the probability theory has holes!
Gerry Myerson
12/1/09
Read Re: the probability theory has holes!
Bart Goddard
12/1/09
Read Re: the probability theory has holes!
eestath
12/2/09
Read Re: the probability theory has holes!
Dik T. Winter
12/2/09
Read Re: the probability theory has holes!
Bart Goddard
12/2/09
Read Re: the probability theory has holes!
eestath
12/2/09
Read Re: the probability theory has holes!
Bart Goddard
12/2/09
Read Re: the probability theory has holes!
eestath
12/3/09
Read Re: the probability theory has holes!
Bart Goddard
12/2/09
Read Re: the probability theory has holes!
eestath
12/1/09
Read Re: the probability theory has holes!
Nick
12/2/09
Read Re: the probability theory has holes!
Dik T. Winter
12/3/09
Read Re: the probability theory has holes!
ostap_bender_1900@hotmail.com
12/3/09
Read Re: the probability theory has holes!
Jim Burns
12/3/09
Read Re: the probability theory has holes!
FredJeffries@gmail.com
12/2/09
Read Re: the probability theory has holes!
Dik T. Winter
12/1/09
Read Re: the probability theory has holes!
Henry
12/1/09
Read Re: the probability theory has holes!
eestath
12/1/09
Read Re: the probability theory has holes!
eestath
12/2/09
Read Re: the probability theory has holes!
Richard Tobin
12/1/09
Read Re: the probability theory has holes!
eestath
12/3/09
Read Re: the probability theory has holes!
ostap_bender_1900@hotmail.com

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