probability has holes seriously and please read before you make a comment!
eestath
power
case 1: a number has as its factor 2 : probability 1/2
case 2: a number has as its factor 2 and 3 : probability 1/
(2*3)
case 3: a number has as its factor 2 and 3 and 5 : probability 1/
(2*3*5)
...
if we cover every case probabilities add up to 1!
So 1=1/2+1/(2*3)+1/(2*3*5)+.....
are you ok? you get it? Is simple is elementary ok?
1=1+1/2+1/(2*3)+1/(2*3*5)+.....<1/2+1/4+1/8.....=1
So 1<1
plus 1+1/2+1/(2*3)+1/(2*3*5)+.... is irrational!
Arturo Magidin
> every integer greater than 2 is a product of primes to an integer
> power
>
> case 1: a number has as its factor 2 : probability 1/2
> case 2: a number has as its factor 2 and 3 : probability 1/
> (2*3)
> case 3: a number has as its factor 2 and 3 and 5 : probability 1/
> (2*3*5)
> ...
>
> if we cover every case probabilities add up to 1!
>
> So 1=1/2+1/(2*3)+1/(2*3*5)+.....
No; you are forgetting many cases. For example, where is the case of a
number that has 3 as a factor, but *not* 2? What about having 2 and 5,
but *not* 3?
In addition, the cases you are considering are *not* mutually
exclusive, so you cannot simply add the probabilities. For example, a
number that has both 2 and 3 as factors gets "counted" twice: once
when you consider the probability that is has 2 as a factor, and then
*again* when you consider that it has 2 *and* 3 as factors. So your
simple-minded addition of probabilibities does *not* equal the
probability that at least one of them occur; it is more.
> are you ok? you get it? Is simple is elementary ok?
I'm perfectly okay; your argument, alas, is terminally ill.
In fact, it was dead on arrival.
--
Arturo Magidin
g.r...@iit.cnr.it
> every integer greater than 2 is a product of primes to an integer
> power
>
> case 1: a number has as its factor 2 : probability 1/2
> case 2: a number has as its factor 2 and 3 : probability 1/(2*3)
These two cases are not independent, thus you cannot add the
probabilities.
It is like you are watching 3 cats, one red, one black and one white
and black,
and you say: I see a red cat, a cat with some white fur and two cats
with some black fur,
1+1+2 > 3.
This is one of the first things about probability that one learns
(I mean about not adding not-independent probs, not about cats).
Before announcing that "probability has holes" you should have the
humility of study it for a few months, imho, or people will assume
you are simply a troll.
g.
--
http://anagram.it : anagrams, alphametics,...
Tim Little
> case 1: a number has as its factor 2 : probability 1/2
> case 2: a number has as its factor 2 and 3 : probability 1/
> (2*3)
Case 0: a number does not have 2 as a factor
> case 3: a number has as its factor 2 and 3 and 5 : probability 1/
> (2*3*5)
> ...
>
> if we cover every case probabilities add up to 1!
>
> So 1=1/2+1/(2*3)+1/(2*3*5)+.....
Wow, you need to learn how to do basic probability. Firstly, you've
excluded all the odd numbers. Secondly, you've used a formula for
disjoint events for cases that are not disjoint - in fact, about as
non-disjoint as you can get.
Once you include the odd numbers and cease using a formula for
disjoint probabilities, you get the correct (but trivial)
1 = 1/2 + 1/2.
- Tim
Ray Vickson
> On Dec 1, 6:11 pm, eestath <stathopoulo...@gmail.com> wrote:
>
> > every integer greater than 2 is a product of primes to an integer
> > power
>
> > case 1: a number has as its factor 2 : probability 1/2
> > case 2: a number has as its factor 2 and 3 : probability 1/(2*3)
>
> These two cases are not independent, thus you cannot add the
> probabilities.
Actually, they are not _mutually exclusive_, and that is why they
cannot be added. *Independence* has nothing to do with the issue
(although, of course, they are also not independent). However, maybe
you are using the word "independent" in a different way from the
standard English probabilistic usage.
> It is like you are watching 3 cats, one red, one black and one white
> and black,
> and you say: I see a red cat, a cat with some white fur and two cats
> with some black fur,
> 1+1+2 > 3.
>
> This is one of the first things about probability that one learns
> (I mean about not adding not-independent probs, not about cats).
> Before announcing that "probability has holes" you should have the
> humility of study it for a few months, imho, or people will assume
> you are simply a troll.
I agree with you on this. The fellow criticizes probability without
exhibiting the most basic understanding.
R.G. Vickson
>
> g.
> --http://anagram.it: anagrams, alphametics,...
Dik T. Winter
> every integer greater than 2 is a product of primes to an integer
> power
>
> case 1: a number has as its factor 2 : probability 1/2
> case 2: a number has as its factor 2 and 3 : probability 1/
> (2*3)
> case 3: a number has as its factor 2 and 3 and 5 : probability 1/
> (2*3*5)
> ...
>
> if we cover every case probabilities add up to 1!
You do not cover every case. Where is the case that a number has 3 as
a factor but not 2?
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/