Re: Zero digits in powers

vkarlamov@xxxxxxxxx wrote:
> Jean-Claude Arbaut wrote:
> > Le 19/06/2005 02:37, dans
> > 1119141430.131756.11410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx,
> > « vkarlamov@xxxxxxxxx » <vkarlamov@xxxxxxxxx> a écrit :
> >
> > > Yes, Jean-Claude. When probabilists talk about "sigma algebra on a
> > > discrete set S", they mean THE sigma algebra which allows you to access
> > > each idividual singleton. I assure you therre is only one.
> >
> > > If two elemets of a set were inseparable,
> > > they would have been combined into one super-element. Look it up in
> > > elementary probability texts.
> >
> > Completely wrong, _yet again_. You have many sigma algebras on a discrete
> > set, even infinitely many if the set is infinite, and there is *no* reason
> > to take particularly one, and call it THE sigma algebra.
> >
>
> I assure you that there is only one sigma algebra that probabilists use
> when talking about a discrete set S. This is the sigma algera which is
> equal to the powerset of S.
>
> If you disagree, I challenge you to provide an example of any other
> sigma algebra that probabilists use when talking about discrete random
> variables.
>
> You fail to understand what I keep on repeating:
>
> >
> > > If two elemets of a set were inseparable,
> > > they would have been combined into one super-element.
> >
>
> If you don't understand this, I give up.
>
> > > You find that surprising? If two elemets of a set were inseparable,
> > > they would have been combined into one super-element. Look it up in
> > > elementary probability texts.
> >
> > You evidently don't know the definition for a sigma algebra.
> > It's not a matter of separable elements here, were are talking
> > about subsets. Do you know what a subset is ?
> >
> > When you have learnt what an integer is, you should have a look at some set
> > theory textbook, and only then, at your peak, find some measure theory
> > textbook. Hopefully you'll learn what you're talking about.
> >
>
> Excuse me but I find it highly unproductive to argue with people who
> seriously concern themselves with the issue of sigma algebras on a
> discrete set.
>
> I assure you that this subject is much more trivial to normal people
> than you think.
>

Look, Jean-Claude. I don't want to turn yourself away from the study of
probability. I just find it that given your unfamiliarity with the
basics of probability theory, your categorical and condescending tone
is highly disturbing and shows that you are not here to learn or solve
problems but to prove your own self-worth by insulting other people.

But let me leave it aside. I took my time to find a good explanation
for you of what probabilists mean when talking about the sigma algebra
on a discrete space.

So I looked - where else? - at Winkpedia's explanation of probability
theory for beginners:

http://en.wikipedia.org/wiki/Probability_theory

"O is a non-empty set, sometimes called the "sample space"

F is a sigma-algebra of subsets of O whose members are called
"events".

P is a probability measure on F, i.e., a measure such that P(O) = 1.

With O denumerable we can define F := powerset(O) which is trivially
a sigma-algebra and the biggest one we can create using O. In a
discrete space we can therefore omit F and just write (O,P) to define
it. "

Does this explanation make more sense to you than my attempts at
expalining it to you?

When we talk about dicrete spaces, we omit listing the sigma algebra F
because we always mean that F is the powerset of O.

My advice to you: if you want to learn something, try not to insult
those who take their time to teach you and to give suggestions as to
how to explain the hypothesis that you want to prove.

.

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