Re: Cantorian pseudomathematics

Tony Orlow <aeo6@xxxxxxxxxxx> writes:

> Jesse F. Hughes said:
>> Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:
>>
>> > OK. Fixing first things first: P(a | n) , meaning: the probability that
>> > a fixed natural number a divides an arbitrary natural number n .
>>
>> Great. But I still haven't a clue what that might mean.
>>
>> What does "a divides an arbitrary natural n" *mean*? What sort of
>> event is that and how am I supposed to understand the probability of
>> this event?
>>
>
> Oh, come on Jesse. Han is talking about the probability that a randomly chosen
> natural n is divisible by any given fixed natural a. If you consider an initial
> segment of the naturals, and the limit of this probability as that initial
> segment approaches oo, the probability approaches 1/a, as Han states. You put
> all the natural numbers on balls in your vase and pick one at random. The
> chances that it is an integral multiple of your pre-chosen a is 1/a. As you
> continue to pick random balls, the ratio of them that are integral multiples of
> a will approach 1/a. You get this. It is obvious. Why play dumb?

I understand the probability a divides n when we have a uniform
distribution on initial segments of N (although my terminology may be
off).

It seems you're right that the limit of these values is 1/a.

But there is no uniform distribution on N, so I don't see what Han
means there and your explanation doesn't clarify it.

--
"I arrest anybody I think needs arresting, Mr. Carter, and I'm not in
the habit of explaining why."
"There's a law about that ---"
"You're in Dodge, Mr. Carter." -- Gunsmoke radio show / John Ashcroft
.

Relevant Pages

  • Re: Cantorian pseudomathematics
    ... >>probability that an arbitrary natural is divisible by a fixed natural ... > But now consider the sequence with each A_n consisting of the n lowest ... Perhaps Han should actually read Jaynes' work. ... on the naturals is possible). ...
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  • Re: Probability in an infinite sample space
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  • Re: Calculus XOR Probability
    ... Han de Bruijn wrote: ... then clearly the probability that Han picks a number ... Not if it is uniform. ... as a uniform distribution on the naturals. ...
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  • Re: Cantorian pseudomathematics
    ... > Oh, come on Jesse. ... Han is talking about the probability that a randomly ... > segment of the naturals, and the limit of this probability as that initial ... their partial sums, and all those partial sums are 0's). ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... If you consider an initial segment of the naturals, ... >>> limit of this probability as that initial segment approaches oo, ... >> But there is no uniform distribution on N, so I don't see what Han ...
    (sci.math)
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