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From: David Barrett-Lennard <dbl.domain.name.hidden>

Date: Wed, 21 Jan 2004 13:51:56 +0800

Kory said...

*>
*

*> At 1/21/04, David Barrett-Lennard wrote:
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*> >This allows us to say the probability that an integer is even is 0.5,
*

or

*> >the probability that an integer is a perfect square is 0.
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*>
*

*> But can't you use this same logic to show that the cardinality of the
*

even

*> integers is half that of the cardinality of the total set of integers?
*

Or

*> to show that there are twice as many odd integers as there are
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integers

*> evenly divisible by four? In other words, how can we talk about
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*> probability
*

*> without implicitly talking about the cardinality of a subset relative
*

to

*> the cardinality of one of its supersets?
*

Saying that the probability that a given integer is even is 0.5 seems

intuitively to me and can be made precise (see my last post). Clearly

there is a weak relationship between cardinality and probability

measures. Why does that matter?

Why do you assume infinity / infinity = 1 , when the two infinities have

the same cardinality? Division is only well defined on finite numbers.

*>
*

*> I'm not denying that your procedure "works", in the sense of actually
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*> generating some number that a sequence of probabilities converges to.
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The

*> question is, what does this number actually mean? I'm suspicious of
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the

*> idea that the resulting number actually represents the probability
*

we're

*> looking for. Indeed, what possible sense can it make to say that the
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*> probability that an integer is a perfect square is *zero*?
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*>
*

*> -- Kory
*

For me, there *is* an intuitive reason why the probability that an

integer is a perfect square is zero. It simply relates to the fact that

the squares become ever more sparse, and in the limit they become so

sparse that the chance of finding a perfect square approaches zero.

- David

Received on Wed Jan 21 2004 - 00:53:34 PST

Date: Wed, 21 Jan 2004 13:51:56 +0800

Kory said...

or

even

Or

integers

to

Saying that the probability that a given integer is even is 0.5 seems

intuitively to me and can be made precise (see my last post). Clearly

there is a weak relationship between cardinality and probability

measures. Why does that matter?

Why do you assume infinity / infinity = 1 , when the two infinities have

the same cardinality? Division is only well defined on finite numbers.

The

the

we're

For me, there *is* an intuitive reason why the probability that an

integer is a perfect square is zero. It simply relates to the fact that

the squares become ever more sparse, and in the limit they become so

sparse that the chance of finding a perfect square approaches zero.

- David

Received on Wed Jan 21 2004 - 00:53:34 PST

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