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From: Kory Heath <kory.heath.domain.name.hidden>

Date: Tue, 20 Jan 2004 23:01:14 -0500

At 1/21/04, David Barrett-Lennard wrote:

*>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.
*

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 integers

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

without implicitly talking about the cardinality of a subset relative to

the cardinality of one of its supersets?

I'm not denying that your procedure "works", in the sense of actually

generating some number that a sequence of probabilities converges to. The

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

probability that an integer is a perfect square is *zero*?

-- Kory

Received on Tue Jan 20 2004 - 23:04:34 PST

Date: Tue, 20 Jan 2004 23:01:14 -0500

At 1/21/04, David Barrett-Lennard wrote:

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 integers

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

without implicitly talking about the cardinality of a subset relative to

the cardinality of one of its supersets?

I'm not denying that your procedure "works", in the sense of actually

generating some number that a sequence of probabilities converges to. The

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

probability that an integer is a perfect square is *zero*?

-- Kory

Received on Tue Jan 20 2004 - 23:04:34 PST

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