Re: Probability of picking a positive rational number at random

On Mon, 17 Mar 2008 08:13:57 -0700 (PDT), S_Paske@xxxxxxxxxxx wrote:

The question is if given a 'random rational r' in this way,

In _what_ way?

what is the probability that it is less than 1? How about < 2?

The rationals are a countable set, so there is no uniform distribution
on the rationals. There _are_ distributions on the rationals,
uncountably many of them. Specifying such a distribution is equivalent
to assigning a probability to _each_ rational (such that the
probabilities are nonnegative and the sum is 1).

Once you specify such a distribution, you can, in principle, answer
probability questions such as the ones you are asking, or, if a closed
form is too difficult, you can always do a simulation to approximate
the desired probabilities. But the choice of such a distribution is
_arbitrary_ (just so long as its a valid distribution), so none of
your questions has an answer which qualifies as universal. The answers
will _depend_ on the choice of distribution.

This has been spelled out to you many times. Why do you still not get
it?

quasi
.

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