Re: Probability of picking a positive rational number at random

On 2008-03-15, Ross A. Finlayson <raf@xxxxxxxxxxxxxxx> wrote:
Maybe that's a misperception. Maybe it just is so that there's an
infinitesimal iota, greatest among infinitesimals

I'm sure such a thing could be defined, but I bet you wouldn't be able
to do arithmetic with it. Is iota+iota infinitesimal?


The notion is basically about using uniformity and symmetry as first
principles in describing densities for probability density
functions, instead of standard measure theoretic ones.

Good luck with that. The rest of us like being able to prove things
like P(A or B) = P(A) + P(A but not B).


Now, that's rather unstructured but those are actually technical
words with specific meanings.

There's a word for sentences that use technical words with specific
meanings in ways that contradict those meanings: technobabble.


In general, given a well- ordering of R, there is absolutely no
idea, no algorithm to conclude, what ordinal o maps to each element
of r.

You already went way beyond the bounds of algorithms in the first
step. But just for laughs, let's see how we get from our real number
to a natural number.


So, by sampling a real (and figuring the order type of c was the same
as the order type of the set of distributions, where having it not be
is funny)

Fortunately the cardinality of distributions over N is c, so it is at
least *possible* to have the same order type. Though the two
well-orderings are completely unnecessary: any bijection will do.
Requiring well-ordering just obfuscates what's going on.


Then, using the distribution that happens to be marked by that
ordinal in a "random" well-ordering of the distributions of the
naturals

So now you're going from a probability distribution over [0,1] defined
by Lebesgue measure to a completely undefined probability distribution
over the set of all well-orderings of distributions of natural
numbers? How do you know that one with the properties you want even
exists?


- Tim
.

Relevant Pages

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  • Re: Probability of picking a positive rational number at random
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