Re: Cantorian pseudomathematics
cbrown@xxxxxxxxxxxxxxxxx wrote:
You are falling prey to exactly what Jaynes is warning about - you are
mixing up properties from "after" the limit is taken with properties
from "before" the limit is taken.
No. It's the other way around: _you_ are making this mistake.
The fact that each P_n is a uniform distribution is not relevant to
whether or not P is a uniform distribution.
Limits come from physical experience that, in the real world, everything
is just finite. Hence the fact that _each_ P_n is a uniform distribution
already _proves_ that P is a uniform distribution as well, with P(x) = 0
infinitesimally small (instead of absolutely zero, speaking in TO terms)
and this explains why it still sums up to unity. There is no point where
all of a sudden finitary properties would cease to exist, because all of
infinity should be approached through the finite, by limits.
Han de Bruijn
.
Relevant Pages
- Re: Cantorian pseudomathematics
... >> whether or not P is a uniform distribution. ... > infinity should be approached through the finite, ... of a sudden finitary properties would cease to exist". ...
(sci.math) - Re: Calculus XOR Probability
... Suppose that we agree there is a uniform distribution on N. Suppose ... and then take the limit as n goes to infinity, ... the expected value of selecting a finite ... probability on N and for each n, the probability that n is selected is ...
(sci.math) - Re: SF: Areas of confusion, infinity
... >> And I suggest you sit down with a book on probability ... For integers, you have to look at the uniform distribution on {1, 2, ... N} and take limits as N goes to infinity. ... In my defense, it was late at night, for a day which was way too long. ...
(sci.math) |
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