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Topic: Probabilities not in [0,1]?
Replies: 8   Last Post: Mar 12, 2013 10:56 PM

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 FredJeffries@gmail.com Posts: 1,845 Registered: 11/29/07
Re: Probabilities not in [0,1]?
Posted: Mar 12, 2013 7:50 PM

On Mar 10, 11:36 am, "Peter Percival" <peterxperci...@hotmail.com>
wrote:
> Is there a theory of probability in which probabilities do not lie in the
> real interval [0,1]?

http://arxiv.org/abs/0912.4767

> More specifically, is there one in which the "space"
> of probabilities may have points x, y, z with x < y, x < z but y and z not
> necessarily comparable?

Not sure what you mean by "not necessarily comparable", but in the
system of smooth infinitesimal analysis we have that if y and z differ
by an infinitesimal then the order relation does not satisfy the
trichotomy law:
(y < z) OR (y < z) OR (y = z)

http://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis
http://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf