# Re: Programming is the Engineering Discipline of the Science that is Mathematics

Date: 11 Jun 2006 06:57:13 -0700

Message-ID: <1150034233.126373.180260_at_y43g2000cwc.googlegroups.com>

Bob Badour wrote:

*> vc wrote:
**>
**> > Keith H Duggar wrote:
**> > [Irrelevant stuff skipped]
**> >
*

> > Assuming Bayesian treatment (which was not specified originally, mind

*> > you), the derivation is still meaningless. Let's try some argument
**> > from authority:
**>
**> [snip]
**>
**> Your whole dismissal, as I recall, depends on your observation:
**>
**> > P(B|A) def P(A and B)/P(A)
*

It does in the frequentist probability interpretation, yes.

*> >
*

> > the requirement for such definition being that P(A) <>0, naturally.

*>
**> Keith used the equivalent definition:
*

"

In our formal probability symbols (those with a capital P)

Please see the book for details.

*>
*

> P(A and B) = P(B|A)P(A), which places no requirements on P(A) because

*> one does not divide by P(A).
*

*>
*

> In the case of P(A) = 0, P(A and B) = 0 and P(B|A) is indeterminate,

*> which is to say, we don't care what it's value might be and it could be
**> any real number; although, as a probability, we restrict it to real
**> numbers in the range [0...1].
**>
**> Thus, both of Keith's proofs were entirely valid because he neither
**> inferred nor concluded using the indeterminate P(B|A). He made the valid
**> conclusion that P(A and B) = 0 when P(A) = 0.
*

Received on Sun Jun 11 2006 - 15:57:13 CEST