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

From: vc <boston103_at_hotmail.com>
Date: 12 Jun 2006 08:10:40 -0700

[...]
> >>Keith already specified the argument applies to a limit.
> >
> > And this is an incorrect answer because the question was not what the
> > limit of P(A and B) is but what exact value of P(A and B) given P(A) =
> > 0 (or P(B)=0). There is an easy way to derive P(false) from Cox's
> > axioms directly or from the sum/product rules.
>
> The exact value of the sum of 1/2^i for i in [0..infinity] is 2. The
> exact value of the sum of 3 times 10^(-k) for k in [1..infinity] is 1/3.
> The exact value of P(A and B) is 0 give P(A) = 0 or P(B) = 0.
>
> One uses limits to ascertain the truth of all three of the above statements.

I've replied to the limit attempt elsewhere.

>
>
> >>>>P(A) = 1
> >>>>P(A or B) = P(~(~A and ~B))
> >>>>P(A or B) = 1 - P(~A and ~B)
> >>>>P(A or B) = 1 - P(~B|~A)P(~A)
> >>>
> >>>
> >>>Since P(~A) equals zero, the above statement does not make sense.
> >>
> >>But Keith stated "in the limit of". Thus, one could read the first line
> >>of what he wrote as
> >>
> >>lim P(A) as P(A) -> 1
> >
> > 'Limit' is not just a magical word, "hey, presto". One has to show
> > that such limit indeed exists, in what sense it exists, and even then
> > it would be a useless exercise because there is a simple and direct