On Thu, 27 Jan 2005 07:36:23 -0500, Steve Decker
wrote:

Mark & Juanita wrote:
On 26 Jan 2005 11:02:38 -0800, "Gus" wrote:

.... snip

I don't agree.

You could say "empirical evidence suggests it won't happen" or
"experience shows us it won't happen".

Stating a probability as exactly identical to zero is inherently incorrect.

Alright, stepping into the realm of pedantry: From the axiomatic
definitions of probabilty theory (Papoullis, Probability, Random Variables,
and Stochastic Processes),
"The probability of an event a is a number P(a) assigned to this event.
This number obeys the following three postulates:
I. P(a) is positive: P(a) = 0
II The probability of the certain event equals 1: P(S) = 1
III. If a and b are mutually exclusive, then: P(a + b) = P(a) + P(b)"
[Version I have at home is McGraw-Hill 1965 version, page 7]

Note: from (I), P(a) = 0 is a valid probability. For the examples
stated, "a bucket of water bursting into flame", or "a unit of helium
bursting into flame", or "conservation of mass in a chemical reaction
holds" the probability of these events can be stated to be zero. Unless
you are going to imply that the laws of physics and chemistry are muteable
--- if that is the case, then the whole fundamental fabric of science and
technology is essentially destroyed. i.e., there is no, zero, zilch, zip,
nada chance that helium will burn (i.e. oxidize) in an chemical reaction --
helium is an inert gas, it cannot combine with oxygen, it *will not* burn.
This is more than "empirical evidence", it is a fundamental element of the
chemical nature and properties of elements. If we can say that there is
some non-zero probability that elements will behave willy-nilly contrary to
their fundamental chemical and nuclear properties, we are wasting our time
with science and technology. Thus, in these cases, one can indicate that
the probability of those events occuring P(a) = 0, and in addition, the
probablity of those events occuring are the impossible event. Further,
from II, it is also possible to have a certain event, for which the
probability = 1.

It is also important to note that one must distinguish between the
impossible event, and those events with probability = 0. For example, the
probability P(t = t1) = 0 may be true, but not necessarily an impossible
event. Same is true that even though the probability of an event = 1,
this is not necessarily the certain event. However, for the impossible
event P(a) = 0, and for the certain event P(a) = 1. But this is a side
detour to the original statement. The fact is that it is *not* inherently
incorrect to state that a probability is exactly identical to zero.





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The absence of accidents does not mean the presence of safety

Army General Richard Cody

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