Re: Positive random number

Johannes Bauer wrote:
James Kuyper schrieb:
...
There might be obscure discussions among mathematicians in which such a
definition is used, but I believe that in almost all contexts, the
overwhelming majority of the mathematically literate population consider
0 to be neither positive nor negative. I don't think it's excessively
dogmatic to insist on interpreting it that way in this context.

They are not obscure. Consider the work of Peano
(http://en.wikipedia.org/wiki/Giuseppe_Peano) which in his older works
state that the positive Integers start at 1, while at a later release
(Peano.G.: Formulaire de mathématiques 5 Bde. Turin, Bocca 1895-1908) he
states they start at zero.

I think that counts as obscure, as far a non-mathematicians are
concerned.

It is *not* something that "almost all mathematicians" agree about, it
is primarily a question of usefulness. Both variants are common, it even

Again, I don't believe that both are common outside of mathematics
departments. Among users of mathematics, rather than producers, the
idea that 0 might count as positive is pretty much unheard of.

depends which university you're attending. Dogmatism are stupid, there
are good reasons why zero should be considered a positive integer and
there are also good reasons why it shouldn't. It's important to base
your decision on reason, not on "that's what I think everybody is doing".

My reason says that if the definition of positive is changed to ">=0",
I will still need a term for ">0", and it will have to be a new term
distinguishable from "positive". If you want to have a new name for
what I've always heard referred to as "non-negative", why not give it
a name that has no prior contradictory associations? I personally have
never use "positive" in a context where the new proposed definition
would be an acceptable replacement, and I don't think I've ever seen
it used in such a context either.

Then again - in a trueley mathematic sense - almost all mathematicians
consider zero to be nonpositive. Almost all of them agree that zero is a
positive number, too. This is because "almost" in a mathematic sense
means "except for a finite number of exceptions" :-)

I'm familiar with this meaning for "almost all", and I think you've
misapplied it. I don't remember the precise definition, but I believe
that the entire set has to be infinitely bigger than the set of
exceptions. For instance, a function that is 0 for all real values,
except that it is 1 for all integers, then that function is 0 "almost
everywhere". I don't believe that the set of mathematicians is
infinitely larger than the subset who hold those opinions.
.

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