Re: Positive random number

Johannes Bauer wrote:
James Kuyper schrieb:
The point is: It's a question a definition. Your answer is much too
dogmatic.
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.

The sets he refers to are often called the "natural numbers", and there *is* difference in the mathematical community as to whether they should be defined to start at 0 or 1. But nobody ever asks the question "Is zero natural?" because it's all a matter of definition, and so long as you're clear which definition you're using, or the result is the same regardless, it doesn't matter.

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

Really? At some point you just have to say "that's what I think everybody is doing" because all you're doing is agreeing on a common language. Which side of the road do you drive on? The same side everyone else does. There is no reason it should be left or right - it just is.

I've never met anyone who considered zero to be positive. Therefore, I do not consider zero to be positive. If I want to say "positive or zero" I'd generally say "nonnegative".

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" :-)

Only when the "all" is an infinite set. Which the set of mathemeticians isn't.

Phil
.

Relevant Pages

  • Re: Positive random number
    ... state that the positive Integers start at 1, ... states they start at zero. ... Dogmatism are stupid, there ... Then again - in a trueley mathematic sense - almost all mathematicians ...
    (comp.lang.c)
  • Re: Positive random number
    ... state that the positive Integers start at 1, ... states they start at zero. ... there are also good reasons why it shouldn't. ... That definition only applies if the set of all mathematicians is infinite. ...
    (comp.lang.c)
  • Re: Interesting math
    ... that allow zero to be both. ... appropriate and accepted words around mathematicians, ... "Listen you two, no matter what number you divide by zero, ... Multiple by an odd number. ...
    (alt.usage.english)
  • Re: OT: must see TV : "America at a Crossroads" | PBS Frontline Series | 11 parts airing all this we
    ... Islam has not produced many notable guitar players. ... European lutes and guitars. ... we received our now indispensable zero digit from ... the Arabs, meaning medieval period Islamic mathematicians, who I do suspect ...
    (alt.guitar.beginner)
  • Re: Are Polynomials really C ^Infinity (Smooth) Differentiable
    ... I am stuck on the first one by a yokel from rural Lincolnshire called Isaac ... function zero is the constant function zero is logically equivalent to ... "Claytons" for every imaginable concept. ... Why does one always have to drag mathematicians kicking and screaming to the ...
    (sci.math)