Re: OT: is zero a mathematically positive number?

Marc,

provided that you have enough time and proper definitions you can
prove almost anything ;)

As for the positive numbers, it depenWs what you call "positive". If
you start with the natural
numbers and call those positive, than you can add zero element,
turning the set into a
semigroup. Zero plays an important role of neutral element, such that
"a+0=a" for any natural
number. At this point, you can also "call" the zero a positive number
as well. However, calling
the natural numbers positive makes little sense, as they have no
opposing elements. They're
just natural :)

If you want to add negative numbers to the game, the resulting set
{...-2, -1, 0, 1, 2 ...} will turn into
an abelian group, with every element having an "inverse" element with
respect to the addition operation.
The neutral element, aka zero plays important role here, in defining
the inverse element. Specifically,
the inverse of "a" is "-a" such that "a + (-a)=0". For every element,
there is an unique inverse element
defined in such way. However, "-0=0" so zero is the inverse of itself.
Though that makes little sense
and does not produce any results you can call zero as both positive
and negative number at the same
time :)

Essentially, my point is that it makes no sense to call zero either
positive or negative, because "positive" and
"negative" are DISTINGUISHED via the zero element. Of course, you can
start a metaphisical discussion
whether zero actually exists, and whether zero is DEFINED via the
positive/negative elements such that
0 = def = a+(-a) [neutrality = good + evil], which is easier to
understand from the perspective of the common
sense. You can continue like this eternally, without producing any
fruitful results though :)

PS
However, if you would look into the area of Non-Standard Analysis, you
will discover the hyperreal numbers and
special "infinitesimal" elements, which are smaller than any real
number, but yet not zero. Now those could be
thought as "almost zero" and could be either positive or negative, if you want.

Further reading:

http://en.wikipedia.org/wiki/Hyperreal_number
http://en.wikipedia.org/wiki/Non-standard_analysis

-- 
Petr Lapukhov, petr_at_INE.com
CCIE #16379 (R&S/Security/SP/Voice)
Internetwork Expert, Inc.
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2009/6/8 Marc La Porte <marc.a.laporte_at_gmail.com>:
> Hi all,
>
> Totally OT, but good fun I guess... just to get out mind off things ;-)
>
> I had a math teacher who was able to mathematically proof that 0 (zero) is a
> positive number (meaning not neutral or negative). Obviously I cannot
> reproduce that, but...
>
> So, for all the math wizards out there (Petr?), amaze me with formulas ;-)
>
> Cheers,
> Marc
>
>
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