I can continue this discussion forever.
The interesting thing is that zero in common sense means nothing, and
"nothing" but it's definition does not exist. Thus in math they
usually tend to refer to it as a "neutral element". From phylosophical
standpoint you can treat "zero" apophatically (negatively) by telling
what zero is NOT. From this standpoint it's neither positive or
negative, nor anything else.
You could also treat zero "dialectially" as a "unity" of both
"negative" and "positive" elements, since 0=1+(-1)+2+(-2)+... This
point of view treats zero as a sum of all "potentials" compensating
each other and has an interesting illustration as physical vacua. As
you know, in quantum mechanics there is no "nothing" - there are
special "zero fluctuatios" which produce pairs of
particles/anti-particles which cancel each other. Other interesting
model of "nothing" available for years is Dirac sea resembles the same
idea. The concept "something out of nothing" is common in many
creationist concepts, which are mostly religious.
Lastly, zero could be viewed as opposite to infinity, e.g. 0=1/inf and
we may think that there are positive and negative infinities leading
to positive and negative "zeroes". This is how they introduce
infinitesimal elements to hyperrial numbers. However, firstly this
leads us to the smallest quantities possible but not the zero. Plus,
in it's "naive" form this interpretation is problematic, as it
replaces one metaphysical concept (nothing) with another (infinity).
There is no consistent theory of inifinity yet (well, maybe with
exception to the success of non-standard analysis) and probably will
never be. Just recall all the paradoxes of the actual infinity.
Besides, right now there is known a whole hierarchy of infinities (N,
Aleph1, and so on if you accept Kanthors theory) which makes it
difficult to select the one opposing the single zero.
As for your example, Jonny, here is a problem. The apex surely has the
"measure" of zero (e.g. Lesbegue measure) but still the cardinal
number of the apex set (roughly, the number of the elements in set) is
non-zero. This is to illustrate the different concepts of "quantity"
available in mathematics :)
-- Petr Lapukhov, petr_at_INE.com CCIE #16379 (R&S/Security/SP/Voice) Internetwork Expert, Inc. http://www.INE.com Toll Free: 877-224-8987 Outside US: 775-826-4344 2009/6/9 Jonny English <redkidneybeans_at_gmail.com>: > 0 can be a positive number only when its followed by a $1. The more 0's the > more positive the 0 becomes...... > > i'm going back to playing at ogame.org now.... > > On Mon, Jun 8, 2009 at 11:16 PM, Marc La Porte <marc.a.laporte_at_gmail.com>wrote: > >> 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 >> >> >> Blogs and organic groups at http://www.ccie.net >> >> _______________________________________________________________________ >> Subscription information may be found at: >> http://www.groupstudy.com/list/CCIELab.html > > > Blogs and organic groups at http://www.ccie.net > > _______________________________________________________________________ > Subscription information may be found at: > http://www.groupstudy.com/list/CCIELab.html Blogs and organic groups at http://www.ccie.netReceived on Tue Jun 09 2009 - 17:05:04 ART
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