Re: OT: is zero a mathematically positive number?

I'm sure you are right Petr,

The maths baffles me but I do recall once asking Scott Morris if a perfect
sphere actually touches anything when on a perfectly flat surface. Seemed to
me that theoretically it might not touch anything as the apex would be
infinitely small. Perhaps that would be an example of an infinitesimal
element? I have no idea.

I suppose an AD of zero might be a positive number if you want to route that
way :) Then again....
----- Original Message -----
From: "Petr Lapukhov" <petr_at_internetworkexpert.com>
To: "Marc La Porte" <marc.a.laporte_at_gmail.com>
Cc: "Cisco certification" <ccielab_at_groupstudy.com>
Sent: Monday, June 08, 2009 2:18 PM
Subject: 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.
> http://www.INE.com
> Toll Free: 877-224-8987
> Outside US: 775-826-4344
>
>
> 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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Received on Mon Jun 08 2009 - 20:52:35 ART