Johannes said:
Well at exactly *that* problem (zero positive or not) there's *no*
"common opinion". Impressively demonstrated by the fact that even Peano
himself (Peano Axioms! A *great* mathematician in the field of integer
arithmetic) had a reason to change his opinion.
Individual mathematicians often differ from orthodoxy. But the "zero
nonpositive" crowd still far outnumber the rest.
Which fits your analogy nicely, as people in Great Britain drive on the
left side of the road and people in the US on the right side. So there
is obviously no dogmatic "correct way", but you have to ask: where
should I drive? In which environment is it *useful*? I will drive on the
left/right side because I an $WHEREEVER.
And everywhere I have been, 0 is nonpositive.
Do you consider it to be intrinsic to the number or just a useful
definition?
I've never met a person speaking Aymara, therefore I consider nobody is
speaking Aymara. Everyone who does is obviosly speaking the wrong language.
Not the same thing at all. It's not in my interests to even consider
learning a word of Aymara, but if people want to speak it then I don't
care, so long as they don't try and speak it with me, and if they do
they should expect not to be understood.
It's not something to argue about, actually: it's a definition (clear by
the meaning of the word "axiom", actually). It's just frustrating to
meet people over and over again who have never heared of any discussion
about this topic and therefore believe their opinion is the only/best
one. Reminds me of all these stupid US Americans who believe Europe is a
country and who become angry when you tell them that Mexico is a part of
America.
Who said I'd never heard discussion on this topic before?
0 is not positive unless stated otherwise. It doesn't have to be this
way, and may in fact change over time [1] but currently it is.
Why get so angry?
Phil
[1] I might have this wrong, but I believe 1 was once considered prime.
Back then it was definitely prime, and these days it is definitely not.