Interesting... Oh those french... ;-)
So do natural numbers in France always include the zero?
To cite my math professor (from Germany) at the time when I was a student.
Null ist alles andere als natürlich.
That's a pun! Remember that it took quite a
long time until the 0 was invented.)
Translation: Zero is everything else than natural.
(Hopefully that is somehow right.)
I've often seen that mathematicians claim that 1 is the smallest natural
number while for computer scientists it's 0.
Well, in the end, it's just a convention. As long as the Peano-Axioms
are met...
So why not starting the natural numbers with 42? Or -1? The start is
simply what you state as an Peano-Axiom.
On http://en.wikipedia.org/wiki/Peano_arithmetic#The_axioms it's Axiom
5. And on http://fr.wikipedia.org/wiki/Arithm%C3%A9tique_de_Peano it's
Axiom 1. ;-)
Ralf
On 02/26/2009 03:56 PM, Florent Hivert wrote:
> Dear Kiran
>
>> Just to make life complicated, have a look at
>>
>> http://en.wikipedia.org/wiki/Positive_number
>>
>> and then
>>
>> http://fr.wikipedia.org/wiki/Nombre_positif
>>
>> Yes, it seems that "positive" means >0 in English and ">=0" in French.
>> (I suppose "nonnegative" means >=0 in English and >0 in French. The
>> French for >0 is "strictement positive").
>
> As you could have imagined if you had knew that I'm french, I perfectly know
> about this one :-) I've never heard something close to "non negative" in
> French. It much to ugly !!!
>
> An even better one: a "non decreasing" function is usually a function f
> s.t. f(x) <= f(y) as soon as x <= y. In French, we call this "croissante"
> (i.e. word-to-word translation of increasing). And if you say "une function
> non croissante" (i.e. w2w non decreasing function) every one understand a
> function which is *not* a non-decreassing function (ie there exist x,y
> s.t. x<y and f(x)>f(y)). I must confess, I never understand this
> non-decreassing, so I mentally translate to "never decreasing"...
>
> I can tell you, it's a real fun for students :-)
>
> Cheers,
>
> Florent
>
>
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