On Mon, Jul 04, 2022 at 07:10:27AM +0200, Uwe Brauer wrote:

[...]

> That really su... (My use case only concerned numbers from 0-10).
> 
> So it boils down to the question: why isn't 0 considered as natural numbers, as, according to the Peano axioms, it is?

I don't know whether you're serious or making fun (Poe's Law and
all that), but actually, Peano's axioms couldn't care less: as
far as they are concerned, natural numbers could well start at
23 or something.

Actually it seems to be some kind of "cultural question" whether
mathematicians start counting at 0 or at 1; my observation is
that they tend to agree across one faculty at one university.
I know positively one that tends to count from 1 (HU Berlin),
another that counts from 0 (Freiburg), both in Germany.

Something for mathematical ethnologists (do those exist?) to mull
over.

I once asked a maths prof and he said foundational folks (set
theorists, math logicians -- that's the typical environment
where you'd tend to stumble upon Peano) tend to favour starting
at 0.

Historically, Peano himself seems to have been a one-counter:

  "Peano's original formulation of the axioms used 1 instead
  of 0 as the "first" natural number,[6] while the axioms in
  Formulario mathematico include zero."  as quoted in [1].

Cheers

[1] https://en.wikipedia.org/wiki/Peano_axioms
-- 
t