On Thursday, 3 June 2021 at 14:04:14 UTC-3, WM wrote:
> Gus Gassmann schrieb am Donnerstag, 3. Juni 2021 um 17:16:54 UTC+2:
> > On Thursday, 3 June 2021 at 11:31:44 UTC-3, WM wrote:
> > > zelos...@gmail.com schrieb am Donnerstag, 3. Juni 2021 um 06:28:46 UTC+2:
> > [...]
> > > > A sequence alone does not natural numbers make.
> > > Therefore the Peano axioms do not construct the natural numbers, like for instance
> > > 1
> > > if n then n+1
> > > + as known from evolution.
> > Euclid's axioms do not "construct" geometry, either.
> They construct Euclidean geometry. Peano's axiom do not construct natural numbers except 0 or 1.
Went right over your head, didn't it? "Point" and "line" are undefined and can be used in different contexts with the *same* axioms. "Geometry", even of the Euclidean variety, does *not* have to look the way we are all used to think of it.

Gus Gassmann schrieb am Freitag, 4. Juni 2021 um 13:41:36 UTC+2:
> On Thursday, 3 June 2021 at 14:04:14 UTC-3, WM wrote:
> > Gus Gassmann schrieb am Donnerstag, 3. Juni 2021 um 17:16:54 UTC+2:

> > > Euclid's axioms do not "construct" geometry, either.
> > They construct Euclidean geometry. Peano's axiom do not construct natural numbers except 0 or 1.
> "Point" and "line" are undefined and can be used in different contexts with the *same* axioms. "Geometry", even of the Euclidean variety, does *not* have to look the way we are all used to think of it.

No, point is clealy defied and cannot be replaced by Bierseidel or else. From this definition line is defined too.

Regards, WM

>Therefore the Peano axioms do not construct the natural numbers, like for instance
>1
>if n then n+1
>+ as known from evolution.

the axioms is the smallest number we need to make the natural numbers, all your sequences sates it so for any of them, we can make natural numbers.

>There is no intuition necessary to define the natual numers correctly.

I didn't say it was needed, only we make it coincide.

>With that uttering you are in contradiction to all other mathematicians which I know. And I know a lot.

Mathematicians know there is no "the set" but "the isomorphic class of natural numbers", we usually however just say "the set of" cause it doesn't matter which one we pick and we know it.

>Ah, your maths is not only despising individual numbers but also sets.

Mathematics (this is not mine) focuses on structures, structures are not unique, but specific sets are.

zelos...@gmail.com schrieb am Montag, 7. Juni 2021 um 10:40:22 UTC+2:

> Mathematicians know there is no "the set" but "the isomorphic class of natural numbers", we usually however just say "the set of" cause it doesn't matter which one we pick and we know it.

Naturals without zero: {1,2,...}
Naturals with zero: {0,1,2,...}
https://en.wikipedia.org/wiki/Natural_number

Regards, WM

It happens that WM formulated :
> zelos...@gmail.com schrieb am Montag, 7. Juni 2021 um 10:40:22 UTC+2:
>
>> Mathematicians know there is no "the set" but "the isomorphic class of
>> natural numbers", we usually however just say "the set of" cause it doesn't
>> matter which one we pick and we know it.
>
> Naturals without zero: {1,2,...}
> Naturals with zero: {0,1,2,...}
> https://en.wikipedia.org/wiki/Natural_number

An example of relabeling the naturals. Nothing is changed by adjoining
zero except that we have a better structure on them. Zero is a
traditional symbol for the additive neutral element.

https://en.wikipedia.org/wiki/Identity_element

måndag 7 juni 2021 kl. 13:08:19 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Montag, 7. Juni 2021 um 10:40:22 UTC+2:
>
> > Mathematicians know there is no "the set" but "the isomorphic class of natural numbers", we usually however just say "the set of" cause it doesn't matter which one we pick and we know it.
> Naturals without zero: {1,2,...}
> Naturals with zero: {0,1,2,...}
> https://en.wikipedia.org/wiki/Natural_number
>
> Regards, WM

You imbecile, again that is how we chose to label it and it becomes "the" cause we can label them all the same regardless of hte underlying objects. So it is "the" in that sense

How hard is it to understand that we label them in this way for our convinience and do not care about the actual objects cause once labeled, they are all the fucking same?

zelos...@gmail.com schrieb am Montag, 7. Juni 2021 um 13:39:51 UTC+2:
> måndag 7 juni 2021 kl. 13:08:19 UTC+2 skrev WM:
> > zelos...@gmail.com schrieb am Montag, 7. Juni 2021 um 10:40:22 UTC+2:
> >
> > > Mathematicians know there is no "the set" but "the isomorphic class of natural numbers", we usually however just say "the set of" cause it doesn't matter which one we pick and we know it.
> > Naturals without zero: {1,2,...}
> > Naturals with zero: {0,1,2,...}
> > https://en.wikipedia.org/wiki/Natural_number
>
> How hard is it to understand that we label them in this way for our convinience

We do not label them. They and only they are the labels.

> and do not care about the actual objects cause once labeled, they are all the fucking same?

No, they can be very different. If you do not care, then you cannot do mathematics.

Regards, WM

>We do not label them. They and only they are the labels.

Yes we do, "1" is not an object, it is a symbol, a label we use to to refer to some object. "One" is not an object, it is a sequence of symbols representing sounds to form a word that we use as a label for an abstract concept and the object it is.

in Von Neumann construction we have 0 be the empty set
1 is {{}}
2 is {{},{{}}}
and so on.
We get them from that and can go on.

>No, they can be very different. If you do not care, then you cannot do mathematics.

We don't need to care because the STRUCTURES is what matters, not the specific objects!

https://en.wikipedia.org/wiki/Natural_numbers_object
https://en.wikipedia.org/wiki/Peano_axioms#Models

zelos...@gmail.com schrieb am Montag, 7. Juni 2021 um 15:44:58 UTC+2:

> We don't need to care because the STRUCTURES is what matters, not the specific objects!
>
The structures may be of interest to some who do not care to be useful members of the society but only play useless games for their fun. In useful mathematics the natural numbers are what counts (pun intended).

Regards, WM

måndag 7 juni 2021 kl. 16:28:53 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Montag, 7. Juni 2021 um 15:44:58 UTC+2:
>
> > We don't need to care because the STRUCTURES is what matters, not the specific objects!
> >
> The structures may be of interest to some who do not care to be useful members of the society but only play useless games for their fun. In useful mathematics the natural numbers are what counts (pun intended).
>
> Regards, WM

Mathematicians are useful you pompous imbecile. And they care only about the structure. They know that natural numbers structure is not unique but it doesn't matter cause we can label things as we see fit and get it to be the intuitive way we want it to be.

You need to educate yourself more in mathematics, much more.

zelos...@gmail.com schrieb am Dienstag, 8. Juni 2021 um 06:45:32 UTC+2:
> måndag 7 juni 2021 kl. 16:28:53 UTC+2 skrev WM:
> > zelos...@gmail.com schrieb am Montag, 7. Juni 2021 um 15:44:58 UTC+2:
> >
> > > We don't need to care because the STRUCTURES is what matters, not the specific objects!
> > >
> > The structures may be of interest to some who do not care to be useful members of the society but only play useless games for their fun. In useful mathematics the natural numbers are what counts (pun intended).
> >
> Mathematicians are useful

Yes.

And they care only about the structure.

No, those are useless.

Regards, WM