torsdag 16 november 2023 kl. 12:46:34 UTC+1 skrev Adam Polak:
> czwartek, 16 listopada 2023 o 09:19:23 UTC+1 FromTheRafters napisał(a):
> > FredJeffries submitted this idea :
> > > On Wednesday, November 15, 2023 at 2:40:05 PM UTC-8, FromTheRafters wrote:
> > >> on 11/15/2023, FredJeffries supposed :
> > >>> On Wednesday, November 15, 2023 at 6:21:19 AM UTC-8, FromTheRafters wrote:
> > >>>> After serious thinking Adam Polak wrote :
> > >>>>> środa, 15 listopada 2023 o 13:37:24 UTC+1 FromTheRafters napisał(a):
> > >>>>>> Adam Polak used his keyboard to write :
> > >>>>>>> środa, 15 listopada 2023 o 00:20:50 UTC+1 FromTheRafters napisał(a):
> > >>>>>>>> Adam Polak used his keyboard to write :
> > >>>>>>>>> poniedziałek, 13 listopada 2023 o 20:24:24 UTC+1 WM napisał(a):
> > >>>>>>>> I believe it is only by convention that we drop the trailing zeros in
> > >>>>>>>> the infinite continued decimal expansion representation and call it
> > >>>>>>>> terminated.
> > >>>>>>>>
> > >>>>>>>> 0.0009999... or 0.000(9) is another unending CDE for that same
> > >>>>>>>> mathematical object.
> > >>>>>>>
> > >>>>>>> Yes, conventions, both good ones and those imperfect ones.
> > >>>>>>>
> > >>>>>>> "Task for children" :) Find the difference between the pictures:
> > >>>>>>>
> > >>>>>>> Pict No. 1 Pict No. 2
> > >>>>>>>
> > >>>>>>> 1/2 0.5
> > >>>>>>>
> > >>>>>>> I'm sure everyone can spot it.
> > >>>>>>> Each "picture" above shows a DIFFERENT object - these are two different
> > >>>>>>> mathematical objects! - the differences are noticeable at first glance.
> > >>>>>>> Both objects have the same qualitative feature, which is their
> > >>>>>>> numerical value.
> > >>>>>> I disagree. Mathematically speaking those are two different symbolic
> > >>>>>> representations of the same mathematical object.
> > >>>>>>
> > >>>>>> [...]
> > >>>>>
> > >>>>> You can, of course, disagree with reality, but you can't change it.
> > >>>>> this: 1
> > >>>>> this: 23/23
> > >>>>> this: 1.00
> > >>>>> this: 1.(0)
> > >>>>> are completely different objects,
> > >>>>
> > >>>> No, they are different symbols for the number one.
> > >>>>
> > >>>
> > >>> It's not necessarily that simplistic, for anyone who subscribes to the
> > >>> 'pure set theory as foundations of mathematics' myth.
> > >>>
> > >>> The first represents the natural number 1, which many say is the set {{}}
> > >>>
> > >>> The second represents a rational number. Rational numbers are usually
> > >>> 'constructed' as sets of ordered pairs of integers satisfying certain
> > >>> requirements. Integers themselves can be constructed as sets of ordered
> > >>> pairs of natural numbers satisfying some other requirements.
> > >>>
> > >>> The third and fourth represent a real number. Real numbers are
> > >>> 'constructed' from sets of sets of (sets of?) rational numbers
> > >>>
> > >>> Anyhow, it ain't necessarily so that they are merely different symbols for
> > >>> the same number one (whatever that is).
> > >> But they are. I would also add that all of those are reals and we have
> > >> rationals as embedded in the reals and integers as embedded in the
> > >> rationals and naturals as embedded in in the integers.
> > >>
> > >> There is no need for naturals or integers to have fractional parts to
> > >> their CDE, to have them implies at least Q.
> > >>
> > >> All of those above symbolize the mathematical concept of the number
> > >> one.
> > >>
> > >
> > > https://en.wikipedia.org/wiki/Abuse_of_notation
> > I'll see that and raise you:
> >
> > https://en.wikipedia.org/wiki/One_half#Mathematics
> PS 2:
>
> The first matrixes constructed by Cantor while working on the Diagonal Method looked like this:
> 1 I MMMMMMMM ...
> 2 I WWWWWWWW ...
> 3 I MWMWWMWW ...
> 4 I MMWMMWMW ...
>
> Can you provide the numerical value represented by any of the objects in the right column?
> (rhetorical question)
>
> without having a qualitative parameter such as a numerical value can any of the objects in the right column be "a number" ?
> (rhetorical question)
>
> An object/symbol that does not represent any numerical value is neither "a number" nor symbol of "a number".
>
> As part of his research using the Diagonal Method matrix, Cantor did not examine numbers, but completely different objects NOT RELATED to numbers. He studied objects such as: MMWMMWMW ...
> more in terms of their "graphic", "geometric" structure than in any way related to a qualitative parameter such as a numerical value.
>
> Using the Diagonal Method matrix, Cantor did not research the numbers! Farther during this works Cantor managed to deceive first himself and then deceive other mathematicians that this is about numbers and quantities in infinite sets of numbers.

None of those are natural numbers.