Re: how

On 4/14/24 3:05 PM, WM wrote:

Le 13/04/2024 à 14:59, Richard Damon a écrit :

On 4/13/24 8:23 AM, WM wrote:

Le 12/04/2024 à 18:58, Richard Damon a écrit :
>

No, "Set Theory" doesn't talk about "differences" based on the values of the elements, because that is outside of the domain of Set Theory.

>
Learn about ordered sets and well-ordered sets. For a start look here https://en.wikipedia.org/wiki/Partially_ordered_set.

 

Which is MATH THEORY, not SET THEORY (which is a SPECIFIC subset of math, DIFFERENT than Order theory).

 Do you know the expression ordinal number? It is related to order. Here are the first chapters from Cantor's fundamental essay:
Beiträge zur Begründung der transfiniten Mengenlehre ........................................ 282
     §  1.  Der Mächtigkeitsbegriff oder die Kardinalzahl ........................................ 282
     §  2.  Das "Größer" und "Kleiner" bei Mächtigkeiten.......................................... 284
     §  3.  Die Addition und Multiplikation von Mächtigkeiten ..................................... 285
     §  4.  Die Potenzierung von Mächtigkeiten ...............................................  287
VII    §  5.  Die endlichen Kardinalzahlen ...............................................  289
     §  6.  Die kleinste transfinite Kardinalzahl Alef-null .........................................  292
     §  7.  Die Ordnungstypen einfach geordneter Mengen.......................................  296
     §  8.  Addition und Multiplikation von Ordnungstypen ....................................... 301
     §  9.  Der Ordnungstypus  der Menge R aller rationalen Zahlen, die größer als 0 und kleiner als 1 sind, in
             ihrer natürlichen Rangordnung .............................................  303
     § 10.  Die in einer transfiniten geordneten Menge enthaltenen Fundamentalreihen .................. 307
     § 11.  Der Ordnungstypus  der Linearkontinuums X ......................................  310
     § 12.  Die wohlgeordneten Mengen .................................................... 312
     § 13.  Die Abschnitte wohlgeordneter Mengen ............................................  314
     § 14.  Die Ordnungszahlen wohlgeordneter Mengen ......
 Note that Ordnung means order.
 Last warning: If you dare again to waste my time by your stupid ignorance I will never again talk to you.
 Regards, WM

And where does he talk about the "Distance" betwen the Set of the Natural Numbers, and the "Number" w?
You huff a lot about the "errors" he has made, but neglect to point out that you complaint is that you don't accept the basis of logic that he uses, and that the problem is the logic you want to try to use can't actually DO the things to define the sets he is using.
Not understanding the rules of logic for the field you are working in is a good way to make errors.
But all of this just seems above your head, so you just call everyone else "wrong" when what you mean is you disagree with them because you refuse to use the logic that they are using, and instead use logic beyond its capability and just ignore all the contradictions it creates which makes you close your eyes to the "darkness" you need to put on things to try to ignore the errors.