> On Tuesday, 16 July 2013 19:16:21 UTC+2, Ralf Bader wrote: >> email@example.com wrote: > On Monday, 15 July 2013 23:52:48 >> UTC+2, Ralf Bader wrote: >> firstname.lastname@example.org wrote: > >> > Modern logic says, for ever n: line L_n of the list > 1 > 1,2 > 1,2,3 > ... >> > contains less naturals than the whole list. That is correct. > >> No, it is wrong. It is wrong that "line L_n contains less naturals..." >> and it is wrong that "modern logic" would say so. > > Indeed?
Indeed. You have written crap.
>>> The list contains more naturals in all lines than in every line. >>> Inclusion monotony, however, proves that all lines cannot contain more >>> than every line. Simple as that. > >> No. > > No inclusion monotony possible in matheology?
You are asking crap.
>>> And even simpler perhaps: Cantor proves by means of definable diagonal >>> numbers that the definable reals are uncountable. But the definable >>> reals are countable. > >> No. Cantor did not prove what you phantasize. > > But he thought he did: ?Unendliche Definitionen" (die nicht in endlicher > Zeit verlaufen) sind Undinge. Wäre Königs Satz, daß alle ?endlich > definirbaren" reellen Zahlen einen Inbegriff von der Mächtigkeit aleph_0 > ausmachen, richtig, so hieße dies, das ganze Zahlencontinuum sei > abzählbar, . (Cantor to Hilbert)
Maybe Cantor was a bit confused about this issue. It has been resolved in the meantime. But probably you wanted to say that as a historian of mathematics you are in the same profound manner totally incompetent as for mathematics proper. However we already knew that.
> And further: Do you really think that it would have stirred up anybody's > blood if Cantor had proved that there are uncountably many undefinable > numbers? Of course undefinable objects cannot be counted.
I am not really very much interested in knowing whose blood pressure went up at the thought of Cantor's set theory 100 years ago. You might have a look on p. 27 of Bishop and Bridges' "Constructive Analysis" which is a presentation of Bishop-style real analysis and Bishop is afair one of those you misuse as spokesmen for your crap. On that page, theorem 2.19 is stated and proved. Don't care for the theorem, although easy it is beyond your grasp anyway. Just read the comment after the proof: "Theorem (2.19) is the famous theorem of Cantor, that the real numbers are uncountable. The proof is esentially Cantor's "diagonal" proof. Both Cantor's theorem and his method of proof are of great importance."
>>> And the simplest contradiction is this: If set theory is correct, then >>> the deal with the devil will leave you blank. But it would not leave me >>> blank. I would maintain at least one $. So I am not as stupid as set >>> theorists. > >> I don't know whta you are talking about. > > Not necessary to emphasize. > > Regards, WM