Re: An uncountable countable set

In article <1156842732.043353.163480@xxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
*** T. Winter schrieb:
....
> Cantor states (analogously) that *all stairs exist*, that the width of
> all ot them is L, but that none of them has hight L. Width [0, 1] and
> height [0, 1).

A quote please. But indeed, the width of all of them is L, but there is
none of them with width L. And the heighth of all of them is L, but there
is none of them with heighth L. So width [0,1] and heighth [0,1]. That
is, if you define both as the smallest box containing the completed stair.
If you define both as the largest numbers that can be obtained, you get
width [0,1) and heighth [0,1).

You are trying to make it difficult, using UTF-8. But this one takes the
cake.
I agree with you. But Cantor said (Werke, p. 409): "So stellt uns
beispielsweise eine veränderliche Größe x, die nacheinander die
verschiedenen endlichen ganzen Zahlwerte 1, 2, 3, ..., v, ...
anzunehmen hat, ein potentiales Unendliches vor, wogegen die durch ein
Gesetz begrifflich durchaus bestimmte Menge (=EF=81=AE) aller ganzen
If "=EF=81=AE" is UTF-8, the Unicode character is U+F06E, which is in the
private area of characters. I have no idea what that symbol stands for,
so I will modify it to N.
endlichen Zahlen N das einfachste Beispiel eines aktual-unendlichen
Quantums darbietet.

Again translated (why do you post so much German in an English speaking
newsgroup while you should know that most readers are not able to read
German?):
Cantor: So while a changing quantity x that successively takes the
various values of finite numbers 1, 2, 3, ..., v, ... , is a
potential infinite, on the other hand, a through the axioms completely
determined set (N) of all integral finite number is an example of an
actually finite quantity.
Nice that you found the quote I have alluded to, and that you did deny
of existing, but that I could not find back.

What Cantor is stating here (and I did already indicate that in an
earlier response), is, translated to current set theory:
The set N is potentially infinite, the size of N is actually infinite.
(In current terminology a set is not a quantity.)

And I am arguing against this actual understanding of infinity.

Try to argue with something beyond Cantor.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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