Re: Cantor Confusion

In article <1169578564.772090.181560@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> imaginatorium@xxxxxxxxxxxxx writes:
....
About Wolfgang Mückenheim.

You've escaped noticing? All around you in this thread is the endless
spewing of our German friend who, inexplicably, is said to _teach_
mathematics at some sort of college. He's just reponded and "confirmed"
that your confusion is "correct". (But all in undefined verbiage.)

Actually I am getting the impression that what he presents here is not
what he presents in the mathematics courses at his University. (A
Fachhochschule is called a University in the Netherlands.) I received
his book and I found no errors in the first four chapters I did read (of
the ten in all). I am only a bit unlucky about his distinction between
(indeed) actual and potential infinity, but that can be clarified later.
Also his statement (in chapter 3) that irrational numbers only exist
due to actual infinity is based on the representation of numbers in some
integral base. That appears (to me) a bit shortsighted (*). On the other
hand, the introduction of rationals, irrationals, algebraic numbers and
whatever is clear (not strict, but clear enough for the intended audience).
Also his explanation of the Peano axioms is correct. So unlike some crank
books, this book does not contain serious errors in the first four
chapters. That may come as a surprise to some (it did to me).

(*): The reason appears to be that irrationals can only be given by a rule
about how to compute it. But I think that:
0.142857142857...
is also nothing more than a rule how to compute it.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

Quantcast