Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: Cantor's absurdity, once again, why not?
Posted:
Mar 14, 2013 6:52 AM


On 14 Mrz., 11:17, fom <fomJ...@nyms.net> wrote: > On 3/14/2013 4:47 AM, david petry wrote: > > > > > In a previous aritcle a while back, "marcus_b" wrote: > > > ** start quote ** > > In math, the great pons asinorum now is Cantor's diagonal proof. There seem to be scads of people out there who just cannot quite get it and who yearn to achieve their rightful 15 minutes of fame by trying to shoot it down, thus thrusting themselves ahead of Cantor in the pantheon of mathematical geniuses. Can you shed some light on the motivation here? > > ** end quote ** > > > The "cranks" who insist on pointing out the absurdity of Cantor's argument are puzzled that mathematicians "cannot quite get it". > > > Cantor's argument relies on accepting the notion of an actual infinite, and that's problematic. > > If you are going to paraphrase Cantor's argument, please do > so correctly. > > Cantor's "argument" is an argument scheme. > > It is an argument for constructing a counterexample > for some particular claim. > > A particular claim must be made before Cantor's argument > can even apply. > > That particular claim is that there is a single infinity > that is referred to in language as an object.
No. That particular claim is that infinity can be complete, that a list of natural numbers can contain all natural numbers such that no further one is possible to add. Then Cantor constructs another real number and shows that it can be included into the list (by mapping n  > n+1). It is a silly claim, inventing time into mathematics.
Every welldefined Cantor diagonal belongs to the countable set of nameable real numbers (named by the definition of the list and of the replacement rule). And undefined Cantorlists do not yield real numbers.
Regards, WM



