By classical logic "Cantor" means "can't or" it is a recursive negative argument built on a cornerstone of limitation. It is a non productive axiom. Same as "Boolean" or "Boo-lean". The purpose of Boolean algebra is to scare or push a truly logical mind from a truly lean and defined set, and it does this by presenting a seemingly sound but bloated statement of limitation. It leans toward limitation instead of governing by an open statement. An open statement is one open to unknown (or "uncountable") possibilities but nonetheless firmly grounded in logic. "Elepants can be colored." is an example of an open statement. Reality: elephants are mostly grey or brown. If you painted an elephant green it could exist. But the notion "seems" absurd so it is blindly dismissed.
Dik T. Winter wrote: > In article <email@example.com> WM <firstname.lastname@example.org> writes: > > On 3 Jun., 04:37, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > ... > > > You apparently do not understand it at all. WM has posted this stuff for > > > years in the German newsgroup on mathematics, in German. Moreover, he > > > has two books about mathematics on his name, in German. > > > > And both say, in effect, about the existence of actual infinity, what > > Kant said about the proof of the existence of God: These assumptions > > (proof of God, axiom of infinity) are as ridiculous as a merchant who > > would try to improve his balance by adding some zeros behind his > > result. > > And you are deluded. An axiom is a statement of something that can not be > proven, neither disproven using the remainder of the theory. So comparing > the "axiom of infinity" with a "proof of God" is pretty stupid. In > mathematics a theory depends on the axioms used. There is nothing sacred > about the axioms, but as long as you are discussing a theory you should > use the axioms of that theory. So, if you are discussion Eucliedan > geometry you should use the parallel axiom. Of course you can reject it, > but in that case you are not discussing Euclidean geometry but something > else. > > > But I am sure that all this Cantor-nonsense would burst > > like a bubble filled with foul gas once the public got to know what > > crap has to be paid by the taxpayer. > > Are you mimicking JSH on purpose? In that case do not forget your uprising > as the best mathematician, hand-shaking with rulers of the world and raking > in large amounts of dollars. > -- > dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/