Re: Cantorian pseudomathematics

In article <MPG.1e35cf5559953eeb98a98b@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> MoeBlee said:

> > Please cite a theorem of set theory such that its negation is a
> > theorem of some other axiomatized theory that you hold to be
> > important. And what are these "other axioms of mathematics" that
> > you have in mind?
> >
> > MoeBlee
> >
> >
> No one axiom needs to be the exact negation of another for
> contradictions to arise between them. Certainly, the notion of an
> infinite number of increments never achieving an infinite value flies
> in the face of infinite series, where a sum can only converge to a
> finite value if the terms have a limit of 0 at oo.

In real mathematics nothing is ever "at" oo, things sometimes are said
to "approach oo" ( which is what "-> oo" means), but one never reaches
it.

Just as in

"lim_{h ->0} [f(x+h)-f(x)]/h = f'(x)"

one never actually has h = 0, so in

"lim_{n -> oo} A_n = B"

one never has n = oo.

Those, like TO, who say otherwise, only advertise their ignorance.
.

Relevant Pages

  • Re: Cantorian pseudomathematics
    ... >> No one axiom needs to be the exact negation of another for contradictions to ... the notion of an infinite number of increments ... I don't know of theorems of set theory that have ... your claim about "axioms" is just hot air. ...
    (sci.math)
  • Re: Logarithm of transfinite numbers
    ... MoeBlee wrote: ... egregious misconceptions of set theory. ... infinite sequence within the set. ... This conveys his concept of the irregulars being "infinitely larger" ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... >>> That's a theorem of set theory already. ... >>> MoeBlee ... >> finite strings on a finite alphabet to be infinite? ... > set of strings of length L, ...
    (sci.math)
  • Re: Logarithm of transfinite numbers
    ... Tony Orlow wrote: ... MoeBlee said: ... axioms of set theory. ... So a line with an infinite length is infinitely long? ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... MoeBlee said: ... >> It means that they contradict other axioms. ... > Please cite a theorem of set theory such that its negation is a theorem ... the notion of an infinite number of increments ...
    (sci.math)