Re: A puzzle for Cantorists


Math1723 wrote:
Despite all your squawking about the characterization being
inaccurate, your post demonstrates what I said about you: You never
addressed Mark's specific point on the proof. Instead, you go on into
an irrelevant tangent about physics and your crankish ideas about
infinity.

It seems you're the one failing to "deal".

No, I've already offered an analysis of Norm Megill's MetaMath's
"ruc", about three years ago, and I referred him to that discussion.
Then I encapsulated some of its points here.

You are making distorting statements.

What's your point? There are quite a few viewpoints about the use of
real infinities in mathematics that have nothing to do with
transfinite cardinals.

I'm sincere, I think infinite sets are equivalent from first
principles and offer direct reasoning why that is so, then I describe
nonstandard functions that are bijections between the naturals and
unit interval of reals, even in Cantorian proofs. (EF is a
function.) EF is a CDF of the naturals, over which I have described a
uniform random probability distribution.

So, no.

Do you not understand that there is a cohesive structure behind these
arguments? That is to say, over the years many key features of the
foundations of set theory have been dissected here, pseudonym, if you
haven't read them, and can't represent them, then those would be
unfounded statements about them.

Consider the recent "Rationals/Irrationals" thread, about them being
NCD2 sets in the reals.

Guy, Fraenkel says transfinite cardinals are a disease.

Ross

.

Relevant Pages

  • Re: Cantors "diagonal argument". My Objection.
    ... then there is no reason why you should not allow me an infinite placement for the digits of possible naturals. ... I can say the same for the reals. ... The E/C/D, standard, way, to represent reals is as a limit of a convergent sequence of rationals. ... In the standard there is 0.5 to 1, but not half infinity to infinity, infinity standardly isn't a scalar. ...
    (sci.logic)
  • Re: Calculus XOR Probability
    ... It is an axiomatic statement in my system that there is a unit infinity N ... intervals, or naturals, on the real line, as well as being the number of ... some power IS zero? ... I.e., TO now requires the the product of two non-zero reals be zero, ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... It is an axiomatic statement in my system that there is a unit infinity N, which is the length of the real line, and therefore the number of unit intervals, or naturals, on the real line, as well as being the number of nipotent infinitesimal reals in the unit interval. ... those axioms, and only those axioms, of your system*, then you can simply ...
    (sci.math)
  • Re: infinity
    ... What if you have two copies of the sets of ordinals, ... the ordinal zero negative infinity or less than any integer. ... I presume your construction of the reals as a product of sets ... So anyways, this thread is about "ubiquitous naturals", the concept ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... All I know is that what we know about infinite ... > the sets I call finite have larges members. ... The set of all finite naturals is not infinite, ... Sets defined by mapping functions from the naturals to the reals which have ...
    (sci.math)