Re: abundance of irrationals!) - rectangles of area 1.bmp [0/1]

In article <MPG.1ceeb62585029a40989c45@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:
> > In article <MPG.1ced6107b1babfda989c32@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >
> > > > If A being a proper subset of B does not mean that A is "smaller than"
> > > > B, in your system, as you remarks about the rationals and reals would
> > > > imply, then why are not the naturals, the odd naturals and the odd
> > > > primes all the same size?
> > > A proper subset IS smaller than the superset, as I have stated. It is you
> > > who
> > > believe this rule evaporates at infinity. When did I ever make such a
> > > statement?
> >
> > When TO claimed that the sets of rational and reals are of the same
> > size!
> Learn to read. I said the rationals constitute a sort of enumeration of the
> reals, but as a representation, it is reall a 2D array of naturals, and
> should
> be considered to be N^2 in size. This is smaller than the reals. My point was
> that they are certainly NOT an equivalent set to the naturals. That's
> balderdash.

If you mean that there is no bijection between the rationasl and the
naturals, you are dead wrong.
> Leanr to read.

Learn to spell! At least when telling people to learn to read.

> >
> > Many people, of considerable talents in mathematics, have tried, and
> > failed, to construct any 'size' definition which incorporates proper
> > subsets as always being smaller that the superset.
> So what? I succeeded. Are you jealous? that's what it sound like.
> >
> > If TO succeeds, it will be a marvel.
> >
> > But he has a long way to go.
> >
> As long as I waste my time here, perhaps.

Then go waste it eslewhere.
.

Relevant Pages

  • Re: Uncountable sets in CZF?
    ... a trivial surjection from R onto any subset of N there is a bijection. ... I don't base my arguments (that the reals and naturals are equivalent) ... from some proper subset of the naturals to the reals, ...
    (sci.math)
  • Re: abundance of irrationals!) - rectangles of area 1.bmp [0/1]
    ... >>> B, in your system, as you remarks about the rationals and reals would ... >>> imply, then why are not the naturals, the odd naturals and the odd ... >> A proper subset IS smaller than the superset, ... I said the rationals constitute a sort of enumeration of the ...
    (sci.math)
  • Re: abundance of irrationals!) - rectangles of area 1.bmp [0/1]
    ... >> thinking on the rationals, that one can get arbitrarily close to any real, ... >> that it therefore constitutes an enumeration of the reals. ... > imply, then why are not the naturals, the odd naturals and the odd ... A proper subset IS smaller than the superset, ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... Your definition of naturals is self ... >>> Order is irrelevant in constructing injections and bijections, ... >>> irrelevant in determining cardinality. ... >>> No such definition which requires a proper subset to be of smaller ...
    (sci.math)
  • Re: Rational Numbers/Irrational Numbers
    ... Rational numbers are proper subset of real numbers. ... All positive reals are a proper subset of all reals, ... the ranges of fand gare _disjoint_ subsets of B. ...
    (sci.math)