Re: infinity

In article <MPG.1da4b27bee4adcf798a3b2@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:
> > In article <MPG.1da34711e2b032de98a38a@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
> >
> > > Virgil said:
> > > > In article <MPG.1da20c30d6b36d7898a36e@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > > Tony Orlow <aeo6@xxxxxxxxxxx> wrote:
> > > >
> > > > >
> > > > > Here, let's change some implications to equivalences and replace 4
> > > > > with
> > > > > 4, 5
> > > > > and 6, so that the three possiblities are mutually exclusive:
> > > > >
> > > > > 1. 0<x<=1 -> finite(x)
> > > > > 2. finite(x) <-> finite(1/x)
> > > > > 3. finite(x) <-> finite(0-x)
> > > > > 4. finite(x) <-> and(not(zero(x)),not(infinite(x)))
> > > > > 5. zero(x) <-> and(not(finite(x)),not(infinite(x)))
> > > > > 6. infinite(x) <-> and(not(zero(x)),not(finite(x)))
> > > >
> > > >
> > > > Then every set which is not a number is an infinite set, according to
> > > > that definition.
> > > >
> > > A set of numbers is not a single number, although EVERY set has some
> > > number
> > > of
> > > elements, finite, infinite, or indeterminate. The above definition does
> > > not
> > > define numbers in terms of sets.
> >
> > Since TO has not restricted the domain of 'x' to numbers or anything
> > else, one must assume that it applies equally well to everything,
> > including sets.
> >
> I was asked, and specified that x is in the real numbers. Pay attention. Your
> failure to remember is not my failure to specify.

Since the (now specified) real numbers, in any standard version, contain
only finite numbers according to TO's own rules above, point (6) is
vacuous for every standard real arithmetic.

So that TO is now obligated to provide a complete definition of TOmatic
real numbers, if he wishes to have access to any but the standard finite
ones.
.

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