Re: Review of Mueckenheims book.

mueckenh@xxxxxxxxxxxxxxxxx wrote:
On 12 Mrz., 22:11, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
mueck...@xxxxxxxxxxxxxxxxx wrote:
On 8 Mrz., 22:46, Tony Orlow <t...@xxxxxxxxxxxxx> wrote:
mueck...@xxxxxxxxxxxxxxxxx wrote:
WM, you don't disagree that there are infinite sets containing just
finite values, such as the reals in [0,1], are you? I certainly agree
that an infinite set of naturals must contain infinite values, but
that's only because they are spaced apart by a unit in value. Isn't tat
your thinking?
If you disregad physical restrictions, then there are infinitely many
real numbers in the interval. Their cardinality, however, is not
larger than "infinite" for any set. Therefore we need no alephs etc.
The binary tree shows that different alephs are self contradictive.
If you take into account the physical restrictions, then there is no
infinite set. And that is the only correct approach.
Regards, WM
Well, since numbers are not physical entities, they don't actually
occupy space on the number line - they are true points. So, between any
two finitely distant points are indeed some infinite number of points.
You say that the only correct approach is to take into account
"physical" restrictions, but where the subject is non-physical, those
restrictions don't exist, though relations do, even if between infinite
nonphysical concepts called numbers.

The subject may be non-physical (it is not). But in order to make it
reasonable (in order to reason about it), you have to attach physical
stuff like written or at least thought symbols. Their number is
finite.

Regards, WM


Ah, but that is only one side of the coin. The language of mathematics consists of symbols, and we can only process a finite number of symbols, but that is not the only physical manifestation of what those symbols represent. Keep in mind geometry. Picture two ripples on a pond, moving toward each other at a finite pace. They meet at a point, which instantly becomes two, moving in opposite directions. How fast do they begin to move apart, at that first moment?

Smiles, TO
.

Relevant Pages

  • Re: Wheres respect? was Re: Corrective interpretation of real numbers
    ... finite or infinite set, might be considered lesser. ... deniers about the charge that a proper superset is definably larger ... the reals with iota-values the pseudo-reals, but I just call them the ...
    (sci.math)
  • Re: Wheres respect? was Re: Corrective interpretation of real numbers
    ... finite or infinite set, might be considered lesser. ... deniers about the charge that a proper superset is definably larger ... the reals with iota-values the pseudo-reals, but I just call them the ...
    (sci.math)
  • Re: infinity
    ... In unary, or base one, the only way to represent reals from the unit ... with an infinite alphabet, again it fails, again, nonstandardly. ... W have discussed the first proof, which essentially has the same result: ... as opposed to your supposedly infinite set with a finite number of successions. ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... >> beyond those indexes found in the infinite set of finite naturals. ... Which shows, as was to be proved in the first place, that the reals ...
    (sci.math)
  • Re: Cantors circular "proof" that evens = integers
    ... this is an inherent property of infinite sets simply ADDS this belief as ... That's an axiom; prove otherwise Jesse! ... For an infinite set x, I can only take that to mean 2 times ... equinumerous with a proper subset of itself. ...
    (sci.logic)
Loading