Re: An uncountable countable set

In article <452a6847@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <4529afa4@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <45296779@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <452946ad@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
Less than any finite distance. Silly!
And what is the smallest finite distance?

Note question not answered!! But the correct answer of zero would have
blown TO's argument to blazes, so one can see why he would not care to
answer it.
I was away a couple days, but I answered this, not paying attention to
that apparent contradiction, since I don't consider 0 really a finite
number at all. It's a point with no measure, as every number is measured
relative to that point.
If zero is not a number, how does TO keep the positive numbers separated
from negatives?
It's not a finite number. It's the origin. A finite number is a finite
distance from the origin. The origin is no distance from itself.

Then TO's set of real numbers is two sets separated by a non-number?

That does not match anyone else's set of reals. So TO casts himself
again into outer darkness re res mathematical.

It's a 1-D continuum with an origin, a metric space.

But where are the values of that metric if zero is not one of them?

When you claim that there are ordinals greater than any finite
ordinal,
are you obligated to name the largest finite ordinal?
When you claim there is a LUB to the reals strictly between 0 and 1,
are you required to name the largest real strictly between 0 and 1?
No. That's my point. Why should I name the smallest object which is not
infinitesimal?
That is not at all what I asked. So TO is doing his STRAW MAN fallacy
thing again.
You have no clue what the line of discussion was at this point, do you?

I have no idea what TO is talking about, and am reasonably sure he
doesn't either.

Then don't make yourself look silly defending questions and comments
that are irrelevant.

A "LUB" of the naturals does not have to be a natural any more than the
LUB of the the reals strictly between 0 and 1 has to be a real
strictly
between 0 and 1.
If it's a discrete set, then I disagree.
The set {(n-1)/n: n in N} is a discrete set with a LUB which is not a
member of the set. In fact every strictly increasing sequence having a
LUB has a LUB which is not a member of the sequence.
That is not "the reals strictly between 0 and 1" but a subset thereof.

So there is still no element within either set which is its LUB.

If the Finlayson reals are used, indeed the LUB is the maximal member of
the set of reals in [0,1). Ross, is that correct?

TO appealing to Ross is the blind asking for a lead from the blind.

Tony
.

Relevant Pages

  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... And what is the smallest finite distance? ... LUB of the the reals strictly between 0 and 1 has to be a real strictly ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... So there is still no element within either set which is its LUB. ... If the Finlayson reals are used, indeed the LUB is the maximal member of ... the set of reals in [0,1). ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... So there is still no element within either set which is its LUB. ... the set of reals in [0,1). ... atomic) particles, the smaller the particles appear to be? ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... > Tony Orlow wrote: ... > reals, so it can't possibly denumerate all of the uncountable reals. ... infinite bitstring to represent in that system, ... will require bit strings of infinite length. ...
    (sci.math)
  • Re: Is continuum completely filled up?
    ... requiring a distance to be zero is not sufficient to ... guarantee the absence of a gap. ... reals that is bounded above. ... there are not enough bits to address the reals (and you would still always have as many open intervals as numbers). ...
    (sci.math)
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