Re: Logarithm of transfinite numbers

Jonathan Hoyle said:
If you think that this process could ever result in an empty vase,
then please explain how it gets empty.

Sure, as soon as you explain to me how a ball with an infinite label
appears there at the end when (by rule) it is never added. Your
"magic" does not seem to be any better than mine. The difference is,
my "magic" doesn't involve a direct logical contradiction, whereas your
does. Mine is merely counter-intuitive.

You remove only one ball at a time, so at some point there must
be 1 ball in the vase for it to empty.

Why do you say that must that be the case? It is certainly not true as
far as I can tell. At *NO* point is there ever one ball in the bin.

Do you ever remove more than one at a time? No. Does the vase become empty?
According to you. So, how many balls were in the vase right before it became
empty? 9*aleph_0? Yes, you have a contradiction here. According to the
gedanken, you must have had -9 balls in order to empty the vase.


It's conclusions like this that motivate me to replace this theory
with something sane.

How sane is it to have balls found in the bin that were never added, as
you claim?

That answer was qualified with "if the gedanken makes any sense at all", or
something. it's based on some notion of a definite end to the set, but it's
just another "largest finite" kind of argument.


I simply cannot accept that this artificial notion of labeling the
balls makes any difference in what is obviously a sum of an
infinite number of 9's.

I simply cannot accept YOUR artificial notion that balls with labels
like "aleph_0" somehow materialize in the bin, when they were never
added.

I didn't label the balls. I don't need labels. Nobody does, to see that the
number of balls grows 9 at a time without bound.


If that's not hoocus pocus, I don't know what is.

Your hocus pocus is no better: Transporting a ball with an aleph_0
labels, in Star Trek fashion, into a bin when it was never never added.

You ask about the labels. I say they don't matter. The balls are all labeled
'1', okay. It doesn't matter. This is one of many reasons I cannot ascribe to
transfinite set theory.


Sorry. All you have done is replace a counter-intuive result with one
which is self-contradictory. I'll take the counter-intuitive one. At
least that one is consistent and honest to the facts of the case.

No I replace your "counterintuitive" answer with a simple straightforward one.
The balls grow without bound, 9 at a time.


Regards,

Jonathan



--
Smiles,

Tony
.

Relevant Pages

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  • Re: Logarithm of transfinite numbers
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  • Re: Logarithm of transfinite numbers
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