Re: Logarithm of transfinite numbers

In article <MPG.1e9b2017605cbc3e98abd2@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

Jonathan Hoyle said:
If you remove only one ball at a time, but first add 10, did you
have -9 balls in the vase at the second to last step?

There is no second to last step, since the set is unbounded. And you
know it. Even you agree that unbounded sets have no last element. If
we are supposed to be engaging in honest discourse here, why do you
write things that you know neither one of us believes?

I am following the rules of the gedanken and your conclusuion is in
contradiction with them. If the vase empties, it is with the removal of a
single ball, since that is the only removal that occurs, according to the
rules
set forth to begin with. There is no way that can occur.

TO forgets the inductive axiom:
If the first ball is removed by the end of the time period
and
if for each ball removed before the end of the time period its
successor is also removed before the end of the time period
then
all balls are removed by the end of the time period.



There is no explanation as to how this could happen, but
there is a very simple explanation that any child can
understand intuitively, that each iteration simply adds 9
balls, and the number grows without bound.

However, no child would "understand intuitively" how balls which were
never added somehow magically materialize in the bin. You added your
own dark magic to the problem, and it will be the undoing of your whole
program.

No one is talking about balls that were not added being in the vase. All
balls
added are in the vase, except the 1/10th that were removed.

TO is talking balls again. Even the ones removed had to be added before
being removed, but by induction, every ball is removed.


You don't need labels, naturals, or any fancy theories to
see that, and if fancy theories contradict such basic logic,
then I can't consider them sound.

Yet your fancy theories which contradict basic logic (fake balls
materializing out of nowhere, and "unbounded finite sets") is any more
sound?

My theory on this issue is about as un-fancy as it gets. You add 9 oo times
and
get 9*oo balls.

But, by induction, EVERY ball is removed.


Sorry, Tony, I think you've finally painted yourself into a corner that
you can't get out of.

Yeah, right, when you explain what happens to make that empty, then we'll
talk
about your corner.

Induction happens.
.

Relevant Pages

  • Re: infinity
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  • Re: infinity
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  • Re: infinity
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  • Re: An uncountable countable set
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  • Re: infinity
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