Date: Feb 17, 2013 9:16 AM
Author: 
Subject: Re: Musatov responds to WM on Cantor: intelligence, <br>	real, judge for yourself: Cantor’s idea seems to me to ass<br>	ume because two sets converge to infinity the nature of infi<br>	nity and the number of elements in each set must become equa<br>	l.

On Thursday, June 17, 2010 5:50:29 PM UTC-7, Transfer Principle wrote:
> On Jun 17, 2:37 am, Simplane Simple Plane Simulate Plain Simple
> <marty.musa...@gmail.com> wrote:

> > COMMENTARY
> >         To contrast my conception to my perception of Cantor?s conception of
> > the infinite. Cantor?s idea seems to me to assume because two sets
> > converge to infinity the nature of infinity and the number of elements
> > in each set must become equal.
> >          Requiring one to one ?mapping? anything other than a one to one
> > correspondence is excluded.
> >         My conception is more as infinite quantities are not mathematically
> > expressible, in the sense we can only conceive of infinity as
> > something consisting forever. You start with something finite and then
> > multiply or divide it forever. In this way two infinite sets are not
> > equal but, as shown in they can be ratio-ed by the finite expression
> > defines the set, but both extend infinitely.
> >         Cantor?s reversal of conceptions,  for some sets (non-d enumerable)
> > uses conception #2. This is a contradiction to conception #1, and it
> > would seem to me it can?t be both ways.

>
> Musatov might be interested in knowing about Tony Orlow,
> who is working on a set size that is very similar to
> Conception #1 above.
>
> In particular, Musatov describes how he uses ratios to
> determine that the size of {2,4,6,8,...} is exactly half
> that of {1,2,3,4,...}, since the elements of the sets
> are in the ratio 2:1. TO uses a similar argument to
> conclude that if {1,2,3,4,...} has the set size (or
> "Bigulosity") tav, then {2,4,6,8,...} would have a
> Bigulosity of tav/2.
>
> TO uses the name "Post-Cantorian" to describe those who
> use what Musatov calls "Conception #1," as opposed to the
> "Cantorian" Conception #2. Thus, Musatov and TO are
> natural allies wrt set size.
>
> On the other hand, Herc and WM are "Anti-Cantorian" in
> that they don't believe in different sizes of infinity. So
> I'm glad that Herc and WM are in this thread together. So
> these two reject both Conceptions #1 and #2.
>
> If Musatov would like to learn more about TO's set size,
> he can click on the current TO thread (warning -- this
> thread now exceeds 500 posts).

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On Thursday, June 17, 2010 5:50:29 PM UTC-7, Transfer Principle wrote:
> On Jun 17, 2:37 am, Simplane Simple Plane Simulate Plain Simple
> <marty.musa...@gmail.com> wrote:

> > COMMENTARY
> >         To contrast my conception to my perception of Cantor?s conception of
> > the infinite. Cantor?s idea seems to me to assume because two sets
> > converge to infinity the nature of infinity and the number of elements
> > in each set must become equal.
> >          Requiring one to one ?mapping? anything other than a one to one
> > correspondence is excluded.
> >         My conception is more as infinite quantities are not mathematically
> > expressible, in the sense we can only conceive of infinity as
> > something consisting forever. You start with something finite and then
> > multiply or divide it forever. In this way two infinite sets are not
> > equal but, as shown in they can be ratio-ed by the finite expression
> > defines the set, but both extend infinitely.
> >         Cantor?s reversal of conceptions,  for some sets (non-d enumerable)
> > uses conception #2. This is a contradiction to conception #1, and it
> > would seem to me it can?t be both ways.

>
> Musatov might be interested in knowing about Tony Orlow,
> who is working on a set size that is very similar to
> Conception #1 above.
>
> In particular, Musatov describes how he uses ratios to
> determine that the size of {2,4,6,8,...} is exactly half
> that of {1,2,3,4,...}, since the elements of the sets
> are in the ratio 2:1. TO uses a similar argument to
> conclude that if {1,2,3,4,...} has the set size (or
> "Bigulosity") tav, then {2,4,6,8,...} would have a
> Bigulosity of tav/2.
>
> TO uses the name "Post-Cantorian" to describe those who
> use what Musatov calls "Conception #1," as opposed to the
> "Cantorian" Conception #2. Thus, Musatov and TO are
> natural allies wrt set size.
>
> On the other hand, Herc and WM are "Anti-Cantorian" in
> that they don't believe in different sizes of infinity. So
> I'm glad that Herc and WM are in this thread together. So
> these two reject both Conceptions #1 and #2.
>
> If Musatov would like to learn more about TO's set size,
> he can click on the current TO thread (warning -- this
> thread now exceeds 500 posts).

On Thursday, June 17, 2010 5:57:58 PM UTC-7, Transfer Principle wrote:
> On Jun 17, 12:59 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> > On Jun 17, 1:54 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > Does ZFC not prove that all constructible numbers are countable?
> > I don't know. What is the definition IN THE LANGUAGE of ZFC of
> > 'constructible number'?

>
> I know that the word "constructible" occurs in the context
> of V=L, where L is called the "constructible universe."
>
> So it is possible to call the elements of L intersect R
> "constructible reals"?
>
> (Of course, even if we can, I'm not sure whatOn Thursday, June 17, 2010 5:57:58 PM UTC-7, Transfer Principle wrote:
> On Jun 17, 12:59 pm, MoeBlee <jazzm...@hotmail.com> wrote:

> > On Jun 17, 1:54 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > Does ZFC not prove that all constructible numbers are countable?
> > I don't know. What is the definition IN THE LANGUAGE of ZFC of
> > 'constructible number'?

>
> I know that the word "constructible" occurs in the context
> of V=L, where L is called the "constructible universe."
>
> So it is possible to call the elements of L intersect R
> "constructible reals"?
>
> (Of course, even if we can, I'm not sure what effect, if
> any, this would have on the cardinality of R.)


effect, if
> any, this would have on the cardinality of R.)