Date: Feb 17, 2013 9:19 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 Sunday, February 17, 2013 6:16:24 AM UTC-8, Musatov wrote:
> 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).
>
> 0
>
> -1 +2 -4 +8
>
> +1 -2 +4 -8
>
> 0
>
> 1 -2 4 -8
>
> -1 2 -4 8
>
> 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.)
.=