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.)