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

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> -1 +2 -4 +8

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> +1 -2 +4 -8

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> 0

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> 1 -2 4 -8

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> -1 2 -4 8

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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.)

.=