The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [...] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp. 303f & 321]

On 12/20/2021 12:46 PM, WM wrote:
> The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [...] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp. 303f & 321]

"... "potentially" infinite in ... mathematics and to suspect them as self-deceptions ..."

Serg io wrote:

> "... "potentially" infinite in ... mathematics and to suspect them as
> self-deceptions ..."

good point.

You can only start at a completed infinity
or a size made up by its inverse element...
infinity multiplied by 1 divided by infinity.
The continuum hypothesis shows how
to build an infinity size by its infinitely small.
This is its inverse fundamental element.

Mitchell Raemsch

måndag 20 december 2021 kl. 19:46:26 UTC+1 skrev WM:
> The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [...] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics.. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp. 303f & 321]
you are so fucking pathetic

On Monday, December 20, 2021 at 1:46:26 PM UTC-5, WM wrote:
> The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [...] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics.. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp. 303f & 321]

So, you don't like infinite sets. Please then define what you mean by a FINITE set, preferably without referring to any numbers.

A set X is said to be FINITE if and only if _______________________________.. (Fill in the blank, no numbers)

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Monday, December 20, 2021 at 10:13:47 PM UTC-8, Dan Christensen wrote:
> On Monday, December 20, 2021 at 1:46:26 PM UTC-5, WM wrote:
> > The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [...] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp. 303f & 321]
> So, you don't like infinite sets. Please then define what you mean by a FINITE set, preferably without referring to any numbers.
>
> A set X is said to be FINITE if and only if _______________________________. (Fill in the blank, no numbers)
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

The continuum hypothesis is right to start at a built size of infinity
made of the unlimited small element..

On Tuesday, December 21, 2021 at 2:22:27 PM UTC-5, mitchr...@gmail.com wrote:
> On Monday, December 20, 2021 at 10:13:47 PM UTC-8, Dan Christensen wrote:
> > On Monday, December 20, 2021 at 1:46:26 PM UTC-5, WM wrote:
> > > The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [....] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp.. 303f & 321]
> > So, you don't like infinite sets. Please then define what you mean by a FINITE set, preferably without referring to any numbers.
> >
> > A set X is said to be FINITE if and only if _______________________________. (Fill in the blank, no numbers)
> >

> The continuum hypothesis is right to start at a built size of infinity
> made of the unlimited small element..

I have found it easier to first define finite sets. Then an infinite set is just one that is not finite. Who could argue with that?

The definition of a Dedekind finite set is relatively easy to justify with a simple thought experiment and a few short, formal proofs. See my blog posting on this topic here: https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Tuesday, December 21, 2021 at 11:44:54 AM UTC-8, Dan Christensen wrote:
> On Tuesday, December 21, 2021 at 2:22:27 PM UTC-5, mitchr...@gmail.com wrote:
> > On Monday, December 20, 2021 at 10:13:47 PM UTC-8, Dan Christensen wrote:
> > > On Monday, December 20, 2021 at 1:46:26 PM UTC-5, WM wrote:
> > > > The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [....] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp. 303f & 321]
> > > So, you don't like infinite sets. Please then define what you mean by a FINITE set, preferably without referring to any numbers.
> > >
> > > A set X is said to be FINITE if and only if _______________________________. (Fill in the blank, no numbers)
> > >
> > The continuum hypothesis is right to start at a built size of infinity
> > made of the unlimited small element..
> I have found it easier to first define finite sets. Then an infinite set is just one that is not finite. Who could argue with that?
>
> The definition of a Dedekind finite set is relatively easy to justify with a simple thought experiment and a few short, formal proofs. See my blog posting on this topic here: https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

an infinite sequence of sameness quantity
is the only infinite set man could complete.
look at the sameness of .9 repeating decimal...
The irrational is repeating differences..
Measuring round shows that we can only
deal with irrationals in a small way.

Mitchell Raemsch

On Tuesday, December 21, 2021 at 2:57:02 PM UTC-5, mitchr...@gmail.com wrote:
> On Tuesday, December 21, 2021 at 11:44:54 AM UTC-8, Dan Christensen wrote:
> > On Tuesday, December 21, 2021 at 2:22:27 PM UTC-5, mitchr...@gmail.com wrote:
> > > On Monday, December 20, 2021 at 10:13:47 PM UTC-8, Dan Christensen wrote:
> > > > On Monday, December 20, 2021 at 1:46:26 PM UTC-5, WM wrote:
> > > > > The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [...] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp. 303f & 321]
> > > > So, you don't like infinite sets. Please then define what you mean by a FINITE set, preferably without referring to any numbers.
> > > >
> > > > A set X is said to be FINITE if and only if _______________________________. (Fill in the blank, no numbers)
> > > >
> > > The continuum hypothesis is right to start at a built size of infinity
> > > made of the unlimited small element..
> > I have found it easier to first define finite sets. Then an infinite set is just one that is not finite. Who could argue with that?
> >
> > The definition of a Dedekind finite set is relatively easy to justify with a simple thought experiment and a few short, formal proofs. See my blog posting on this topic here: https://dcproof.wordpress.com/2014/09/17/infinity-the-story-so-far/
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com
> an infinite sequence of sameness quantity
> is the only infinite set man could complete.
> look at the sameness of .9 repeating decimal...
> The irrational is repeating differences..
> Measuring round shows that we can only
> deal with irrationals in a small way.
>

I prefer the example of the set of natural numbers. Much simple and much more intuitive. Every natural number has a unique successor. If a number has a predecessor, then it too is unique. There is a "first number" with no predecessor. Believe it or not, this alone guarantees that the set of natural number is infinite. (See the above link.)

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

tisdag 21 december 2021 kl. 20:22:27 UTC+1 skrev mitchr...@gmail.com:
> On Monday, December 20, 2021 at 10:13:47 PM UTC-8, Dan Christensen wrote:
> > On Monday, December 20, 2021 at 1:46:26 PM UTC-5, WM wrote:
> > > The author aims [...] to make cognizant numerically the exterior as well as the interior finite limits of controllably regulated mathematics [....] At a time where metamathematical considerations still are based on set theory it may appear bold or foolish if one tackles on such a low level to criticize not only the ideas of "actual" infinities in classical mathematics but also the attitude to the "potentially" infinite in constructivistic mathematics and to suspect them as self-deceptions by "verbally" suggested topics. [E. Wette: "Vom Unendlichen zum Endlichen", Dialectica 24,4 (1970) pp.. 303f & 321]
> > So, you don't like infinite sets. Please then define what you mean by a FINITE set, preferably without referring to any numbers.
> >
> > A set X is said to be FINITE if and only if _______________________________. (Fill in the blank, no numbers)
> >
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com
> The continuum hypothesis is right to start at a built size of infinity
> made of the unlimited small element..
you still do not know what the continuum hypothesis says