Matheology §252

[WM]

Matheology §252

The table T

1
2, 1
3, 2, 1
...
n, ..., 3, 2, 1
...

is a sequence of finite initial segments (1, ..., n) of natural
numbers. It contains every natural number that can be somewhere. Every
number in the sequence T is in one line L_n and in all further lines
by construction of T (always the last line is added). Every number in
T is in the first column C (and in every other column too).

forall n : (1, ..., n) c C ==> (1, ..., n) e T
forall n : (1, ..., n) e T ==> (1, ..., n) c C

Therefore it is impossible that C contains more than T and more than
any line L_n of T. But we know that there is no line L_n with an
actually infite set |N of numbers (because T is a sequence of finite
lines L_n). Conclusion: An actually infinite set |N cannot be in the
first column either (and nowhere else).

Regards, WM

[fom]

On 4/17/2013 7:18 AM, WM wrote:
> Matheology §252
>
> The table T
>
> 1
> 2, 1
> 3, 2, 1
> ...
> n, ..., 3, 2, 1
> ...
>
> is a sequence of finite initial segments (1, ..., n) of natural
> numbers. It contains every natural number that can be somewhere.

WM is an unabashed ultrafinitist who refuses to fix
a largest finite number. Each "n" in his description
depends on the subsequence of triangular numbers.

> F(n)=Sum_i(1..n)(i)
>
> 1 :=> 1
> 2 :=> 3
> 3 :=> 6
> 4 :=> 10
>
> and so on

According to Brouwerian intuitionistic reasoning,
when WM's construction reaches the point where
the sequence of triangular numbers exceeds the
ultrafinitist limit, the contradiction nullifies
the construction.

This is WM's model of mathematics:

http://en.wikipedia.org/wiki/Finite_model_property

until he reaches his contradiction and
it vanishes.

[Virgil]

In article
<7e4d8d16-1361-4e90...@f18g2000vbs.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> Matheology �252
>
> The table T
>
> 1
> 2, 1
> 3, 2, 1
> ...
> n, ..., 3, 2, 1
> ...
>
> is a sequence of finite initial segments (1, ..., n) of natural
> numbers. It contains every natural number that can be somewhere. Every
> number in the sequence T is in one line L_n and in all further lines
> by construction of T (always the last line is added).

If there is a last line, then what WM claims of T is false.

Every number in
> T is in the first column C (and in every other column too).
>
> forall n : (1, ..., n) c C ==> (1, ..., n) e T
> forall n : (1, ..., n) e T ==> (1, ..., n) c C
>
> Therefore it is impossible that C contains more than T and more than
> any line L_n of T.

Only half true. A column contains no more that the whole table but
always contains more than any one row/line of that table.

> But we know

What WM claims to know is far too often only knownable within
Wolkenmuekenheim, from which all sane mathematicians are, thankfully,
forever banned by their sanity and logic.
--

[Virgil]

In article
<7e4d8d16-1361-4e90...@f18g2000vbs.googlegroups.com>,
WM <muec...@rz.fh-augsburg.de> wrote:

> Matheology �252
>
> The table T
>
> 1
> 2, 1
> 3, 2, 1
> ...
> n, ..., 3, 2, 1
> ...
>
> is a sequence of finite initial segments (1, ..., n) of natural
> numbers. It contains every natural number that can be somewhere. Every
> number in the sequence T is in one line L_n and in all further lines
> by construction of T (always the last line is added). Every number in
> T is in the first column C (and in every other column too).
>

>

> Therefore it is impossible that C contains more than T and more than
> any line L_n of T.

The first column of T, indeed any column of T, clearly contains more
that any row/line in T.

For any line n of T, every column contains at least max(line n) + 1,
which is never in line n.

So once again, as usual, WM is entirely wrong!
--

[WM]

On 17 Apr., 22:09, Virgil <vir...@ligriv.com> wrote:
> In article
> <7e4d8d16-1361-4e90-b2f3-8f75eeca2...@f18g2000vbs.googlegroups.com>,

>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > Matheology 252
>
> > The table T
>
> > 1
> > 2, 1
> > 3, 2, 1
> > ...
> > n, ..., 3, 2, 1
> > ...
>
> > is a sequence of finite initial segments (1, ..., n) of natural
> > numbers. It contains every natural number that can be somewhere. Every
> > number in the sequence T is in one line L_n and in all further lines
> > by construction of T (always the last line is added).
>
> If there is a last line, then what WM claims of T is false.
>
> Every number in
>
> > T is in the first column C (and in every other column too).
>
> > forall n : (1, ..., n) c C ==> (1, ..., n) e T
> > forall n : (1, ..., n) e T ==> (1, ..., n) c C
>
> > Therefore it is impossible that C contains more than T and more than
> > any line L_n of T.
>
> Only half true. A column contains no more that the whole table  but
> always contains more than any one row/line of that table.

Up to any line L_n it is clear that C contains not more than that
line.
If C should contain more than all lines, then it has to go beyond all
lines.
That is matheology.

C is a subset of the union of all lines.
The union of all lines cannot contain more natural numbers than the
sets of the sequence T of all lines, can it?

Do you really claim that when unioning the elements of T you get more
natural numbers than are in the elements of T?

Then you have an opinion

> from which all sane mathematicians are, thankfully,
> forever banned by their sanity and logic.

Then you can act like a God and do abiogenesis: You union sets and get
more elements than are in the sets. Of course you cannot name any one
of the new elements. But you are sure, they have been created by you,
Virgil, acting like a God.

And if you union again? Again create some creatures? Will this
continue? Or is there some supremum?

My godness. What a perverted concept of the formerly so respected
mathematics!

Regards, WM

[fom]

On 4/18/2013 1:07 AM, WM wrote:
>
>
> Or is there some supremum?
>

You first.

WM is an unabashed ultrafinitist who refuses to fix
a largest finite number. Each "n" in his description
depends on the subsequence of triangular numbers.

> F(n)=Sum_i(1..n)(i)
>
> 1 :=> 1
> 2 :=> 3
> 3 :=> 6
> 4 :=> 10
>
> and so on

According to Brouwerian intuitionistic reasoning,
when WM's construction reaches the point where
the sequence of triangular numbers exceeds the
ultrafinitist limit, the contradiction nullifies
the construction.

This is WM's model of mathematics:

http://en.wikipedia.org/wiki/Finite_model_property

until he reaches his contradiction and
it vanishes.

=====================================

The triangular numbers correspond with
the number of 'marks' representing numerals
or significant denotations occurring in any
of WM' representations of the form:

1
2, 1
3, 2, 1
...
n, ..., 3, 2, 1
...

-------------------------------------

This number of 'marks' satisfies a structural
feature of the natural numbers called a
directed set:

Defintion

A binary relation >= in a set D is said
to direct D if and only if D is nonempty
and the following three conditions are
satisfied:

DS1)

If a is an element of D, then a>=a

DS2)

If a, b, c are elements of D such
that a>=b and b>=c, then a>=c

DS3)

If a and b are elements of D, then there
exists an element c of D such that c>=a
and c>=b


So, WM's geometric reasoning for any given
n obtains a finite model domain with its
cardinality given by the associated
triangular number. The triangular number
is the "element c" of condition DS3 from
the definition.

-------------------------------------

Finally, Brouwer's explanation for finitary
reasoning is used because WM refuses to
commit to any mathematical statement with
coherent consistent usage.

Brouwer distinguishes between results with
regard to 'endless', 'halted' and
'contradictory' in his explanations

"A set is a law on the basis of
which, if repeated choices of
arbitrary natural numbers are made,
each of these choices either
generates a definite sign series,
with or without termination of the
process, or brings about the
inhibition of the process together
with the definitive annihilation
of its result."

WM cannot be an ultrafinitist and
expect others to not hold him to
task for it. In constrast to
Brouwer, he repeatedly states
that there is absolutely no
completed infinity. Therefore,
there must be a maximal natural
number for his model of
mathematics. Beyond that
number, there is no mathematics.

That is WM's belief as surmised
from statements and reasoning
as opposed to what he says with
rhetoric.

[WM]

On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:

> WM cannot be an ultrafinitist and
> expect others to not hold him to
> task for it.

There is a third way: potential infinity.

>  In constrast to
> Brouwer, he repeatedly states
> that there is absolutely no
> completed infinity.

Brouwer also states that. Brouwer accepts infinite sequences that can
be defined by a finite definition like 0.111... Why the finite
definition? because there is no chance to get an actually infinite
chain of symbols 1 (or any other period).

> Therefore,
> there must be a maximal natural
> number for his model of
> mathematics.

There is no fixed maximal number! The upper threshold depends on many
circumstances, including time and the state of the observer or
mathematician.

Relativity is always difficult to understand and hard to swallow. In
physics that was not different:
http://www.ekkehard-friebe.de/Hundert-Autoren.pdf

Regards, WM

[fom]

On 4/18/2013 1:42 AM, WM wrote:
> On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
>
>> WM cannot be an ultrafinitist and
>> expect others to not hold him to
>> task for it.
>
> There is a third way: potential infinity.
>

WM had been given examples of how that
third way is implemented *mathematically*.

WM cannot understand his own beliefs.

WM cannot be an ultrafinitist and
expect others to not hold him to

task for it. In constrast to

Brouwer, he repeatedly states
that there is absolutely no

completed infinity. Therefore,

there must be a maximal natural
number for his model of

[fom]

On 4/18/2013 1:42 AM, WM wrote:

> On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
>
>> In constrast to
>> Brouwer, he repeatedly states
>> that there is absolutely no
>> completed infinity.
>
> Brouwer also states that. Brouwer accepts infinite sequences that can
> be defined by a finite definition like 0.111... Why the finite
> definition? because there is no chance to get an actually infinite
> chain of symbols 1 (or any other period).
>

Brouwer speaks of rule-governed
endless process.

The Russian constructivists represent
that with algorithms.

WM does not know what a mathematical
rule-governed process is.

WM rejects cosntructive mathematics.

WM cannot be an ultrafinitist and
expect others to not hold him to

task for it. In constrast to

Brouwer, he repeatedly states
that there is absolutely no

completed infinity. Therefore,

there must be a maximal natural
number for his model of

[fom]

On 4/18/2013 1:42 AM, WM wrote:

> On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
>
>> Therefore,
>> there must be a maximal natural
>> number for his model of
>> mathematics.
>
> There is no fixed maximal number!

To quote from the end of the passage
which follows:

"That is WM's belief as surmised
from statements and reasoning
as opposed to what he says with
rhetoric."

WM cannot be an ultrafinitist and
expect others to not hold him to

task for it. In constrast to

Brouwer, he repeatedly states
that there is absolutely no

completed infinity. Therefore,

there must be a maximal natural
number for his model of

[WM]

On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
> On 4/18/2013 1:42 AM, WM wrote:
>
> > On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
>
> >>   In constrast to
> >> Brouwer, he repeatedly states
> >> that there is absolutely no
> >> completed infinity.
>
> > Brouwer also states that. Brouwer accepts infinite sequences that can
> > be defined by a finite definition like 0.111... Why the finite
> > definition? because there is no chance to get an actually infinite
> > chain of symbols 1 (or any other period).
>
> Brouwer speaks of rule-governed
> endless process.

And in contrast to matheologians he knows that a rule is a finite
definition.

>
> The Russian constructivists represent
> that with algorithms.

Finite, anyhow.

>
> WM does not know what a mathematical
> rule-governed process is.

Divide 1 by 9, then you have an example probably easy enough for you
to understand.

> According to Brouwerian intuitionistic reasoning,
> when WM's construction reaches the point where
> the sequence of triangular numbers exceeds the
> ultrafinitist limit, the contradiction nullifies
> the construction.

But not according to potential infinity. On the other hand, it is
clear that there is no number with 20 digits on a pocket calculator.
In MatheRealism there is no largest number but a largest komplexity of
number definitions.

>
> This is WM's model of mathematics:

No.

Regards, WM

[fom]

On 4/18/2013 1:42 AM, WM wrote:
>
>

> The upper threshold depends on many
> circumstances, including time and the state of the observer or
> mathematician.
>

Yes. There is a Zen notion about
trees falling and noises being made.

In that sense, WM is correct. But,
then, WM should not deny how that
colors his belief:

WM cannot be an ultrafinitist and
expect others to not hold him to

task for it. In constrast to

Brouwer, he repeatedly states
that there is absolutely no

completed infinity. Therefore,

there must be a maximal natural
number for his model of

[fom]

On 4/18/2013 2:07 AM, WM wrote:

> On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
>>
>> WM does not know what a mathematical
>> rule-governed process is.
>
> Divide 1 by 9, then you have an example probably easy enough for you
> to understand.
>

Yes. Something -- namely, an algorithm --
by which the rule-governed constructive
mathematics of Markov and Sanin developed
Brouwer's idea of rule-governed mathematics.

WM DENIED THIS MATHEMATICS AND SHOULD
BE EMBARRASSED TO SUGGEST THAT HE DID
NOT!!!!!!!!!!!

WM is an unabashed ultrafinitist who refuses to fix
a largest finite number. Each "n" in his description
depends on the subsequence of triangular numbers.

> F(n)=Sum_i(1..n)(i)
>
> 1 :=> 1
> 2 :=> 3
> 3 :=> 6
> 4 :=> 10
>
> and so on

According to Brouwerian intuitionistic reasoning,
when WM's construction reaches the point where
the sequence of triangular numbers exceeds the
ultrafinitist limit, the contradiction nullifies
the construction.

This is WM's model of mathematics:

task for it. In constrast to

Brouwer, he repeatedly states
that there is absolutely no

[fom]

On 4/18/2013 2:07 AM, WM wrote:

> On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
>
>> According to Brouwerian intuitionistic reasoning,
>> when WM's construction reaches the point where
>> the sequence of triangular numbers exceeds the
>> ultrafinitist limit, the contradiction nullifies
>> the construction.
>
> But not according to potential infinity.

WM had been offered the opportunity to
embrace the definition of quantification
over constructive objects developed by
Markov.

WM REFUSED TO ACCEPT THE CONSTRUCTIVE
INTERPRETATION OF QUANTIFICATION.

WM HAS NEVER DEFINED 'POTENTIAL INFINITY'
IN A PRECISE MATHEMATICAL SENSE THAT IS
DIFFERENTIATED FROM THE DOMAIN OF THE
AXIOMS HE DENIES!!!!!

WM is an unabashed ultrafinitist who refuses to fix
a largest finite number. Each "n" in his description
depends on the subsequence of triangular numbers.

> F(n)=Sum_i(1..n)(i)
>
> 1 :=> 1
> 2 :=> 3
> 3 :=> 6
> 4 :=> 10
>
> and so on

According to Brouwerian intuitionistic reasoning,
when WM's construction reaches the point where
the sequence of triangular numbers exceeds the
ultrafinitist limit, the contradiction nullifies
the construction.

This is WM's model of mathematics:

task for it. In constrast to

Brouwer, he repeatedly states
that there is absolutely no

[Virgil]

In article
<7256d794-e1a7-4366...@b3g2000vbo.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:


> Up to any line L_n it is clear that C contains not more than that
> line.

So a suitably truncated column cotains no more than some line, but when
not truncated contains more than any one line.

> If C should contain more than all lines, then it has to go beyond all
> lines.

C does go past every line, unless WM can name a line that it does not go
past.

>
> C is a subset of the union of all lines.

Just as |N is a subset of the union of all FISONs, by not a subset of
any one FISON.

>
> Then you can act like a God and do abiogenesis: You union sets and get
> more elements than are in the sets.

I union all FISONs and get |N, but there is no element in |N that is not
is infinitely many FISONs.

>
> My godness. What a perverted concept of the formerly so respected
> mathematics!

Perversion of mathematics in the name of the game in WMytheology.
--

[Virgil]

In article
<4ab7c57a-19d2-4302...@f18g2000vbs.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
>
> > WM cannot be an ultrafinitist and
> > expect others to not hold him to
> > task for it.
>
> There is a third way: potential infinity.

If there is a form of consistent mathematics using only potential
infiniteness, WM has yet to find it, as what he claims in
Wolkenmuekenheim, is not at all self-consistent, nor honest mathematics.
--

[Virgil]

In article
<2df0c0d7-5d79-4ad4...@c9g2000vbr.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On the other hand, it is
> clear that there is no number with 20 digits on a pocket calculator.

Many of them can deal with 10^20 , which is a 20 digit number, and a
few, like mine, can deal with the digital form of 10^20 -1, with or
without commas.

And I have it in my pocket as I write this, and usually carry it in my
pocket everywhere.
--

[Bergholt Stuttley Johnson]

WM wrote:
> On the other hand, it is
> clear that there is no number with 20 digits on a pocket calculator.

http://www.wolframalpha.com/input/?i=1000!

2568 digits

[WM]

On 18 Apr., 09:15, fom <fomJ...@nyms.net> wrote:
> On 4/18/2013 2:07 AM, WM wrote:
>
> > On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
>
> >> WM does not know what a mathematical
> >> rule-governed process is.
>
> > Divide 1 by 9, then you have an example probably easy enough for you
> > to understand.
>
> Yes. Something -- namely, an algorithm --
> by which the rule-governed constructive
> mathematics of Markov and Sanin developed
> Brouwer's idea of rule-governed mathematics.
>
> WM DENIED THIS MATHEMATICS

No. The algorithm exists. But it will never yield a complete infinite
decimal string equal to 1/9. Every index of a 1 of that string that
you can name, imagine, or think is finite. Obviously it is the
greatest you can name, when attempting to name the greates you can
(why should you have chated yourself?). Mathematics is discussing
topics of numbers and figures. If you cannot discuss about a greater
number than that one you just imagine, then there is not a greater
number for you at just this time. That does not mean that number
remains always your greates. Simple as that.

Regards, WM

[fom]

On 4/18/2013 3:38 AM, WM wrote:
> On 18 Apr., 09:15, fom <fomJ...@nyms.net> wrote:
>> On 4/18/2013 2:07 AM, WM wrote:
>>
>>> On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
>>
>>>> WM does not know what a mathematical
>>>> rule-governed process is.
>>
>>> Divide 1 by 9, then you have an example probably easy enough for you
>>> to understand.
>>
>> Yes. Something -- namely, an algorithm --
>> by which the rule-governed constructive
>> mathematics of Markov and Sanin developed
>> Brouwer's idea of rule-governed mathematics.
>>
>> WM DENIED THIS MATHEMATICS
>
> No.

YES. WM DID.

I SPENT A LOT OF TIME WHEN I
FIRST STARTED READING THESE
THREADS TRYING TO CORRELATE
WM'S STATEMENTS WITH STANDARD
MATHEMATICS.

WM IS BEING DISHONEST

WM IS EXACTLY WHAT THE ANALYSIS
CLAIMS

[WM]

On 18 Apr., 09:22, Virgil <vir...@ligriv.com> wrote:
> In article

> <7256d794-e1a7-4366-9f47-c6294e2d3...@b3g2000vbo.googlegroups.com>,

>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > Up to any line L_n it is clear that C contains not more than that
> > line.
>
> So a suitably truncated column cotains no more than some line, but when
> not truncated contains more than any one line.

More than any "given" line. But here the question reads: Does A
contain more than any present line?

By construction every set of numbers of T is a subset of some line.
You can see this, when, during construction of T, all lines L_n with n
< m are removed when line L_m is added. This will yield a sequence
T = (1), (1, 2), (1, 2, 3), ...

Is there any natural number in this sequence at all?
Is there any natural number in this sequence that is missing in the
first column C?
Is there any natural number in C that is missing in T?

How do your answers change, when the construction of T is done by
unioning instead of appending?
All lines L_n with n < m are uniond with L_m when line L_m is added.

Regards, WM

[WM]

On 18 Apr., 09:26, Virgil <vir...@ligriv.com> wrote:
> In article

> <4ab7c57a-19d2-4302-b030-8552e90c4...@f18g2000vbs.googlegroups.com>,

>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
>
> > > WM cannot be an ultrafinitist and
> > > expect others to not hold him to
> > > task for it.
>
> > There is a third way: potential infinity.
>
> If there is a form of consistent mathematics using only potential
> infiniteness, WM has yet to find it,

Cauchy, Gauss, Weierstraß, Kronecker, Poincaré, Brouwer have left a
lot of writings about that system. No need to re-invent it. Read it!

Regards, WM

[WM]

On 18 Apr., 09:30, Virgil <vir...@ligriv.com> wrote:
> In article

> <2df0c0d7-5d79-4ad4-8e10-b239c016b...@c9g2000vbr.googlegroups.com>,

>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > On the other hand, it is
> > clear that there is no number with 20 digits on a pocket calculator.
>
> Many of them can deal with 10^20 , which is a 20 digit number, and a
> few, like mine, can deal with the digital form of 10^20 -1, with or
> without commas.
>
> And I have it in my pocket as I write this, and usually carry it in my
> pocket everywhere.
> --

You must be lucky man.
Of course I addressed those who are less lucky.

Regards, WM

[fom]

On 4/18/2013 3:52 AM, WM wrote:
> On 18 Apr., 09:22, Virgil <vir...@ligriv.com> wrote:
>> In article
>> <7256d794-e1a7-4366-9f47-c6294e2d3...@b3g2000vbo.googlegroups.com>,
>>
>> WM <mueck...@rz.fh-augsburg.de> wrote:
>>> Up to any line L_n it is clear that C contains not more than that
>>> line.
>>
>> So a suitably truncated column cotains no more than some line, but when
>> not truncated contains more than any one line.
>
> More than any "given" line. But here the question reads: Does A
> contain more than any present line?
>
> By construction every set of numbers of T is a subset of some line.

Nope.

T is the table.

T has the count of a triangular number.

WM is an unabashed ultrafinitist who refuses to fix
a largest finite number. Each "n" in his description
depends on the subsequence of triangular numbers.

> F(n)=Sum_i(1..n)(i)
>
> 1 :=> 1
> 2 :=> 3
> 3 :=> 6
> 4 :=> 10
>
> and so on

According to Brouwerian intuitionistic reasoning,
when WM's construction reaches the point where
the sequence of triangular numbers exceeds the
ultrafinitist limit, the contradiction nullifies
the construction.

This is WM's model of mathematics:

http://en.wikipedia.org/wiki/Finite_model_property

until he reaches his contradiction and
it vanishes.

=====================================

The triangular numbers correspond with
the number of 'marks' representing numerals
or significant denotations occurring in any
of WM' representations of the form:

1
2, 1
3, 2, 1
...
n, ..., 3, 2, 1
...

WM cannot be an ultrafinitist and
expect others to not hold him to

[fom]

Only WM is re-inventing anything.

There is an entire body of mathematics based on
properly defined principles that has been developed.

WM will not abide by those principles. The comparison
is illusory.

WM cannot be an ultrafinitist and
expect others to not hold him to

task for it. In constrast to

Brouwer, he repeatedly states
that there is absolutely no

completed infinity. Therefore,

there must be a maximal natural
number for his model of

[WM]

On 18 Apr., 10:46, fom <fomJ...@nyms.net> wrote:
> On 4/18/2013 3:38 AM, WM wrote:
>
>
>
>
>
> > On 18 Apr., 09:15, fom <fomJ...@nyms.net> wrote:
> >> On 4/18/2013 2:07 AM, WM wrote:
>
> >>> On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
>
> >>>> WM does not know what a mathematical
> >>>> rule-governed process is.
>
> >>> Divide 1 by 9, then you have an example probably easy enough for you
> >>> to understand.
>
> >> Yes. Something -- namely, an algorithm --
> >> by which the rule-governed constructive
> >> mathematics of Markov and Sanin developed
> >> Brouwer's idea of rule-governed mathematics.
>
> >> WM DENIED THIS MATHEMATICS
>
> > No.
>
> YES.  WM DID.
>
> I SPENT A LOT OF TIME

Obviously not enough. The required time depends on the state of the
person too.
Compare Brouwer who answered a request for slowing down in class by:
"I'll try to speak as slow as the gentlemen can think." But it is hard
to stick to such constrictions.

Regards, WM

[fom]

On 4/18/2013 4:05 AM, WM wrote:
> On 18 Apr., 10:46, fom <fomJ...@nyms.net> wrote:
>> On 4/18/2013 3:38 AM, WM wrote:
>>
>>
>>
>>
>>
>>> On 18 Apr., 09:15, fom <fomJ...@nyms.net> wrote:
>>>> On 4/18/2013 2:07 AM, WM wrote:
>>
>>>>> On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
>>
>>>>>> WM does not know what a mathematical
>>>>>> rule-governed process is.
>>
>>>>> Divide 1 by 9, then you have an example probably easy enough for you
>>>>> to understand.
>>
>>>> Yes. Something -- namely, an algorithm --
>>>> by which the rule-governed constructive
>>>> mathematics of Markov and Sanin developed
>>>> Brouwer's idea of rule-governed mathematics.
>>
>>>> WM DENIED THIS MATHEMATICS
>>
>>> No.
>>
>> YES. WM DID.
>>
>> I SPENT A LOT OF TIME
>
> Obviously not enough.

MORE THAN ENOUGH.

THERE IS A LAZY SIMPLETON WHO DOES NOT READ POSTS.

THAT IS NOT ME.

[Alan Smaill]

WM <muec...@rz.fh-augsburg.de> writes:

> On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
>
>> WM cannot be an ultrafinitist and
>> expect others to not hold him to
>> task for it.
>
> There is a third way: potential infinity.
>
>>  In constrast to
>> Brouwer, he repeatedly states
>> that there is absolutely no
>> completed infinity.
>
> Brouwer also states that.

Where?

He has no problem with omega as an ordinal number ....


> Regards, WM

--
Alan Smaill

[Virgil]

In article
<5671c13a-7063-4f88...@c7g2000vbe.googlegroups.com>,

Such luck is merely a matter of having the purchase price and knowing
where to shop.
--

[Virgil]

In article
<c3db7102-72fe-495f...@b3g2000vbo.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 18 Apr., 09:26, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <4ab7c57a-19d2-4302-b030-8552e90c4...@f18g2000vbs.googlegroups.com>,
> >
> > �WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
> >
> > > > WM cannot be an ultrafinitist and
> > > > expect others to not hold him to
> > > > task for it.
> >
> > > There is a third way: potential infinity.
> >
> > If there is a form of consistent mathematics using only potential
> > infiniteness, WM has yet to find it,
>

> Cauchy, Gauss, Weierstra�, Kronecker, Poincar�, Brouwer have left a

> lot of writings about that system. No need to re-invent it. Read it!

If WM has read it, it has been to no avail for him, as whatever he has
learnt from it , it is not mathematics.
--

[Virgil]

In article
<35855cb7-5814-4120...@x14g2000vba.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 18 Apr., 09:22, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <7256d794-e1a7-4366-9f47-c6294e2d3...@b3g2000vbo.googlegroups.com>,
> >
> > �WM <mueck...@rz.fh-augsburg.de> wrote:
> > > Up to any line L_n it is clear that C contains not more than that
> > > line.
> >
> > So a suitably truncated column cotains no more than some line, but when
> > not truncated contains more than any one line.
>
> More than any "given" line. But here the question reads: Does A
> contain more than any present line?

Mote than any one line however selected.

>
> By construction every set of numbers of T is a subset of some line.

Wrong! Outside of Wolkenmuekenheim there is a set having one member of
from line which is not a subset of any line.

> You can see this, when, during construction of T

I cannot cross my eyes far enough to see that.

>
> How do your answers change, when the construction of T is done by
> unioning instead of appending?
> All lines L_n with n < m are uniond with L_m when line L_m is added.

Quite so, but there is no last line, even though |N is the union of all
lines.
--

[Virgil]

In article
<a0d9bff8-d403-4900...@s9g2000vba.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 18 Apr., 09:15, fom <fomJ...@nyms.net> wrote:
> > On 4/18/2013 2:07 AM, WM wrote:
> >
> > > On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
> >
> > >> WM does not know what a mathematical
> > >> rule-governed process is.
> >
> > > Divide 1 by 9, then you have an example probably easy enough for you
> > > to understand.
> >
> > Yes. Something -- namely, an algorithm --
> > by which the rule-governed constructive
> > mathematics of Markov and Sanin developed
> > Brouwer's idea of rule-governed mathematics.
> >
> > WM DENIED THIS MATHEMATICS
>
> No. The algorithm exists. But it will never yield a complete infinite
> decimal string equal to 1/9. Every index of a 1 of that string that
> you can name, imagine, or think is finite.

It is not the size of any one index but the number of different indices
that is not finite.

> Obviously it is the
> greatest you can name

Why even try to name what does not exist, a greatest member.

> when attempting to name the greates

Why even try to name what does not exist, a greatest member.

you can
> (why should you have chated yourself?). Mathematics is discussing
> topics of numbers and figures. If you cannot discuss about a greater
> number than that one you just imagine, then there is not a greater
> number for you at just this time. That does not mean that number
> remains always your greates. Simple as that.

Given any alleged "greatest" natural, one can always double it proving
that it was not a greatest natural after all.

Or does WM claim to be able to produce a natural which cannot be
multiplied by 2 to give yet a larger natural?
--

[Virgil]

In article
<b0a315c9-ceb0-405c...@m1g2000vbe.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 18 Apr., 10:46, fom <fomJ...@nyms.net> wrote:
> > On 4/18/2013 3:38 AM, WM wrote:
> >
> >
> >
> >
> >
> > > On 18 Apr., 09:15, fom <fomJ...@nyms.net> wrote:
> > >> On 4/18/2013 2:07 AM, WM wrote:
> >
> > >>> On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote:
> >
> > >>>> WM does not know what a mathematical
> > >>>> rule-governed process is.
> >
> > >>> Divide 1 by 9, then you have an example probably easy enough for you
> > >>> to understand.
> >
> > >> Yes. Something -- namely, an algorithm --
> > >> by which the rule-governed constructive
> > >> mathematics of Markov and Sanin developed
> > >> Brouwer's idea of rule-governed mathematics.
> >
> > >> WM DENIED THIS MATHEMATICS
> >
> > > No.
> >
> > YES. �WM DID.
> >
> > I SPENT A LOT OF TIME
>
> Obviously not enough. The required time depends on the state of the
> person too.

Which explains why WM is too slow to ever reach infinite sets.
--

[fom]

On 4/18/2013 3:38 AM, WM wrote:
>

> Mathematics is discussing
> topics of numbers and figures.
>

Look! No functions.

Look! No relations.

WM needs to stop reminiscing about the
good old days of Euler and the purity
of Neolithic Man before him.

======================================

[fom]

On 4/18/2013 1:46 AM, fom wrote:
> On 4/18/2013 1:42 AM, WM wrote:

>> On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote:
>>
>>> WM cannot be an ultrafinitist and
>>> expect others to not hold him to
>>> task for it.
>>

>> There is a third way: potential infinity.
>>
>

> WM had been given examples of how that
> third way is implemented *mathematically*.
>
> WM cannot understand his own beliefs.
>

http://en.wikipedia.org/wiki/Doxastic_logic#Types_of_reasoners

see "peculiar reasoner"
-necessarily inaccurate

compare "conceited reasoner"
-will lapse into inaccuracy

from "peculiar reasoner"
http://en.wikipedia.org/wiki/Moore%27s_paradox

"There is currently no generally accepted explanation
of Moore's Paradox in the philosophical literature.
However, while Moore's Paradox remains a philosophical
curiosity, Moorean-type sentences are used by logicians,
computer scientists, and those working in the artificial
intelligence community as examples of cases in which a
knowledge, belief, or information system is unsuccessful
in updating its knowledge/belief/information store in
light of new or novel information"

[fom]

from "moore's paradox"

"Many philosophers -- though by no means all -- also hold
that Moore's Paradox arises not only at the level of
assertion but also at the level of belief. Interestingly,
one who believes an instance of a Moorean sentence is
tantamount to one who is subject to or engaging in
self-deception, at least on one standard way of
describing it.

http://en.wikipedia.org/wiki/Self-deception

In other words, does this describe what the readers
of this thread consider to be the state of affairs
for WM?

"WM believes that

(|N is a completed infinity and WM does not believe
that |N is a completed infinity)"

[WM]

On 18 Apr., 22:09, Virgil <vir...@ligriv.com> wrote:

> > No. The algorithm exists. But it will never yield a complete infinite
> > decimal string equal to 1/9. Every index of a 1 of that string that
> > you can name, imagine, or think is finite.
>
> It is not the size of any one index but the number of different indices
> that is not finite.

The number of indices is a number. Up to any finite index it is a
finite number.

>
> > Obviously it is the
> > greatest you can name
>
> Why even try to name what does not exist, a greatest member.

Try to name the greatest number that you can name. Or try to name a
greater number than all you have known.

Regards, WM

[fom]

On 4/19/2013 4:23 AM, WM wrote:
> On 18 Apr., 22:09, Virgil <vir...@ligriv.com> wrote:
>
>>> No. The algorithm exists. But it will never yield a complete infinite
>>> decimal string equal to 1/9. Every index of a 1 of that string that
>>> you can name, imagine, or think is finite.
>>
>> It is not the size of any one index but the number of different indices
>> that is not finite.
>
> The number of indices is a number. Up to any finite index it is a
> finite number.

Prove what is surmised from the statement of your
objection to Virgil.

What is the maximum number?

Remember: if your choice is not falsifiable,
it is not scientific.

---------------------------------------------------

[fom]

On 4/19/2013 4:23 AM, WM wrote:

> Try to name the greatest number that you can name. Or try to name a
> greater number than all you have known.
>

Speaking of what must be tried.

WM has been asked to produce a falsifiably
scientific largest natural number as
evidence of his mathematics.

WM challenges the received paradigm. Thus,
the onus of proof rests with him.

[WM]

On 19 Apr., 12:34, fom <fomJ...@nyms.net> wrote:
> On 4/19/2013 4:23 AM, WM wrote:
>
> > Try to name the greatest number that you can name. Or try to name a
> > greater number than all you have known.
>
> Speaking of what must be tried.
>
> WM has been asked to produce a falsifiably
> scientific largest natural number as
> evidence of his mathematics.

You have not understood the relativity of mathematics. There is no
fixed largest number in mathematics.

Regards, WM

[fom]

First, you understand nothing
about mathematics.

Second, you are the one who makes
the claim that there is a fixed
largest number.

The fact that you do not understand
your own statements is documented
and noted:

"That is WM's belief as surmised
from statements and reasoning
as opposed to what he says with
rhetoric."

----------------------------------------------

[fom]

On 4/19/2013 9:29 AM, WM wrote:

>

> You have not understood the relativity of mathematics.

Perhaps you should read something that use
language like that without contempt or
derision.

It is just one of a handful that came up with
a search on "relativity of mathematics"

http://www.mathematik.uni-dortmund.de/~prediger/veroeff/06-Fotfs-epistemic-exception.pdf

Didn't see anything at all that looked like
crayon marks or stone triangles.


--------------------------------------------------

[fom]

On 4/19/2013 9:29 AM, WM wrote:

The statement

>
> "WM believes that
>
> (|N is a completed infinity and WM does not believe
> that |N is a completed infinity)"
>

may be found at the end of the post
in relation to prior analysis.

The fact that WM manages to turn on a laser
or two without hurting himself is not
evidence that he understands the meaning
of words when he uses them.

For example, "the natural numbers"
is a phrase WM seems unable to comprehend.

------------------------------------------

[Virgil]

In article
<43eba938-697b-4834...@o9g2000vbk.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 18 Apr., 22:09, Virgil <vir...@ligriv.com> wrote:
>
> > > No. The algorithm exists. But it will never yield a complete infinite
> > > decimal string equal to 1/9. Every index of a 1 of that string that
> > > you can name, imagine, or think is finite.
> >
> > It is not the size of any one index but the number of different indices
> > that is not finite.
>
> The number of indices is a number. Up to any finite index it is a
> finite number.

Then you should be aqble to give us the allegedly finite number of
indices. Unless here are more of them that an finite number.

>
> >
> > > Obviously it is the
> > > greatest you can name
> >
> > Why even try to name what does not exist, a greatest member.
>
> Try to name the greatest number that you can name. Or try to name a
> greater number than all you have known.

Every natural number has a successor which is larger than itself, so
that any attempt to name or claim a greatest is as foolish as WM always
is.
--

[Virgil]

In article
<42604d3a-10a7-48c8...@y14g2000vbk.googlegroups.com>,

Because for every positive number, whether natural, integral, rational
or real, there is another twice as large.

As soon as any positive number has been identified, so has its double.
--

[WM]

On 19 Apr., 21:37, Virgil <vir...@ligriv.com> wrote:

> > > It is not the size of any one index but the number of different indices
> > > that is not finite.
>
> > The number of indices is a number. Up to any finite index it is a
> > finite number.
>
> Then you should be aqble to give us the allegedly finite number of
> indices. Unless here are more of them that an finite number.

The number of indices up to index n is n (unless you count 0 as an
index, then the number is n + 1). The numbers of indices and the
values of indices are in bijection.

Regards, WM

Regards, WM

[WM]

On 19 Apr., 21:41, Virgil <vir...@ligriv.com> wrote:

> > You have not understood the relativity of mathematics. There is no
> > fixed largest number in mathematics.
>
> Because for every positive number, whether natural, integral, rational
> or real,  there is another twice as large

and finite and belonging to a finite set.

>
> As soon as any positive number has been identified, so has its double.

Not as soon! Every calculation, even the easiest, requires some time.

Regards, WM

[netzweltler]

Nowadays a PC can calculate 1+1 in less than one nanosecond. Does this
mean, that the result 2 doesn't exist before the calculation is
executed? I.e . one nanosecond after number 1 exists? Do in a finite
set { 10, 11, 12, 13, 14, 15 } all six numbers exist at the same time?

[WM]

On 20 Apr., 09:53, netzweltler <reinhard_fisc...@arcor.de> wrote:
> On 20 Apr., 09:01, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>
> > On 19 Apr., 21:41, Virgil <vir...@ligriv.com> wrote:
>
> > > > You have not understood the relativity of mathematics. There is no
> > > > fixed largest number in mathematics.
>
> > > Because for every positive number, whether natural, integral, rational
> > > or real,  there is another twice as large
>
> > and finite and belonging to a finite set.
>
> > > As soon as any positive number has been identified, so has its double.
>
> > Not as soon! Every calculation, even the easiest, requires some time.
>
> > Regards, WM
>
> Nowadays a PC can calculate 1+1 in less than one nanosecond. Does this
> mean, that the result 2 doesn't exist before the calculation is
> executed?

Not in the PC.

> I.e . one nanosecond after number 1 exists? Do in a finite
> set { 10, 11, 12, 13, 14, 15 } all six numbers exist at the same time?

On a sheet of paper, after having been written, or in an electronic
memeory, after having been stored, certainly. But not before.

Regards, WM

[netzweltler]

The number 15 must have existed before I assigned it to the set { 10,
11, 12, 13, 14, 15 }. How else could I assign it to the set?

[WM]

On 20 Apr., 14:23, netzweltler <reinhard_fisc...@arcor.de> wrote:

> The number 15 must have existed before I assigned it to the set  { 10,

> 11, 12, 13, 14, 15 }. How else could I assign it to the set?-

Three questions to answer:
- Why do you think they teach Das kleine Einmaleins in school?
- Has Michelangelo's David existed before he was excavated from the
marble block?
- Did your consciousness exist before you knew it?

Regards, WM

[netzweltler]

On 20 Apr., 14:33, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 20 Apr., 14:23, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
> > The number 15 must have existed before I assigned it to the set  { 10,
> > 11, 12, 13, 14, 15 }. How else could I assign it to the set?-
>
> Three questions to answer:
> - Why do you think they teach Das kleine Einmaleins in school?
> - Has Michelangelo's David existed before he was excavated from the
> marble block?

The idea (or maybe even David) existed before. If Michelangelo
excavated a big 15 out of the marble block, this doesn't mean, that
the number 15 didn't exist before. Numbers are ideas, in most cases
just possible ideas.
There are uncountably many versions of David Michaelangelo could have
created.

[fom]

The fact that n=n for each n is not in doubt. It is an ontological
assumption in the standard account of identity.

So, to say "for every n that is a number, n is a number" and
"if n is finite, n is finite" provides no answer.

What has been asked for is the specific counterexample to
Virgil's statement -- namely, that number of indices beyond
which it can be proven that there exist no more indices.

==========================================================

from his statements and reasonings

[fom]

But there is no calculation involved. Virgil's statement gives
no specific numerical value to which to apply the axioms.

Once again WM demonstrates that he is a conceited reasoner,
a peculiar reasoner, and victim to the self-deception intrinsic
to these views.

That is, he assumes and abides by the axioms in which he claims
not to believe. In addition, he believes in the correctness
of his own beliefs concerning this state of affairs.

=========================================================

from his statements and reasonings

[fom]

Amazing. No, literally.

Numbers appear to man as revealed knowledge of the
universe as needed.

Who, other than WM, knew?

======================================================

from his statements and reasonings

[fom]

On 4/20/2013 7:33 AM, WM wrote:
> On 20 Apr., 14:23, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
>> The number 15 must have existed before I assigned it to the set { 10,
>> 11, 12, 13, 14, 15 }. How else could I assign it to the set?-
>
> Three questions to answer:
> - Why do you think they teach Das kleine Einmaleins in school?

It is believed that children require knowledge.

Codified knowledge is a community concern. It exists
in the community. And, the fact that it has meaning
rests with a non-solipsistic view of the world.

> - Has Michelangelo's David existed before he was excavated from the
> marble block?

According to Michelangelo? Yes.

> - Did your consciousness exist before you knew it?

By all evidence that comes from watching babies and
toddlers grow into children? Yes.

WM, however, is either a Zen master who does not
understand the purpose of Zen teachings or a
solipsist.

Perhaps that is the cause of his peculiar reasoning.

[WM]

On 20 Apr., 16:09, netzweltler <reinhard_fisc...@arcor.de> wrote:
> On 20 Apr., 14:33, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > On 20 Apr., 14:23, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
> > > The number 15 must have existed before I assigned it to the set  { 10,
> > > 11, 12, 13, 14, 15 }. How else could I assign it to the set?-
>
> > Three questions to answer:
> > - Why do you think they teach Das kleine Einmaleins in school?
> > - Has Michelangelo's David existed before he was excavated from the
> > marble block?
>
> The idea (or maybe even David) existed before.

But not in your brain before you were born.

> If Michelangelo
> excavated a big 15 out of the marble block, this doesn't mean, that
> the number 15 didn't exist before.

But not in the marble block.

Existence is a function of space and time, like a wave.

> There are uncountably many versions of David Michaelangelo could have
> created.

There are relatively few atoms and not far more relative positions
they can take according to the physical laws.

All atoms of the accessible universe and all positions they can take
belong to a finite set.

Regards, WM

[WM]

On 20 Apr., 17:07, fom <fomJ...@nyms.net> wrote:
> On 4/20/2013 1:56 AM, WM wrote:
>
> > On 19 Apr., 21:37, Virgil <vir...@ligriv.com> wrote:
>
> >>>> It is not the size of any one index but the number of different indices
> >>>> that is not finite.
>
> >>> The number of indices is a number. Up to any finite index it is a
> >>> finite number.
>
> >> Then you should be aqble to give us the allegedly finite number of
> >> indices. Unless here are more of them that an finite number.
>
> > The number of indices up to index n is n (unless you count 0 as an
> > index, then the number is n + 1). The numbers of indices and the
> > values of indices are in bijection.
>
> The fact that n=n for each n is not in doubt.  It is an ontological
> assumption in the standard account of identity.

Of course. Every finite number counts its place thereby proving that
it belongs to a finite set (1, ..., n).

>
> So, to say "for every n that is a number, n is a number" and
> "if n is finite, n is finite" provides no answer.
>

But it provides the truth.

> What has been asked for is the specific counterexample to
> Virgil's statement -- namely, that number of indices beyond
> which it can be proven that there exist no more indices.

That is not asked for by persons who know mathematics.

Regards, WM

[WM]

On 20 Apr., 17:15, fom <fomJ...@nyms.net> wrote:
> On 4/20/2013 2:01 AM, WM wrote:
>
> > On 19 Apr., 21:41, Virgil <vir...@ligriv.com> wrote:
>
> >>> You have not understood the relativity of mathematics. There is no
> >>> fixed largest number in mathematics.
>
> >> Because for every positive number, whether natural, integral, rational
> >> or real,  there is another twice as large
>
> > and finite and belonging to a finite set.
>
> >> As soon as any positive number has been identified, so has its double.
>
> > Not as soon! Every calculation, even the easiest, requires some time.
>
> But there is no calculation involved.  Virgil's statement gives
> no specific numerical value to which to apply the axioms.

No problem. Every numerical value is finite. The axioms are to be
applied to finite naturals only, because only a finite natural changes
its value when 1 is added. And the result is again a finite value,
counting the elements of a finite set. This does never change.

Regards, WM

[fom]

On 4/20/2013 12:10 PM, WM wrote:
> On 20 Apr., 17:07, fom <fomJ...@nyms.net> wrote:
>> On 4/20/2013 1:56 AM, WM wrote:
>>
>>> On 19 Apr., 21:37, Virgil <vir...@ligriv.com> wrote:
>>
>>>>>> It is not the size of any one index but the number of different indices
>>>>>> that is not finite.
>>
>>>>> The number of indices is a number. Up to any finite index it is a
>>>>> finite number.
>>
>>>> Then you should be aqble to give us the allegedly finite number of
>>>> indices. Unless here are more of them that an finite number.
>>
>>> The number of indices up to index n is n (unless you count 0 as an
>>> index, then the number is n + 1). The numbers of indices and the
>>> values of indices are in bijection.
>>
>> The fact that n=n for each n is not in doubt. It is an ontological
>> assumption in the standard account of identity.
>
> Of course. Every finite number counts its place thereby proving that
> it belongs to a finite set (1, ..., n).

n=n as an ontological assumption in the standard account of
identity has nothing to do with the natural numbers.

[fom]

On 4/20/2013 12:10 PM, WM wrote:

> On 20 Apr., 17:07, fom <fomJ...@nyms.net> wrote:
>
>>
>> So, to say "for every n that is a number, n is a number" and
>> "if n is finite, n is finite" provides no answer.
>>
> But it provides the truth.
>

It does.

[fom]

On 4/20/2013 12:10 PM, WM wrote:

To the contrary. That is the fundamental
issue here.

[fom]

On 4/20/2013 12:03 PM, WM wrote:
>
>
> Existence is a function of space and time, like a wave.
>

You are welcome to believe that.

But, can you explain it without a perfect
Polish space?


==========================================================

from his statements and reasonings

[fom]

Sadly, this is the kind of statement which
makes apparent your failure to understand.

Constants and closed terms do not change
values.

Succession defines how natural numbers are
situated with respect to one another.

One of Frege's contributions had been to
address the confusion over constants and
variables in the practice of nineteenth
century mathematics. However, no one really
paid attention.

[Virgil]

In article
<40af0ba0-d08b-4882...@b10g2000vbu.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 19 Apr., 21:41, Virgil <vir...@ligriv.com> wrote:
>
> > > You have not understood the relativity of mathematics. There is no
> > > fixed largest number in mathematics.
> >
> > Because for every positive number, whether natural, integral, rational
> > or real, �there is another twice as large
>
> and finite and belonging to a finite set.

But there are infinitely many such finite sets.

> >
> > As soon as any positive number has been identified, so has its double.
>
> Not as soon!

Given any n there is simultaneously a 2*n, and a 3*n, and so on.
--

[Virgil]

In article
<e2255911-51b5-42d6...@m1g2000vbe.googlegroups.com>,

Every finite set of naturals has a largest member, so WM is claiming
that there is a largest natural in the set of naturals.
--

[Virgil]

In article
<a96ccafa-7263-40b5...@cm2g2000vbb.googlegroups.com>,

But mathematics takes place in the mind. What appears on paper or in
computer memories is only a record of what minds have made. And in one's
mind one can envision infinite sets, just as one can envision continuous
lines having a continuum of points in them.
--

[Virgil]

In article
<54a6af59-042b-4007...@a6g2000vbm.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 20 Apr., 14:23, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
> > The number 15 must have existed before I assigned it to the set �{ 10,
> > 11, 12, 13, 14, 15 }. How else could I assign it to the set?-
>

> questions to answer:

> - Has Michelangelo's David existed before he was excavated from the
> marble block?

According to Michelangelo, yes!

> - Did your consciousness exist before you knew it?

Doesn't that depend on whether one believes in souls or not?
--

[Virgil]

In article
<353378ab-45a9-452c...@s4g2000vbr.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> All atoms of the accessible universe and all positions they can take
> belong to a finite set.

That presumes both that the universe is finite and not continuous, and
not one of infinitely many universes, none of which has yet been proven
beyond doubt.
--

[Virgil]

In article
<448eb2a3-a329-42dc...@c9g2000vbr.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 19 Apr., 21:37, Virgil <vir...@ligriv.com> wrote:
>
> > > > It is not the size of any one index but the number of different indices
> > > > that is not finite.
> >
> > > The number of indices is a number. Up to any finite index it is a
> > > finite number.
> >
> > Then you should be aqble to give us the allegedly finite number of
> > indices. Unless here are more of them that an finite number.
>
> The number of indices up to index n

That is not what was asked for. If there is only a finite number of
naturals possible the WM should be able to give us that number.


Otherwise there is no reason to assume that there can exist any natural
numbers without successors, or doubles, or triples, etc.
--

[Virgil]

In article
<9aa25785-6b61-45de...@j14g2000vbk.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 20 Apr., 17:07, fom <fomJ...@nyms.net> wrote:
> > On 4/20/2013 1:56 AM, WM wrote:
> >
> > > On 19 Apr., 21:37, Virgil <vir...@ligriv.com> wrote:
> >
> > >>>> It is not the size of any one index but the number of different indices
> > >>>> that is not finite.
> >
> > >>> The number of indices is a number. Up to any finite index it is a
> > >>> finite number.
> >
> > >> Then you should be aqble to give us the allegedly finite number of
> > >> indices. Unless here are more of them that an finite number.
> >
> > > The number of indices up to index n is n (unless you count 0 as an
> > > index, then the number is n + 1). The numbers of indices and the
> > > values of indices are in bijection.
> >
> > The fact that n=n for each n is not in doubt.  It is an ontological
> > assumption in the standard account of identity.
>
> Of course. Every finite number counts its place thereby proving that
> it belongs to a finite set (1, ..., n).

But unless WM can come up with a natural number which can be shown not
to have a successor, or a double , or a triple, etc., what evidence does
he have that the sequence must end finitely?

> >
> > So, to say "for every n that is a number, n is a number" and
> > "if n is finite, n is finite" provides no answer.
> >
> But it provides the truth.

A truth

>
> > What has been asked for is the specific counterexample to
> > Virgil's statement -- namely, that number of indices beyond
> > which it can be proven that there exist no more indices.
>
> That is not asked for by persons who know mathematics.

It is asked by almost all mathematicians outside of Wolkenmuekenheim,
and what goes on inside Wolkenmuekenheim is not mathematics.
--

[fom]

On 4/20/2013 12:03 PM, WM wrote:
>

> All atoms of the accessible universe and all positions they can take
> belong to a finite set.
>

Well, that is a strange statement given
that they are forming Bose-Einstein
condensates with atoms now.

Anyway, what scientifically falsifiable
natural number does WM assert to be the
number of positions available to the
atoms of the accessible universe?

[Virgil]

In article <KdGdnfqxb_A8gu7M...@giganews.com>,

fom <fom...@nyms.net> wrote:

> On 4/20/2013 12:03 PM, WM wrote:
> >
> > All atoms of the accessible universe and all positions they can take
> > belong to a finite set.
> >
>
> Well, that is a strange statement given
> that they are forming Bose-Einstein
> condensates with atoms now.

Not to mention:
"As far as the laws of mathematics refer to
reality, they are not certain; and as
far as they are certain, they do not refer
to reality.

Albert Einstein

--

[netzweltler]

On 20 Apr., 19:03, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> All atoms of the accessible universe and all positions they can take
> belong to a finite set.
>
> Regards, WM

How do we prove, that the number of possible positions an atom can
take along a line of 1 cm is finite?

[WM]

On 21 Apr., 10:02, netzweltler <reinhard_fisc...@arcor.de> wrote:
> On 20 Apr., 19:03, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
> > All atoms of the accessible universe and all positions they can take
> > belong to a finite set.
>

> How do we prove, that the number of possible positions an atom can
> take along a line of 1 cm is finite?

By accepting quantum mechanics and excluding theology (these
assumptions taken as axioms for those who believe (as an axiom) to
need axioms) a proof is given here:
http://arxiv.org/ftp/arxiv/papers/0709/0709.4102.pdf
pages 2-3.

Regards, WM

[netzweltler]

What about a position between two quanta? Should there be no decimal
fraction for a position between two adjacent quanta along this line of
1 cm?

[WM]

> 1 cm?-

Quantum theory tells us, contrary to Einsteins's false beliefs, that
unmeasurable events do not exist. The electron or photon does not
simultaneously have fixed position and momentum (that would contradict
some results of interference experiments).

Mathematics, contrary to Einstein's false beliefs, is nothing but a
condensation of reality. This should answer your question.

Nobody can hinder you to believe in things that nobody can say, think,
identify, measure. But that is not science. It is theology or
superstition, or, in the worst case, matheology. I say "worst case"
because many naive people believe that matheology is a science run by
intelligent proponents.

Regards, WM

[netzweltler]

On 21 Apr., 16:03, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 21 Apr., 12:22, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
>
>
>
>
>
>
>
>
> > On 21 Apr., 11:07, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > On 21 Apr., 10:02, netzweltler <reinhard_fisc...@arcor.de> wrote:
>
> > > > On 20 Apr., 19:03, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > > All atoms of the accessible universe and all positions they can take
> > > > > belong to a finite set.
>
> > > > How do we prove, that the number of possible positions an atom can
> > > > take along a line of 1 cm is finite?
>
> > > By accepting quantum mechanics and excluding theology (these
> > > assumptions taken as axioms for those who believe (as an axiom) to
> > > need axioms) a proof is given here:http://arxiv.org/ftp/arxiv/papers/0709/0709.4102.pdf
> > > pages 2-3.
>
> > > Regards, WM
>
> > What about a position between two quanta? Should there be no decimal
> > fraction for a position between two adjacent quanta along this line of
> > 1 cm?-
>
> Quantum theory tells us, contrary to Einsteins's false beliefs, that
> unmeasurable events do not exist. The electron or photon does not
> simultaneously have fixed position and momentum (that would contradict
> some results of interference experiments).

If non-measurable distances don't exist, don't we face another
problem? Let's say, d is the smallest distance that can be measured.
Distances below d don't exist. So, d/2 is a non-existing distance. Is
it still valid, that d/2 + d/2 = d then? I mean, how can distance d
exist, if it is composed of two non-existing distances d/2?

[WM]

> exist, if it is composed of two non-existing distances d/2?-

The old problem of Aristotle: How can a resting body come to move?
There must be a point of time where rest and movement are
simultaneously realized. But that is impossible.

Concerning mathematics, there is d/2 even for d = 10^-1000000 fm.
Thats facilitated by invention of the system of fractions. But you had
asked for real atoms.

Regards, WM

[WM]

On 21 Apr., 02:25, Virgil <vir...@ligriv.com> wrote:

> Not to mention:
> "As far as the laws of mathematics refer to
> reality, they are not certain; and as
> far as they are certain, they do not refer
> to reality.
>
> Albert Einstein

Nevertheless wrong.
No army of mathematicians can calculate the movement of 100
gravitating bodies better than 100 gravitating bodies.

Regards, WM

[fom]

On 4/21/2013 9:03 AM, WM wrote:
> On 21 Apr., 12:22, netzweltler <reinhard_fisc...@arcor.de> wrote:
>> On 21 Apr., 11:07, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>
>>
>>
>>
>>> On 21 Apr., 10:02, netzweltler <reinhard_fisc...@arcor.de> wrote:
>>
>>>> On 20 Apr., 19:03, WM <mueck...@rz.fh-augsburg.de> wrote:
>>
>>>>> All atoms of the accessible universe and all positions they can take
>>>>> belong to a finite set.
>>
>>>> How do we prove, that the number of possible positions an atom can
>>>> take along a line of 1 cm is finite?
>>
>>> By accepting quantum mechanics and excluding theology (these
>>> assumptions taken as axioms for those who believe (as an axiom) to
>>> need axioms) a proof is given here:http://arxiv.org/ftp/arxiv/papers/0709/0709.4102.pdf
>>> pages 2-3.
>>
>>> Regards, WM
>>
>> What about a position between two quanta? Should there be no decimal
>> fraction for a position between two adjacent quanta along this line of
>> 1 cm?-
>
> Quantum theory tells us, contrary to Einsteins's false beliefs,

Once again, claims without proof. When have the significant
theories of Einstein been falsified? And, why are quantum theorists
so anxious to obtain a quantum gravity that does not contradict
Einstein?

> that
> unmeasurable events do not exist.

No. Just imaginary worlds.

http://en.wikipedia.org/wiki/Many-worlds_interpretation

> The electron or photon does not
> simultaneously have fixed position and momentum (that would contradict
> some results of interference experiments).

Of course, that would be explained by the fact that
the mathematics describing continuous motion requires
differentiable neighborhoods around each point.

One cannot have physics that contradicts the mathematics
just because the WM's of the world turn simple mathematics
into quantum voodoo.

And, the recognition of this fact may have come from the
study of general relativity rather than quantum mechanics.

http://en.wikipedia.org/wiki/Scale_relativity

Scale relativity addresses the possibility that differentiability
necessarily breaks down in small domains.

>
> Mathematics, contrary to Einstein's false beliefs, is nothing but a
> condensation of reality. This should answer your question.
>

Perhaps. But that condensation involves the principle
that statements are either true or false. The problem
did not come out of the mathematics of the late-nineteenth
century. Rather, it lay with the mathematics as it came
into the nineteenth century. The foundational debates
arise from the fact that the philosophy of physicists
such as WM is often inadequate to their beliefs.

> Nobody can hinder you to believe in things that nobody can say, think,
> identify, measure. But that is not science.

It would be more correct to say that that is "science".

When do scientists make the effort to actually justify their
positions to the general public? They do not. They use their
influence with respect to the economics of technology corporations
and universities to establish their positions through the
fundamental totalitarian power of government authority.

The same mathematics that WM complains about is used for
economic analysis. The economics of paying for governments is
bound to the profits of corporations. There is a great deal
of competition between governments over these matters that
is fundamentally disrespectful of the general citizenry.

The heroic view of "science" is a lie. WM's statement would
suggest that anyone can walk into CERN and conduct an
experiment for themselves. No. That is not how it works.
So, for most people, "science" is being told what to believe
without being able to verify it for themselves. That they
accept what they are told stems for the fact that it is mostly
irrelevant to their day-to-day lives.

==============================================

[fom]

Right.

This is why negation and identity relate to the modern
mathematics of boundaries. What mathematics would that
be?

> "What St. Thomas affirms on this point
> about angels or intelligences ('that
> here every individual is a lowest
> species') is true of all substances,
> provided one takes the specific
> difference in the way that geometers
> take it with regard to their figures."
>
> Leibniz
>
>
>
> "If m_1, m_2, ..., m_v, ... is any
> countable infinite set of elements
> of [the linear point manifold] M of
> such a nature that [for closed
> intervals given by a positive
> distance]:
>
> lim [m_(v+u), m_v] = 0 for v=oo
>
> then there is always one and only one
> element m of M such that
>
> lim [m_(v+u), m_v] = 0 for v=oo"
>
> Cantor to Dedekind
>


To have parts, one must have limits delineating
parts.

The interval when a body is at rest is different
from the interval when a body is in motion. There
is a boundary.

Associated with macroscopic objects will be an
acceleration. Thus, there will be a force.

Impulse is force applied over time. As noted in
the link,

http://en.wikipedia.org/wiki/Impulse_(physics)

it is a quantity and not an event.

If one considers the family of bell curves having
the an area equal to a given impulse, but with
decreasing intervals of time, one obtains the
Dirac delta which can be used to model impulse
as noted in the link

http://en.wikipedia.org/wiki/Dirac_delta_function#Overview

Aristotle's problem is represented in the limit,
and, importantly, this limit is represented in the
computer models of such events. As the link

http://en.wikipedia.org/wiki/Impulse_(physics)

notes, the changes are represented ideally with
step functions.

That is the thing about "computational representation".

Such representation depends on the ideal mathematics
WM rejects.

Then he says these things as if he has but one neuron.

[fom]

So now WM is asserting that the universe
is a computer, finite resources and all.

[Bergholt Stuttley Johnson]

fom wrote:
> So now WM is asserting that the universe
> is a computer, finite resources and all.

And WM is the Pentium bug.
http://en.wikipedia.org/wiki/Pentium_FDIV_bug

[netzweltler]

Yes. I am still asking for _real_ distances.

[gus gassmann]

On 21/04/2013 3:18 PM, fom wrote:
> On 4/21/2013 11:11 AM, WM wrote:
>> On 21 Apr., 02:25, Virgil <vir...@ligriv.com> wrote:
>>
>>> Not to mention:
>>> "As far as the laws of mathematics refer to
>>> reality, they are not certain; and as
>>> far as they are certain, they do not refer
>>> to reality.
>>>
>>> Albert Einstein
>>
>> Nevertheless wrong.
>> No army of mathematicians can calculate the movement of 100
>> gravitating bodies better than 100 gravitating bodies.
>>
>
> So now WM is asserting that the universe
> is a computer, finite resources and all.

Hardly a new idea. Douglas Adams used it, ca. 1978.

[netzweltler]

Yes. I am still asking for _real_ distances.

If there is a d/2 for any d, how can we say, that the number of
positions of an atom is finite?

[Virgil]

In article
<747ed7d3-8241-4823...@cd3g2000vbb.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 21 Apr., 02:25, Virgil <vir...@ligriv.com> wrote:
>
> > Not to mention:
> > "As far as the laws of mathematics refer to
> > reality, they are not certain; and as
> > far as they are certain, they do not refer
> > to reality.
> >
> > Albert Einstein
>
> Nevertheless wrong.

Why is it wrong when your own statement below supports it?

> No army of mathematicians can calculate the movement of 100
> gravitating bodies better than 100 gravitating bodies.

WM's claim supports, rather than opposes, Einstein's aphorism.

So WM is blowing both hot and cold.
--

[Virgil]

In article
<8c0fc691-66cb-4f6d...@c15g2000vbl.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 21 Apr., 10:02, netzweltler <reinhard_fisc...@arcor.de> wrote:
> > On 20 Apr., 19:03, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> > > All atoms of the accessible universe and all positions they can take
> > > belong to a finite set.
> >
> > How do we prove, that the number of possible positions an atom can
> > take along a line of 1 cm is finite?
>
> By accepting quantum mechanics

Where in quantum field theory does it say that?

Or is this just another of WM's lies?
--

[Virgil]

In article
<7737ecdb-c100-4196...@a6g2000vbm.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 21 Apr., 12:22, netzweltler <reinhard_fisc...@arcor.de> wrote:
> > On 21 Apr., 11:07, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >
> > > On 21 Apr., 10:02, netzweltler <reinhard_fisc...@arcor.de> wrote:
> >
> > > > On 20 Apr., 19:03, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > All atoms of the accessible universe and all positions they can take
> > > > > belong to a finite set.
> >
> > > > How do we prove, that the number of possible positions an atom can
> > > > take along a line of 1 cm is finite?
> >
> > > By accepting quantum mechanics and excluding theology (these
> > > assumptions taken as axioms for those who believe (as an axiom) to
> > > need axioms) a proof is given
> > > here:http://arxiv.org/ftp/arxiv/papers/0709/0709.4102.pdf
> > > pages 2-3.
> >
> > > Regards, WM
> >
> > What about a position between two quanta? Should there be no decimal
> > fraction for a position between two adjacent quanta along this line of
> > 1 cm?-
>
> Quantum theory tells us, contrary to Einsteins's false beliefs, that
> unmeasurable events do not exist. The electron or photon does not
> simultaneously have fixed position and momentum (that would contradict
> some results of interference experiments).

Does quantum theory actually say that a particle cannot have both a
position and a momentum simultaneously HAVE, or does it merely say that
we cannot accurately determine both its position and momemtum
simultaneously?

>
> Mathematics, contrary to Einstein's false beliefs, is nothing but a
> condensation of reality. This should answer your question.

Given a choice between following WM's WMytheology or following
Einstein's worldview, I suggest one follow Einstein.

>
> Nobody can hinder you to believe in things that nobody can say, think,
> identify, measure. But that is not science. It is theology or
> superstition, or, in the worst case, matheology. I say "worst case"
> because many naive people believe that matheology is a science run by
> intelligent proponents.

Since WM declares that Einstein is one of those matheologists, the world
is on their side in opposition to WM's WMytheology.
--

[Bergholt Stuttley Johnson]

WM wrote:
> Quantum theory ...

Quantum *THEORY* not Quantum truth.
WM is an idiot!

[WM]

In reality there is not a d/2 for every d. The shortest possible wave
cannot be shortened and cannot be used to find a shorter d than its
wavelength or a finite fraction of it. Further, if the shortest
possible wave is created, there are no atoms marking a distance any
longer and no men to measure it, because all energy has been used to
create the wave.

Regards, WM

[WM]

On 21 Apr., 22:51, Virgil <vir...@ligriv.com> wrote:

> > Quantum theory tells us, contrary to Einsteins's false beliefs, that
> > unmeasurable events do not exist. The electron or photon does not
> > simultaneously have fixed position and momentum (that would contradict
> > some results of interference experiments).
>
> Does quantum theory actually say that a particle cannot have both a
> position and a momentum simultaneously HAVE, or does it merely say that
> we cannot accurately determine both its position and momemtum
> simultaneously?

"Have" would be the correct answer.

>
> Given a choice between following WM's WMytheology or following
> Einstein's worldview, I suggest one follow Einstein.

Typical case of belief in authority. Quite frequent among
matheologians.

> Since WM declares that Einstein is one of those matheologists.

No, I never did.

Regards, WM

[netzweltler]

If I am travelling to target T and I am as close as one shortest
possible wavelength w to target T, is this the same as reaching T in
reality? So, T - w = T? Or is w still a real distance to travel
(without having to travel halfway this distance, because halfway
doesn't exist)?

[Virgil]

In article
<e55452cc-4f89-4987...@c15g2000vbl.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 21 Apr., 22:51, Virgil <vir...@ligriv.com> wrote:
>
> > > Quantum theory tells us, contrary to Einsteins's false beliefs, that
> > > unmeasurable events do not exist. The electron or photon does not
> > > simultaneously have fixed position and momentum (that would contradict
> > > some results of interference experiments).
> >
> > Does quantum theory actually say that a particle cannot have both a
> > position and a momentum simultaneously HAVE, or does it merely say that
> > we cannot accurately determine both its position and momemtum
> > simultaneously?
>
> "Have" would be the correct answer.
> >
> > Given a choice between following WM's WMytheology or following
> > Einstein's worldview, I suggest one follow Einstein.
>
> Typical case of belief in authority.

WRONG! It is merely a choice between whether to consider Einstein or WM
a more reliable source of information.


And given the choice between accepting WM as a reliable source of
information and accepting Einstein a reliable source of information,
only WM would accept WM.

>
> > Since WM declares that Einstein is one of those matheologists.
>
> No, I never did.

Then WM must be accepting Einstein as a reliable source of information.

In which case:

"As far as the laws of mathematics refer to reality,
they are not certain;
and as far as they are certain,
they do not refer to reality."

Albert Einstein

--

[Virgil]

In article
<ff0500c8-ddab-48b3...@r4g2000vbf.googlegroups.com>,

WM <muec...@rz.fh-augsburg.de> wrote:

> On 21 Apr., 21:32, netzweltler <reinhard_fisc...@arcor.de> wrote:
> > On 21 Apr., 18:06, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > On 21 Apr., 16:56, netzweltler <reinhard_fisc...@arcor.de> wrote:
> >
> > > > If non-measurable distances don't exist, don't we face another
> > > > problem? Let's say, d is the smallest distance that can be measured.
> > > > Distances below d don't exist. So, d/2 is a non-existing distance. Is
> > > > it still valid, that d/2 + d/2 = d then? I mean, how can distance d
> > > > exist, if it is composed of two non-existing distances d/2?-
> >
> > > The old problem of Aristotle: How can a resting body come to move?
> > > There must be a point of time where rest and movement are
> > > simultaneously realized. But that is impossible.
> >
> > > Concerning mathematics, there is d/2 even for d = 10^-1000000 fm.
> > > Thats facilitated by invention of the system of fractions. But you had
> > > asked for real atoms.
> >
> > Yes. I am still asking for _real_ distances.
> >
> > If there is a d/2 for any d, how can we say, that the number of
> > positions of an atom is finite?
>
> In reality there is not a d/2 for every d.

But mathematics is not strictly about reality.

[netzweltler]

If I am travelling to target T and I am as close as one shortest
possible wavelength w to target T, is this the same as reaching T in
reality? So, T - w = T? Or is w still a real distance to travel
(without having to travel halfway this distance, because halfway
doesn't exist)?

Whatever wavelength w is, it must have the same properties as 0 has in
mathematics. Only for w = 0 it is valid, that T - w = T.

> In reality there is not a d/2 for every d.

Even in mathematics there is not a d/2 for every d. If d = 0.

[Virgil]

> In reality there is not a d/2 for every d. The shortest possible wave
> cannot be shortened and cannot be used to find a shorter d than its
> wavelength or a finite fraction of it. Further, if the shortest
> possible wave is created, there are no atoms marking a distance any
> longer and no men to measure it, because all energy has been used to
> create the wave.
>
> Regards, WM

Whether there is a physical distance of d/2 for every physical distance
g is as irrelevant to mathematics as the undoubtable existence of a
positive mathematical distance of d/2 for every positive mathematical
distance d is irrelevant to physics.

WM may know a little physics, but he clearly knows considerably less
about mathematics.

[WM]

On 22 Apr., 23:43, netzweltler <reinhard_fisc...@arcor.de> wrote:

>
> If I am travelling to target T and I am as close as one shortest
> possible wavelength w to target T, is this the same as reaching T in
> reality? So, T - w = T?

How would you measure that? You have no sharp surface limit. You are a
wave-packet.
(And as long as you and the target exist, the shortest possible wave
does not exist, because some energy is missing.)

> Or is w still a real distance to travel
> (without having to travel halfway this distance, because halfway
> doesn't exist)?
>
> Whatever wavelength w is, it must have the same properties as 0 has in
> mathematics. Only for w = 0 it is valid, that T - w = T.
>
> > In reality there is not a d/2 for every d.
>
> Even in mathematics there is not a d/2 for every d. If d = 0.

Of course there is d/2, but is does not differ from d.

Regards, WM

[WM]

On 22 Apr., 21:03, Virgil <vir...@ligriv.com> wrote:

> > > Since WM declares that Einstein is one of those matheologists.
>
> > No, I never did.
>
> Then WM must be accepting Einstein as a reliable source of information.
>

Strange logic.

Regards, WM