Matheology § 152

[WM]

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Weitere Optionen 16 Nov., 10:35

Newsgroups: sci.logic, sci.math
Von: WM <mueck...@rz.fh-augsburg.de>
Datum: Fri, 16 Nov 2012 01:35:48 -0800 (PST)
Lokal: Fr. 16 Nov. 2012 10:35
Betreff: Matheology § 152
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Matheology § 152


Consider the following sequence of decimal numbers, consisting of
digits 0 and 1


01.
0.1
010.1
01.01
0101.01
010.101
01010.101
0101.0101
...


which, when indexed by natural numbers, yilooks like this:


0_2 1_1 .
0_2 . 1_1
0_4 1_3 0_2 . 1_1
0_4 1_3 . 0_2 1_1
0_6 1_5 0_4 1_3 . 0_2 1_1
0_6 1_5 0_4 . 1_3 0_2 1_1
0_8 1_7 0_6 1_5 0_4 . 1_3 0_2 1_1
0_8 1_7 0_6 1_5 . 0_4 1_3 0_2 1_1
...


What is the limit of the sequence of the sets of indexes on the left
hand side?
What is the limit of the decimal numbers?


Regards, WM

[William Hughes]

A set.

> What is the limit of the decimal numbers?
>

A value.

[WM]

The empty set.

>
> > What is the limit of the decimal numbers?
>
> A value.

Not a value, but infinity, i.e., the infinite of analysis: potential
infinity, a continuous growth.

And we see the poor numbers, which must hold the position on the left
hand side of the decimal point, existing without indices which have
been stripped off. But what is a digit of a decimal number without its
index? Shouldn't we call such numbers crippled numbers? Or is
"mathematically challenged" the correct wording?

Regards, WM

[William Hughes]

On Nov 16, 5:46 am, WM <mueck...@rz.fh-augsburg.de> wrote:

A set.

> What is the limit of the decimal numbers?
>

A value.

[LudovicoVan]

"WM" <muec...@rz.fh-augsburg.de> wrote in message
news:99101a42-d1ac-4b5e...@d3g2000vbj.googlegroups.com...

Wrong: and you even agree that it is wrong.

-LV

[WM]

On 16 Nov., 16:13, "LudovicoVan" <ju...@diegidio.name> wrote:
> "WM" <mueck...@rz.fh-augsburg.de> wrote in message

>
> news:99101a42-d1ac-4b5e...@d3g2000vbj.googlegroups.com...
>
>
>
>
>
> > On 16 Nov., 13:58, William Hughes <wpihug...@gmail.com> wrote:
> >> On Nov 16, 5:46 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> >> > 1.  WM    Profil anzeigen   bersetzen in die Sprache:
> >> > Deutsch bersetzt (Original anzeigen)

Of course it is wrong, but it is a necessary requirement of set
theory.

Regards, WM

[WM]

"LudovicoVan" <ju...@diegidio.name> wrote:

> What is the limit of the sequence of the sets of indexes on the left
> hand side?

{oo}

oo is not a natural number but indices are natural numbers because
they determine a position. oo is not a position.

> What is the limit of the decimal numbers?

oo

By the same basic arithmetic: note that if you disallow the first,
you
should disallow the second on exactly the same grounds.

Talking about the limit oo does not mean that it is assumed. It means
that the sequence grows beyond every finite positive number.

Also the sequence (1/n) does never assume its limit 0. Only the
difference between 1/n and 0 shrinks below every positive number.

Regards, WM

[forbi...@gmail.com]

I want to make sure I understand what you mean by "on the left
had side." Do you mean the set whose successors is "0_2 1_1 ."?

> > > What is the limit of the decimal numbers?
> >
> > A value.
>
> Not a value, but infinity, i.e., the infinite of analysis: potential
> infinity, a continuous growth.

Dealing with unbound sets can be a problem. There are times one
wants to deal with the discrete and time when one wants to deal with
the continuous. Achelles really does make it through the door even
though he must make it half way to the door first. Just as 0 was
added to the natural numbers so one can talk about the cardinality
of the empty set,(all empty sets, the null set,) so was infinity,
represented by the greek letter omega, introduced to talk about the
limit of an unbound sequence for those who must have limits on their
sequences. Omega takes on the skin of memebers of the set and stands
in where no limit exists.

> And we see the poor numbers, which must hold the position on the left
> hand side of the decimal point, existing without indices which have
> been stripped off. But what is a digit of a decimal number without its
> index? Shouldn't we call such numbers crippled numbers? Or is
> "mathematically challenged" the correct wording?

The way one constructs the actual definition for a number represented
as a sequence of numeric characters and a period (I gather some languages
switch our period and optional injection of commas so the comma represents
the start of the part beyond the natural number portion of the seqence)
is to represent the position to the left of the period as the number
mulitiplied by the base raised to the 0th power, then for every successor
position to the left raise to one greater power and for ever successor
position to the right raise to one less power, yes negative numbers have
to be introduced before reading these numbers, the number represented
is the sum of the parts.

OK, there is some foundational work to do but that's a universal problem
since I've seen no satisfactory definition of the domain of the set of
numbers. For instance, where do they exist?, what are their attributes?,
what is the role of numbers in a language?, etc.

[WM]

I mean the limit of the sequence of sets of indexes of the digits left
to the decimal point.

Regards, WM

[forbi...@gmail.com]

This is why I talk about omega being a stand in for a limit where there
is none. While a river has a head at one end and a mouth at the other,
I needn't see either end to dip water from it. Some sets are open at
both ends and some are only open at one end. It doesn't matter. One
needn't see the ends to take from the set as long as one is positioned
within it.

[LudovicoVan]

"WM" <muec...@rz.fh-augsburg.de> wrote in message

news:f551d5a6-d25a-4509...@l12g2000vbj.googlegroups.com...

> "LudovicoVan" <ju...@diegidio.name> wrote:
>
> >> What is the limit of the sequence of the sets of indexes on the left
> >> hand side?
>
> > {oo}
>
> oo is not a natural number but indices are natural numbers because
> they determine a position. oo is not a position.

Was that an objection? We are just using limits as usual.

Let's make it formal, with the original balls and vase problem where at each
step we simply put 10 new balls in and remove the oldest one.

That translates to a sequence of sets, in fact a sequence of intervals of
natural numbers so defined:

s(n) := { i in N | n+1 <= i <= 10*n } =
= [ n+1; 10*n ]

For example, that gives:

s(0) := { } // empty
s(1) := [ 2; 10 ]
s(2) := [ 3; 20 ]
s(2) := [ 4; 30 ]
etc.

The limit of that sequence is:

lim_{n->oo} s(n) =
= lim_{n->oo} [ n+1; 10*n ] =
= [ lim_{n->oo} n+1; lim_{n->oo} 10*n ] =
= [ oo; oo ] =
= { oo }

> >> What is the limit of the decimal numbers?
>
> > oo
>
> > By the same basic arithmetic: note that if you disallow the first,
> > you should disallow the second on exactly the same grounds.
>
> Talking about the limit oo does not mean that it is assumed. It means
> that the sequence grows beyond every finite positive number.
>
> Also the sequence (1/n) does never assume its limit 0. Only the
> difference between 1/n and 0 shrinks below every positive number.

Just the same as above.

-LV

[Uirgil]

In article
<24e2d593-d2fc-4163...@l18g2000vbv.googlegroups.com>,

First, you need to show, formally, that those sequences actually have
limits.

Which you have not done.

[Uirgil]

In article
<99101a42-d1ac-4b5e...@d3g2000vbj.googlegroups.com>,

Claimed but not proven!

> >
> > > What is the limit of the decimal numbers?
> >
> > A value.
>
> Not a value, but infinity, i.e., the infinite of analysis: potential
> infinity, a continuous growth.

In standard mathematics, either a limit exists or it does not exist,
there is none of this potential but not actual nonsense.

[Uirgil]

In article
<0a78eb55-881b-4c43...@q1g2000vbx.googlegroups.com>,

Being wrong is only necessary in WM's version of a set theory, not in
any sane set theory.

[WM]

> within it.- Zitierten Text ausblenden -

Well, rivers are interesting objects. But here we discuss the question
whether the indices left of the decimal points disappear in the limit
of the set theoretic calculation and remain there in the limit of the
mathematical calculation. And whether this is a contradiction.

Regards, WM

[WM]

On 16 Nov., 22:40, Uirgil <uir...@uirgil.ur> wrote:
> In article
> <24e2d593-d2fc-4163-96f0-7f812a47f...@l18g2000vbv.googlegroups.com>,

>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > 1.  WM    Profil anzeigen   bersetzen in die Sprache:

> > Deutsch bersetzt (Original anzeigen)

No. Every mathematician knows that the sequence of numbers grows
without limit. This can be proved by taking any numbr n and showing
that there is a number k such that all for terms a(j) of the sequence
with k > j we have a(j) > n. Proof: For given n take k = n + 10.

Every set theorist knows that the sequence of sets of indices left of
the decimal point has the limit empty set. This is an requirement of
set theory.

And finally everybody knows that decimal numbers, by definition,
cannot consist of digits that have no indexs.

Regards, WM

[LudovicoVan]

"WM" <muec...@rz.fh-augsburg.de> wrote in message

news:f58b4287-182c-4a02...@b12g2000vbg.googlegroups.com...

> And finally everybody knows that decimal numbers, by definition,
> cannot consist of digits that have no indexs.

With all due respect, you are an incorrigible fart who is committing himself
to denying the meaningfulness of lim_{n->oo} n = oo.

Unless I have misunderstood your remark: should that be where the heck,
eventually, the infinitely many balls (indices) have gone in that {oo}, then
note that, formally, succ(oo) := oo (in the most basic extension), hence we
have non-finite (i.e. limit) indices all along, not distinguishable one
another (within the calculus!), so amounting to a singleton set.

Incidentally, I insist, as a critical point, that we should be using N*, not
N, for any "infinite endeavours": asking what happens to the vase in the
limit is intrinsically a super-task and then, maybe, I start understanding
why set theory (any set theory) compels actual infinities.

-LV

[LudovicoVan]

"LudovicoVan" <ju...@diegidio.name> wrote in message
news:k87hne$8l7$1...@dont-email.me...

Where rather than why... Eventually, still no essential difference between
arithmetic and set theory.

-LV

[WM]

On 17 Nov., 09:26, "LudovicoVan" <ju...@diegidio.name> wrote:

> Incidentally, I insist, as a critical point, that we should be using N*, not
> N, for any "infinite endeavours": asking what happens to the vase in the
> limit is intrinsically a super-task and then, maybe, I start understanding
> why set theory (any set theory) compels actual infinities.

Please note: Here I am not dealing with whatever you may propose but
with set theory and real numbers of analysis as they presently are.

Regards, WM

[LudovicoVan]

"WM" <muec...@rz.fh-augsburg.de> wrote in message

news:0e1157e6-1304-424b...@bx4g2000vbb.googlegroups.com...

It is at least interesting to distinguish between irrecoverable
incongruencies and reparable mistakes. The balls and vase problem rather
belongs to the second category (as I have repeatedly tried to show). Then
the relevance is obvious as it affects the actual import of your endeavour.
Most notably: what have you to say that my mathematics is out of standard?

-LV

[William Hughes]

Note that *set* limits have some important properties.

Given a sequence of sets {B_1,B_2,B_3,...}
then the set limit always exists (it
may be the empty set).


If we have

A = set limit {B_1,B_2,B_3....}

Then

A is a set
A cannot contain an element that is not contained
in any of the B's

[LudovicoVan]

"William Hughes" <wpih...@gmail.com> wrote in message
news:28bff553-f679-4e23...@c17g2000yqe.googlegroups.com...

Williams going around, in circles:

It was already mentioned that it is wrong to use that specific definition to
solve the balls and vase problem.

<http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Special_case:_discrete_metric>

-LV

[William Hughes]

On Nov 17, 9:59 am, "LudovicoVan" <ju...@diegidio.name> wrote:
> "William Hughes" <wpihug...@gmail.com> wrote in message

> <http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Specia...>
>


The problem is the above applies to *any* definition of a *set* limit.

[LudovicoVan]

"William Hughes" <wpih...@gmail.com> wrote in message

news:1ec0c2cc-f926-4fd4...@y8g2000yqy.googlegroups.com...

>> <http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Special_case:_discrete_metric>

>
> The problem is the above applies to *any* definition of a *set* limit.

But those definitions are a *specific* case of these:

<http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Sequences_of_sets>

I sometimes wonder which planet you come from.

-LV

[Uirgil]

In article
<f58b4287-182c-4a02...@b12g2000vbg.googlegroups.com>,

While every real mathematician knows that SOME sequences grow without
limits, they also know that others don't, something that WM seems not to
know, which puts him in his place..

> This can be proved by taking any numbr n and showing
> that there is a number k such that all for terms a(j) of the sequence
> with k > j we have a(j) > n. Proof: For given n take k = n + 10.

ow does that work for the sequence a(j) = 0 for all j?

>
> Every set theorist knows that the sequence of sets of indices left of
> the decimal point has the limit empty set. This is an requirement of
> set theory.

Then let us see which axiom, or set of axioms, of some set theory which
actually requires such nonsense. say among the axioms for ZFC, for
example.

>
> And finally everybody knows that decimal numbers, by definition,
> cannot consist of digits that have no indexs.

Numbers (decimal or otherwise) can exist without any digits of any sort,
but decimal numerals can not.

Since a numeral is merely a name for a number, and not actually the
thing named, treating numerals as if they were numbers is the sort of
error that only putzers like WM are prone to making.

[Uirgil]

In article
<0e1157e6-1304-424b...@bx4g2000vbb.googlegroups.com>,

Actually WM is not at all dealing with any part of either set theory or
real analysis as they presently are, or as they ever have been, but only
as WM (falsely) imagines them to be.

[Uirgil]

In article
<1ec0c2cc-f926-4fd4...@y8g2000yqy.googlegroups.com>,

And, at least as far as I know, EVERY such definition.

[Uirgil]

In article <k88h5n$eeo$1...@dont-email.me>,

Irrelevant Ad Hom noted!

Actually, William HUghes' "definition" is quite carefully non-specific,
and while it certainly includes both a lim_sups and a lim_infs, is in no
way limiter to only those.

So that, as usual, LV has things inverted.

[WM]

On 17 Nov., 18:57, Uirgil <uir...@uirgil.ur> wrote:

> > > > Consider the following sequence of decimal numbers, consisting of
> > > > digits 0 and 1
>
> > > > 01.
> > > > 0.1
> > > > 010.1
> > > > 01.01
> > > > 0101.01
> > > > 010.101
> > > > 01010.101
> > > > 0101.0101
> > > > ...
>
> > > > which, when indexed by natural numbers, yilooks like this:
>
> > > > 0_2 1_1 .
> > > > 0_2 . 1_1
> > > > 0_4 1_3 0_2 . 1_1
> > > > 0_4 1_3 . 0_2 1_1
> > > > 0_6 1_5 0_4 1_3 . 0_2 1_1
> > > > 0_6 1_5 0_4 . 1_3 0_2 1_1
> > > > 0_8 1_7 0_6 1_5 0_4 . 1_3 0_2 1_1
> > > > 0_8 1_7 0_6 1_5 . 0_4 1_3 0_2 1_1
> > > > ...

> While every real mathematician knows

This sequence grows without limit.
>
> > This can be proved by taking any number n and showing

> > that there is a number k such that all for terms a(j) of the sequence
> > with k > j we have a(j) > n. Proof: For given n take k = n + 10.
>
> ow does that work for the sequence a(j) = 0 for all j?

Is 0 larger than any number n?

>
> > Every set theorist knows that the sequence of sets of indices left of
> > the decimal point has the limit empty set. This is an requirement of
> > set theory.
>
> Then let us see which axiom,  or set of axioms, of some set theory which
> actually requires such nonsense. say among the axioms for ZFC, for
> example.

Try to learn it. Look what William Hughes just explains here.

>
>
>
> > And finally everybody knows that decimal numbers, by definition,
> > cannot consist of digits that have no indexs.
>
> Numbers (decimal or otherwise) can exist without any digits of any sort,
> but decimal numerals can not.

But the numbers in above list exist with their digits.

>
> Since a numeral is merely a name for a number,

the set of all numbers is countable.

Regards, WM

[Uirgil]

> "WM" <muec...@rz.fh-augsburg.de> wrote in message
> news:f58b4287-182c-4a02...@b12g2000vbg.googlegroups.com...
>

...

> Incidentally, I insist, as a critical point, that we should be using N*,
> not N, for any "infinite endeavours"

Fortunately for the health of mathematics, WM has no power to compel
compliance with his idiotic insistings, other than by those innocents
unfortunate enough to be compelled to enroll in his classes.

Which, if there is a just God, WM will be called to answer for later.

[WM]

On 17 Nov., 19:16, Uirgil <uir...@uirgil.ur> wrote:
> > "WM" <mueck...@rz.fh-augsburg.de> wrote in message

And Virgil will be the public prosecutor?
Just a remark, I am not the author of above application.

Regards, WM

[LudovicoVan]

"Uirgil" <uir...@uirgil.ur> wrote in message
news:uirgil-B4A0C7....@BIGNEWS.USENETMONSTER.COM...

The one who has got something inverted here is you.

You are again invited to stop the spam and disturbance and kindly get lost.

-LV

[William Hughes]

On Nov 17, 1:23 pm, "LudovicoVan" <ju...@diegidio.name> wrote:
> "William Hughes" <wpihug...@gmail.com> wrote in message
>
> news:1ec0c2cc-f926-4fd4...@y8g2000yqy.googlegroups.com...
>
>
>
>
>
>
>
>
>
> > On Nov 17, 9:59 am, "LudovicoVan" <ju...@diegidio.name> wrote:
> >> "William Hughes" <wpihug...@gmail.com> wrote in message
> >>news:28bff553-f679-4e23...@c17g2000yqe.googlegroups.com...
>
> >> > Note that *set* limits have some important properties.
>
> >> > Given a sequence of sets {B_1,B_2,B_3,...}
> >> > then the set limit always exists (it
> >> > may be the empty set).
>
> >> > If we have
>
> >> > A = set limit {B_1,B_2,B_3....}
>
> >> > Then
>
> >> >     A is a set
> >> >     A cannot contain an element that is not contained
> >> >       in any of the B's
>
> >> Williams going around, in circles:
>
> >> It was already mentioned that it is wrong to use that specific definition
> >> to
> >> solve the balls and vase problem.
>

> >> <http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Specia...>

>
> > The problem is the above applies to *any* definition of a *set* limit.
>
> But those definitions are a *specific* case of these:
>

> <http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Sequen...>


Well, I could defend myself by pointing out that these are talking
about limits of sets (and any limit, e.g. the usual limit on real
numbers can be considered the limit of sets) and I was talking about
set limits. However, I don't think this is very convincing.
I will simply point out that the first defintion, does not apply
in this case.

A more fundemental problem is that there is no reason to
expect the cardinality of the B's to have anything to do
with the cardinality of A.

Eg. B_n = [-1/n,1/n]. Then A is {0}

More like the current situation.

B_n: {all rational numbers, q |
q can be written as k/n^2 (k an integer) AND q in [-1/n,1/n]}

Then B_n is finite. |B_n| grows without bound.
A= {0}, |A| = 1 (if you want A the empty set,the add the condition
that
q is nonzero)

So there is no reason to change the limit to make the cardinality of
the
limit equal to the limit of the cardinalities
(nor is there a problem that WM two limits are different)

[WM]

On 17 Nov., 21:21, William Hughes <wpihug...@gmail.com> wrote:

> (nor is there a problem that WM two limits are different)-

Interesting. A nice claim.
The limit of a sequence may depend on the method which is used to
calculate it? Perhaps it may even depend on the person who calculates
it?

Piffle. Mathematics serves as a tool to predict scientific results.
Therefore its results must be independent of the method and of the
person.
If the value of the continued fraction
((((((10^0)/10)+10^1)/10)+10^2)/10)+…
is infinite, then set theory cannot yield a result < 1 (because for no
digit left to the decimal point there remains an index - but digits of
decimal representations cannot exist without indexes). If both results
were tolerated, then mathematics would lose its state of being a
useful tool for scientific applications.

Therefore the result of set theory is humbug.

Regards, WM

[William Hughes]

On Nov 17, 5:23 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 17 Nov., 21:21, William Hughes <wpihug...@gmail.com> wrote:
>
> > (nor is there a problem that WM two limits are different)-
>
> Interesting. A nice claim.
> The limit of a sequence may depend on the method which is used to
> calculate it?

Nope, but it does depend on which limit is used. The fact
that in Wolkenmuekenheim the two limits are the same does
not mean that you are using the same limit both times.

[Uirgil]

In article
<6a251495-fced-4fe0...@w1g2000vbx.googlegroups.com>,

You are certainly author of even worse!

[Uirgil]

In article <k88p6q$sd$1...@dont-email.me>,

> > way limited to only those.

> >
> > So that, as usual, LV has things inverted.
>
> The one who has got something inverted here is you.

Another in the long line of LV's irrelevant ad homs noted!

>
> You are again invited to stop the spam and disturbance
>

> -LV
>
I would, but I have no power to shut off either WM or LV.

[Virgil]

In article
<126c3310-d023-4f33...@o8g2000yqh.googlegroups.com>,

There is no number which is larger than any number.

>
> >
> > > Every set theorist knows that the sequence of sets of indices left of
> > > the decimal point has the limit empty set. This is an requirement of
> > > set theory.
> >
> > Then let us see which axiom,  or set of axioms, of some set theory which
> > actually requires such nonsense. say among the axioms for ZFC, for
> > example.
>
> Try to learn it. Look what William Hughes just explains here.
> >
> >
> >
> > > And finally everybody knows that decimal numbers, by definition,
> > > cannot consist of digits that have no indexs.
> >
> > Numbers (decimal or otherwise) can exist without any digits of any sort,
> > but decimal numerals can not.
>
> But the numbers in above list exist with their digits.
> >
> > Since a numeral is merely a name for a number,
>
> the set of all numbers is countable.

Every numeral being a number does not limit the number of numbers,
it only, at most, limits the number of numerals.

So that, as usual, LV has things backwards.
--

[Uirgil]

In article
<ace820dc-9361-4752...@ib4g2000vbb.googlegroups.com>,

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

> On 17 Nov., 21:21, William Hughes <wpihug...@gmail.com> wrote:
>
> > (nor is there a problem that WM two limits are different)-
>
> Interesting. A nice claim.
> The limit of a sequence may depend on the method which is used to
> calculate it? Perhaps it may even depend on the person who calculates
> it?

When WM calculates it, the result may also depend on WHEN he calculates
it, as there is no guarantee that WM will get the same result twice n a
row!

>
> Piffle. Mathematics serves as a tool to predict scientific results.

Among many other uses, some of which have no scientific applications.

>
> Therefore the result of set theory is humbug.

Only when set theory is being mis-manipulated by humbugs like WM.

[WM]

On 17 Nov., 23:08, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 17, 5:23 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > On 17 Nov., 21:21, William Hughes <wpihug...@gmail.com> wrote:
>
> > > (nor is there a problem that WM two limits are different)-
>
> > Interesting. A nice claim.
> > The limit of a sequence may depend on the method which is used to
> > calculate it?
>
> Nope, but it does depend on which limit is used.

The Cauchy-limit or the Cantor-limit?
1/((((((10^0)/10)+10^1)/10)+10^2)/10)+… = 0 (Cauchy)
1/((((((10^0)/10)+10^1)/10)+10^2)/10)+… > 1 (Cantor)

Look into matheology § 154 to learn the consequences.

Regards, WM

[gus gassmann]

Ahem. Virgil, that is as nonsensical as anything WM spews forth.

First, you left out the 'n', which in the context of this exchange
clearly is meant to be integer. And yes, there are numbers that are
larger than every integer.

Consider also this: Let x be any number.
Then x+1 is larger than x.
You complete the syllogism...

[William Hughes]

On Nov 18, 7:13 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 17 Nov., 23:08, William Hughes <wpihug...@gmail.com> wrote:
>
> > On Nov 17, 5:23 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > On 17 Nov., 21:21, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > (nor is there a problem that WM two limits are different)-
>
> > > Interesting. A nice claim.
> > > The limit of a sequence may depend on the method which is used to
> > > calculate it?
>
> > Nope, but it does depend on which limit is used.
>
> The Cauchy-limit or the Cantor-limit?

Niether.

The fact that in Wolkenmuekenheim the two limits

are assumed to be the same does

[WM]

Is it correct in mathematics to claim:
1/((((((10^0)/10)+10^1)/10)+10^2)/10)+… = 0 ?
And is it also correcr to claim
1/((((((10^0)/10)+10^1)/10)+10^2)/10)+… > 1 ?
Is it is therefore correct to claim 0 > 1?

Or can you give some guidelines for beginners, when and why which of
the limits has to be applied?

Regards, WM

[William Hughes]

On Nov 18, 2:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
<snip>

> Or can you give some guidelines for beginners,

When someone says you are using two different limits
do not ask "Which of these two methods should I use
to evaluate one limit?"

[WM]

On 18 Nov., 19:21, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 18, 2:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> <snip>
>
> > Or can you give some guidelines for beginners,
>
> When someone says you are using two different limits

the he should point out the difference and not remain in sibylline
murmuring. If set theory is correct, then we can calculate limits of
sets of indexes and apply the results in mathematics. We get
1/((((((10^0)/10)+10^1)/10)+10^2)/10)+… = 0
and
1/((((((10^0)/10)+10^1)/10)+10^2)/10)+… > 1

Regards, WM

[William Hughes]

On Nov 18, 2:40 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 18 Nov., 19:21, William Hughes <wpihug...@gmail.com> wrote:
>
> > On Nov 18, 2:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > <snip>
>
> > > Or can you give some guidelines for beginners,
>

You should avoid cutting someone off in mid sentence.

[WM]

Why, when nothing is said by him?

Regards, WM

[Ralf Bader]

I am sure that the limit of your stupidity has not yet been reached.

[Vurgil]

In article
<b8d67bf3-ec24-4451...@y6g2000vbb.googlegroups.com>,

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

> On 17 Nov., 23:08, William Hughes <wpihug...@gmail.com> wrote:
> > On Nov 17, 5:23 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > On 17 Nov., 21:21, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > (nor is there a problem that WM two limits are different)-
> >
> > > Interesting. A nice claim.
> > > The limit of a sequence may depend on the method which is used to
> > > calculate it?
> >
> > Nope, but it does depend on which limit is used.
>
> The Cauchy-limit or the Cantor-limit?

> 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+Š = 0 (Cauchy)
> 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+Š > 1 (Cantor)

Theses are not, as claimed by WM inin another post, anything like
continued fractions, so it is not clear what the finite terms are
supposed to be.

And without knowing that, no limit can possibly be determined.

Now if is just that "1/((((((10^0)/10)+10^1)/10)+10^2)/10)+Š" is
sufficiently ambiguous that Cauchy and Cantor disagree on what the
finite sequences are which leads to this expression, I am not at all
surprized.

[Vurgil]

In article
<e5d33c50-6d57-48c9...@o8g2000yqh.googlegroups.com>,

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

> On 18 Nov., 18:45, William Hughes <wpihug...@gmail.com> wrote:
> > On Nov 18, 7:13 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > On 17 Nov., 23:08, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Nov 17, 5:23 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > On 17 Nov., 21:21, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > > > (nor is there a problem that WM two limits are different)-
> >
> > > > > Interesting. A nice claim.
> > > > > The limit of a sequence may depend on the method which is used to
> > > > > calculate it?
> >
> > > > Nope, but it does depend on which limit is used.
> >
> > > The Cauchy-limit or the Cantor-limit?
> >
> > Niether.
> >
> > The fact  that in Wolkenmuekenheim the two limits
> > are assumed to be the same does
> > not mean that you are using the same limit both times.
>
> Is it correct in mathematics to claim:

> 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+Š = 0 ?

> And is it also correcr to claim

> 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+Š > 1 ?

> Is it is therefore correct to claim 0 > 1?
>
> Or can you give some guidelines for beginners, when and why which of
> the limits has to be applied?
>

I see no reason to suppose that the expression is well enough defined to
have anything like a unique limit.
If it is expressible as the limit of a sequence at all, then show us
the terms of such a sequence.

[Vurgil]

In article
<9c51d4c7-cfee-41b5...@ez26g2000vbb.googlegroups.com>,

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

> On 18 Nov., 19:21, William Hughes <wpihug...@gmail.com> wrote:
> > On Nov 18, 2:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > <snip>
> >
> > > Or can you give some guidelines for beginners,
> >
> > When someone says you are using two different limits
>
> the he should point out the difference and not remain in sibylline
> murmuring. If set theory is correct, then we can calculate limits of
> sets of indexes and apply the results in mathematics. We get

> 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+Š = 0
> and
> 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+Š > 1

Until you can show that these expressions have some unambiguous meaning,
it is not clear that anyone can get anything but a headache from them.

[Vurgil]

In article
<74f6d87d-52e0-42e8...@s14g2000vba.googlegroups.com>,

But then nothing of any value was said by you either.

[Jesse F. Hughes]

To Virgil:

Why the fuck do you keep changing your "From:" line?

You are no better than the trolls to whom you reply. If someone wants
to killfile you (and Lord knows there are reasons), then fucking well
let them.

Escaping killfiles by morphing your From line is despicable, son.

--
Jesse F. Hughes
"And a journal can beg me for the right to publish it [...] because
I'd rather see it in "People" magazine [...]"
--James Harris on his simple proof of Fermat's last theorem

[Virgil]

In article <87k3titj...@phiwumbda.org>,

"Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> To Virgil:
>
> Why the fuck do you keep changing your "From:" line?
>
> You are no better than the trolls to whom you reply. If someone wants
> to killfile you (and Lord knows there are reasons), then fucking well
> let them.

Sorry!

I try to remember not to do it in what should be serious NG's like this
sci.logic and sci.math, but only in ones like alt.atheism where
creatinists try to ignore us atheists.
--

[WM]

On 19 Nov., 01:10, Vurgil <Vur...@arg.erg> wrote:
> In article
> <b8d67bf3-ec24-4451-8573-aa0a52799...@y6g2000vbb.googlegroups.com>,

>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 17 Nov., 23:08, William Hughes <wpihug...@gmail.com> wrote:
> > > On Nov 17, 5:23 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 17 Nov., 21:21, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > (nor is there a problem that WM two limits are different)-
>
> > > > Interesting. A nice claim.
> > > > The limit of a sequence may depend on the method which is used to
> > > > calculate it?
>
> > > Nope, but it does depend on which limit is used.
>
> > The Cauchy-limit or the Cantor-limit?

> > 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+ = 0 (Cauchy)
> > 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+ > 1 (Cantor)

>
> Theses are not, as claimed by WM inin another post, anything like
> continued fractions, so it is not clear what the finite terms are
> supposed to be.

It is clear to every sufficiently intelligent reader.

>
> And without knowing that, no limit can possibly be determined.
>

> Now if is just that "1/((((((10^0)/10)+10^1)/10)+10^2)/10)+ " is

> sufficiently ambiguous that Cauchy and Cantor disagree on what the
> finite sequences are which leads to this expression, I am not at all

> surprized.-

Thank you for implicitly confessing that you do not see a way how the
set theoretical limit { } of the indices of the integer-digits in

> > 0_2 1_1 .
> > 0_2 . 1_1
> > 0_4 1_3 0_2 . 1_1
> > 0_4 1_3 . 0_2 1_1
> > 0_6 1_5 0_4 1_3 . 0_2 1_1
> > 0_6 1_5 0_4 . 1_3 0_2 1_1
> > 0_8 1_7 0_6 1_5 0_4 . 1_3 0_2 1_1
> > 0_8 1_7 0_6 1_5 . 0_4 1_3 0_2 1_1
> > ...

can be avoided or how the application of set theory in calculating the
limit can be interpreted as "another" limit.

Regards, WM

[WM]

On 19 Nov., 01:14, Vurgil <Vur...@arg.erg> wrote:

>
> I see no reason to suppose that the expression is well enough defined to
> have anything like a unique limit.
> If it is  expressible as the limit of a sequence at all, then show us

> the terms of such a sequence.- Zitierten Text ausblenden -

Here you are:

> > 01.
> > 0.1
> > 010.1
> > 01.01
> > 0101.01
> > 010.101
> > 01010.101
> > 0101.0101
> > ...

Is this in fact more difficult to grasp than, say, the Conway
sequence? Should I be proud for that reason?

Regards, WM

[Vurgil]

In article
<f2d00db5-e13a-47d9...@y6g2000vbb.googlegroups.com>,

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

> On 19 Nov., 01:14, Vurgil <Vur...@arg.erg> wrote:
>
> >
> > I see no reason to suppose that the expression is well enough defined to
> > have anything like a unique limit.
> > If it is  expressible as the limit of a sequence at all, then show us
> > the terms of such a sequence.

> Here you are:
> > > 01.
> > > 0.1
> > > 010.1
> > > 01.01
> > > 0101.01
> > > 010.101
> > > 01010.101
> > > 0101.0101
> > > ...
> Is this in fact more difficult to grasp than, say, the Conway
> sequence? Should I be proud for that reason?

It is STILL not at all clear that the sequence you indicated has any
limit according to any standard definition of limit of a sequence.

What definition (with a URL which will verify its authenticity) do you
propose to use on your sequence

[Vurgil]

In article
<4304750f-ea45-46e7...@o30g2000vbu.googlegroups.com>,

Does WW now claim that

1/((((((10^0)/10)+10^1)/10)+10^2)/10)+

somehow produces the sequence

0_2 1_1 .
0_2 . 1_1
0_4 1_3 0_2 . 1_1
0_4 1_3 . 0_2 1_1
0_6 1_5 0_4 1_3 . 0_2 1_1
0_6 1_5 0_4 . 1_3 0_2 1_1
0_8 1_7 0_6 1_5 0_4 . 1_3 0_2 1_1
0_8 1_7 0_6 1_5 . 0_4 1_3 0_2 1_1
...

?


And I certainly DO see ways how WM's nonsense can be avoided.

A simple PLONK would do it, but I find more amusement in seeing WMs
struggles to maintain what little sanity he has left and still support
the insupportable.