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Groups > sci.math > #424760 > unrolled thread
| Started by | transfinity01@gmail.com |
|---|---|
| First post | 2018-10-02 03:07 -0700 |
| Last post | 2018-10-04 19:00 -0500 |
| Articles | 19 on this page of 79 — 9 participants |
Back to article view | Back to sci.math
The structure of |N transfinity01@gmail.com - 2018-10-02 03:07 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-02 03:39 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-02 03:42 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-02 05:34 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-02 11:34 -0700
Re: The structure of |N me <dvhaus.dresden@gmail.com> - 2018-10-02 11:45 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-03 03:07 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-03 22:40 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-03 03:17 -0700
Re: The structure of |N me <dvhaus.dresden@gmail.com> - 2018-10-03 04:13 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-03 09:11 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-04 02:43 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-03 22:42 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-04 06:49 -0700
Re: The structure of |N Python <python@python.invalid> - 2018-10-04 21:37 +0200
Re: The structure of |N Python <python@python.invalid> - 2018-10-04 21:33 +0200
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-03 22:38 -0700
Re: The structure of |N me <dvhaus.dresden@gmail.com> - 2018-10-02 11:57 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-03 22:39 -0700
Re: The structure of |N Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-10-02 13:18 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-03 03:08 -0700
Re: The structure of |N Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-10-03 19:34 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-04 06:45 -0700
Re: The structure of |N Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-10-04 13:29 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-05 03:05 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-05 04:19 -0700
Re: The structure of |N me <dvhaus.dresden@gmail.com> - 2018-10-05 04:32 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-05 04:22 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-05 04:29 -0700
Re: The structure of |N me <dvhaus.dresden@gmail.com> - 2018-10-05 04:36 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-05 13:15 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-05 13:47 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-05 13:49 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-05 23:37 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-06 03:35 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-06 08:17 -0700
Re: The structure of |N me <dvhaus.dresden@gmail.com> - 2018-10-06 09:07 -0700
Re: The structure of |N WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-07 08:15 -0700
Re: The structure of |N Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-10-05 06:30 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-05 13:13 -0700
Re: The structure of |N Dan Christensen <Dan_Christensen@sympatico.ca> - 2018-10-05 18:53 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-07 23:01 -0700
Re: The structure of |N WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-08 09:14 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-08 22:32 -0700
Re: The structure of |N WM <wolfgang.mueckenheim@hs-augsburg.de> - 2018-10-09 01:38 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-09 05:20 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-09 09:20 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-09 09:31 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-10 03:51 -0700
Re: The structure of |N Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-09 17:37 +0100
Re: The structure of |N transfinity01@gmail.com - 2018-10-10 03:51 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-10 22:27 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-10 23:16 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-10 23:18 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-11 02:20 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-11 02:57 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-12 03:49 -0700
Re: The structure of |N Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-12 14:04 +0100
Re: The structure of |N transfinity01@gmail.com - 2018-10-13 09:11 -0700
Re: The structure of |N Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-13 20:03 +0100
Re: The structure of |N transfinity01@gmail.com - 2018-10-14 02:50 -0700
Re: The structure of |N Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2018-10-13 20:09 +0100
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-14 22:49 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-15 02:37 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-20 01:59 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-21 22:56 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-10 22:21 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-10 23:16 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-04 22:31 -0700
Re: The structure of |N Zelos Malum <zelos.malum@gmail.com> - 2018-10-03 22:41 -0700
Re: The structure of |N transfinity01@gmail.com - 2018-10-04 06:49 -0700
Re: The structure of |N "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-10-02 19:00 -0500
Re: The structure of |N transfinity01@gmail.com - 2018-10-03 03:09 -0700
Re: The structure of |N "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-10-03 21:12 -0500
Re: The structure of |N transfinity01@gmail.com - 2018-10-04 06:52 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-04 07:58 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-04 14:13 -0700
Re: The structure of |N bursejan@gmail.com - 2018-10-04 14:24 -0700
Re: The structure of |N "Shobe, Martin" <martin.shobe@yahoo.com> - 2018-10-04 19:00 -0500
Page 4 of 4 — ← Prev page 1 2 3 [4]
| From | transfinity01@gmail.com |
|---|---|
| Date | 2018-10-14 02:50 -0700 |
| Message-ID | <3e6dd0a9-045f-433a-8c2e-587b296a9f96@googlegroups.com> |
| In reply to | #425507 |
Am Samstag, 13. Oktober 2018 21:05:10 UTC+2 schrieb Alan Smaill: > transfinity01@gmail.com writes: > > > Am Freitag, 12. Oktober 2018 15:05:10 UTC+2 schrieb Alan Smaill: > >> transfinity01@gmail.com writes: > >> > >> > Am Donnerstag, 11. Oktober 2018 11:58:06 UTC+2 schrieb Zelos Malum: > >> > > >> >> >If only two lines arise, then we have as many lines as split > >> >> > points. If you cannot understand so simple mathematics > >> >> > >> >> The one not understanding is you, you assume that the amount from > >> >> finite cases has any effect on infinite, it does not. > >> > > >> > Why then should this happen in the diagonal argument? > >> > >> For the same reason that it is possible to show that > >> the square root ot 2 is not rational -- a proof that you accept, > > > > Because it is based on mathematics. If Zelos Malum was right, the > > proof would not hold "in the limit". > > But what on earth is the difference between the two cases, in your > opinion? > (other than that you personally accept one and reject the other) There is no difference in my opinion. For sqrt2 there is a sequence 1. 1.4 1.41 1.414 ... approaching but never reaching the limit 1.414... This limit can be calculated to every desired precision. But it cannot be expressed by fractions (digits) - not even by infinitely many. In Cantor's diagonal argument we can prove that every entry differs from the diagonal number constructed up to that entry. But in order to obtain the complete diagonal number, we would need an actually infinite, uninterrupted sequence of digits that represent the diagonal number. That is impossible because a real number defined by a digit sequence would have to be fixed, i.e., it would need a last digit. In the Binary Tree we have the atomic structure | / \ Every sequence of such structures is bounded by less than aleph_0 paths. In order to get a limit of uncountably many paths, we would need a gap. Contradiction. > > >> despite knowing that however many pairs of naturals (n,m) you examine, > >> there are *always* infinitely many pairs that have not been examined > > > > and that could supply a fraction sqrt2. In fact everybody accepting an > > infinite decimal fraction for sqrt2 assumed this. > > "everyone accepts" is not a reason for WM to accept. As I said above: An infinite sequence cannot define a real number. > > In one case you take the presence of infinitely many unexamined cases as > blocking a proof, in the other you disregard this problem. > Logic requires you to explain this divergence. I do not. Above I answered Zelos who denied that finite cases have any effect on infinite. I showed him that this is incorrect and would destroy Cantor's diagonal argument. > > Double standards!! I accept only those infinite results which are compatible with the finite terms of a corresponding sequence - in all cases. I accept that the antidiagonal is not in Cantor's list, but I do not accept that it ever completes the defintion of a real number. Regards, WM
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2018-10-13 20:09 +0100 |
| Message-ID | <fweftx9mzoe.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #425503 |
transfinity01@gmail.com writes: > Am Freitag, 12. Oktober 2018 15:05:10 UTC+2 schrieb Alan Smaill: >> transfinity01@gmail.com writes: >> >> > Am Donnerstag, 11. Oktober 2018 11:58:06 UTC+2 schrieb Zelos Malum: >> > >> >> >If only two lines arise, then we have as many lines as split >> >> > points. If you cannot understand so simple mathematics >> >> >> >> The one not understanding is you, you assume that the amount from >> >> finite cases has any effect on infinite, it does not. >> > >> > Why then should this happen in the diagonal argument? >> >> For the same reason that it is possible to show that >> the square root ot 2 is not rational -- a proof that you accept, > > Because it is based on mathematics. If Zelos Malum was right, the > proof would not hold "in the limit". But why exactly is there a difference here? Forget what Zelos Malum says, explain why *you* treat the two cases differently. (Simply saying that one is mathematics, and the other is not, does not provide an explanation.) >> despite knowing that however many pairs of naturals (n,m) you examine, >> there are *always* infinitely many pairs that have not been examined > > and that could supply a fraction sqrt2. In fact everybody accepting an > infinite decimalfraction for sqrt2 assumed this. "Everybody accepts" is not a reason for WM to accept. In one case you say that the presence of infinitely many unexamined cases blocks a proof, in the other you ignore the problem. Logic requires you to explain this divergence. Double standards!! > Regards, WM -- Alan Smaill
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| From | Zelos Malum <zelos.malum@gmail.com> |
|---|---|
| Date | 2018-10-14 22:49 -0700 |
| Message-ID | <6fa63658-bb85-41e9-a4fd-d08d56925f0e@googlegroups.com> |
| In reply to | #425468 |
>Why then should this happen in the diagonal argument? It doesn't, it at no point argues from the finite, the infinite. >No. The infinite of mathematics can be determined from the finite. The sequence of (nodes - paths) 0, 0, 0, ... cannot have another limit than 0. Not studied much topology I take it? It can have non-zero limits and even have multiple limits. >Because it is based on mathematics. If Zelos Malum was right, the proof would not hold "in the limit". At what step does it arguefrom the finite the infinite? >As I said above: An infinite sequence cannot define a real number. Considering real numbesr can be constructed from cauchy sequences of rational numbers, you are simply wrong. >I do not. Above I answered Zelos who denied that finite cases have any effect on infinite. I showed him that this is incorrect and would destroy Cantor's diagonal argument. It woudln't cause it at no point argues a finite case. You got an infinite list of ifninite decimals and get a new infinite decimal number that. Never ifnite >I accept only those infinite results which are compatible with the finite terms of a corresponding sequence - in all cases. I accept that the antidiagonal is not in Cantor's list, but I do not accept that it ever completes the defintion of a real number. That arguemenet however is selfcontradictory.
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| From | transfinity01@gmail.com |
|---|---|
| Date | 2018-10-15 02:37 -0700 |
| Message-ID | <c51ea236-31fd-4026-a219-374b580e79d9@googlegroups.com> |
| In reply to | #425567 |
Am Montag, 15. Oktober 2018 07:49:53 UTC+2 schrieb Zelos Malum: > >Why then should this happen in the diagonal argument? > > It doesn't, it at no point argues from the finite, the infinite. The diagonal number is infinite. But only its finite parts are available. > > >No. The infinite of mathematics can be determined from the finite. The sequence of (nodes - paths) 0, 0, 0, ... cannot have another limit than 0. > > Not studied much topology I take it? Most of topology is nonsense. > > >Because it is based on mathematics. If Zelos Malum was right, the proof would not hold "in the limit". > > At what step does it argue from the finite the infinite? The diagonal number: Only digits at finite positions in finite lines are available. But you argue that the infinite sequence is not in the infinite list. Every bijection: Only pairs (like n, q) at finite positions are available. You argue that all elements can be paired. Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-10-20 01:59 -0700 |
| Message-ID | <e743bc95-77e9-49ab-ac60-205b640d9f93@googlegroups.com> |
| In reply to | #425578 |
What measurement should "The diagonal number
is infinite. But only its finite parts
are available." be?
Take your other example 2) alle Endsegments are
infinite and 1) there is no number in all Endsegments.
This is true if inifnite is infinite:
n
E_1 : ******************|*******...
E_2 : o*****************|*******...
E_3 : oo****************|*******...
E_4 : ooo***************|*******...
...
E_m : oooooooooooooooooo|o******...
E_m+1 : oooooooooooooooooo|oo*****...
...
Are both true if infinite is not infinite?
Lets say, infinite means collection of finite,
a kind of modal logic with multiple possible
worlds. Then a possible world would be:
Possible World 1:
E_1 : ***************
E_2 : o**************
E_3 : oo*************
E_4 : ooo************
...
E_k-2 : ooooooooooooo**
E_k-1 : oooooooooooooo*
E_k : ooooooooooooooo
Possible World 2:
n
E_1 : ******************|******
E_2 : o*****************|******
E_3 : oo****************|******
E_4 : ooo***************|******
...
E_m : oooooooooooooooooo|o*****
E_m+1 : oooooooooooooooooo|oo****
...
E_k-2 : ooooooooooooooooooooooo**
E_k-1 : oooooooooooooooooooooooo*
E_k : ooooooooooooooooooooooooo
Now there are a lot of questions. Possibly
2) is now false. The endsegments are not anymore
infinite. A further question is when we have
some n, what worlds are reachable. Is it
possible that we have n, with no E_m, such
that n not in E_m.
Looks compared to FOL+ZFC, it could result in
an extremly complex formalization of Muckamatics,
with a lot of decisions that need to be made,
to get a coherent model of Muckamatics. Mostlikely
the simplest attempt already yields to some inconsistency
that is not found in FOL+ZFC, but is part of the
problem of the immature Muckamatics. All these
inconsistencies are problems of Muckamatics, which
only Prof Mucke Funk can heal, if this is at all
possible. Maybe its sympthom of a broken mind, without
some systematics and cannot be healed. If there is no
axiom system so far, there might be
also none in the future, even not in 3000 years.
Am Montag, 15. Oktober 2018 11:37:29 UTC+2 schrieb transf...@gmail.com:
> Am Montag, 15. Oktober 2018 07:49:53 UTC+2 schrieb Zelos Malum:
> > >Why then should this happen in the diagonal argument?
> >
> > It doesn't, it at no point argues from the finite, the infinite.
>
> The diagonal number is infinite. But only its finite parts are available.
> >
> > >No. The infinite of mathematics can be determined from the finite. The sequence of (nodes - paths) 0, 0, 0, ... cannot have another limit than 0.
> >
> > Not studied much topology I take it?
>
> Most of topology is nonsense.
> >
> > >Because it is based on mathematics. If Zelos Malum was right, the proof would not hold "in the limit".
> >
> > At what step does it argue from the finite the infinite?
>
> The diagonal number: Only digits at finite positions in finite lines are available. But you argue that the infinite sequence is not in the infinite list.
>
> Every bijection: Only pairs (like n, q) at finite positions are available. You argue that all elements can be paired.
>
> Regards, WM
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| From | Zelos Malum <zelos.malum@gmail.com> |
|---|---|
| Date | 2018-10-21 22:56 -0700 |
| Message-ID | <85ea9c5b-da01-418f-ad0f-41e1db6bb76c@googlegroups.com> |
| In reply to | #425578 |
>The diagonal number is infinite. But only its finite parts are available. No, all of it is because agian "available" isn't a defined predicate. >Most of topology is nonsense. You not understanding it does not make it nonsense >The diagonal number: Only digits at finite positions in finite lines are available. But you argue that the infinite sequence is not in the infinite list. Yes but then again I don't argue in strict mathematics. I grab it whole way infinite. >Every bijection: Only pairs (like n, q) at finite positions are available. You argue that all elements can be paired. Not at all, you assume only finite.
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| From | Zelos Malum <zelos.malum@gmail.com> |
|---|---|
| Date | 2018-10-10 22:21 -0700 |
| Message-ID | <90e93514-148f-4af8-b38a-3f51d01f1a59@googlegroups.com> |
| In reply to | #425276 |
Den tisdag 9 oktober 2018 kl. 18:21:05 UTC+2 skrev transf...@gmail.com: > Am Dienstag, 9. Oktober 2018 14:20:27 UTC+2 schrieb Zelos Malum: > > > > > Think over that! There is nothing restricted to finite levels. ALL of the Binary Tree is covered. Parts without that basic structure simply are not existing. > > > > I have thoguht it over and none of that even matters, when you ahve infinitely many levels, things can become quite different than what you expect. > > The basic structure > > | > o > / \ > > extends into the infinite. It shows that the number of nodes +1 is an upper bound for the number of lines. This restriction is true everywhere. There is no change in the infinite possible. > > Regards, WM That doesn't change but that doesn't mean there are ONLY countably many cause you assume what is finite extends to infinite.
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| From | transfinity01@gmail.com |
|---|---|
| Date | 2018-10-10 23:16 -0700 |
| Message-ID | <7cb98a04-91f1-48fc-8c84-b1f2cff25b48@googlegroups.com> |
| In reply to | #425403 |
Am Donnerstag, 11. Oktober 2018 07:21:15 UTC+2 schrieb Zelos Malum: > Den tisdag 9 oktober 2018 kl. 18:21:05 UTC+2 skrev transf...@gmail.com: > > Am Dienstag, 9. Oktober 2018 14:20:27 UTC+2 schrieb Zelos Malum: > > > > > > > > Think over that! There is nothing restricted to finite levels. ALL of the Binary Tree is covered. Parts without that basic structure simply are not existing. > > > > > > I have thoguht it over and none of that even matters, when you ahve infinitely many levels, things can become quite different than what you expect. > > > > The basic structure > > > > | > > o > > / \ > > > > extends into the infinite. It shows that the number of nodes +1 is an upper bound for the number of lines. This restriction is true everywhere. There is no change in the infinite possible. > > That doesn't change but that doesn't mean there are ONLY countably many cause you assume what is finite extends to infinite. Do you believe that "in the infinite" more than two lines can arise from one node or split-point? Regards, WM
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| From | Zelos Malum <zelos.malum@gmail.com> |
|---|---|
| Date | 2018-10-04 22:31 -0700 |
| Message-ID | <61de4f20-0d94-4a6e-8013-d25eebb375c9@googlegroups.com> |
| In reply to | #424922 |
>In order to get an answer. This answer is easy given in mathematics. I wonder whether it can be given in ZFC too.
Asking the question "What colour is invisible?" is just as meaningful as your questions.
>Why should I derive what probably has already been done?
Because it hasn't, ZFC is not known to have any contradictions, that is why it stands to this day.
>The collection consists of single elements only. Further there must be a smallest collection required. We know that 1, 2, 3, ..., n do not b
elong to it. For every natural number n.
aleph_0 and any set with that cardinality is the smallest and yes, |N is such.
>There is no infinite level. Nodes are existing only at finite levels. What are paths if not sequences of nodes at finite levels?
Tehre is no infinitTH level but there are infinitely many levels so paths spanning all of them are is uncountable and that is not a contradiction.
>I know that the set |N \ {1, 2, 3, ..., n} is said to be infinite for every n in |N. That shows that even sets without elements can be infinite.
No it doesn't you blabbering buffoon.
|N \ {1, 2, 3, ..., n}
is NON-EMPTY!
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| From | Zelos Malum <zelos.malum@gmail.com> |
|---|---|
| Date | 2018-10-03 22:41 -0700 |
| Message-ID | <06923026-5d4e-4718-94e3-8a4f3dd7292d@googlegroups.com> |
| In reply to | #424847 |
Den onsdag 3 oktober 2018 kl. 12:09:03 UTC+2 skrev transf...@gmail.com: > Am Dienstag, 2. Oktober 2018 22:19:06 UTC+2 schrieb Dan Christensen: > > > > Recall that to demonstrate an inconsistency in set theory, you would have derive two contradictory theorems using ONLY the axioms of set theory. > > Is it possible to define the complete infinite Binary Tree in ZFC and to show that there are never more than ℵ0 infinite paths distinguishable by nodes at any level? Is it further possible to show that the sequence 1, 2, 4, 8, ... of nodes has the limit ω? > > Regards, WM Not a contradiction in set theory though cause it doesn't state at any finite level, there is aleph_1 paths.
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| From | transfinity01@gmail.com |
|---|---|
| Date | 2018-10-04 06:49 -0700 |
| Message-ID | <d4cb5934-4f3b-4278-b05c-7bb1672abab4@googlegroups.com> |
| In reply to | #424904 |
Am Donnerstag, 4. Oktober 2018 07:41:54 UTC+2 schrieb Zelos Malum: > Den onsdag 3 oktober 2018 kl. 12:09:03 UTC+2 skrev transf...@gmail.com: > > Am Dienstag, 2. Oktober 2018 22:19:06 UTC+2 schrieb Dan Christensen: > > > > > > > Recall that to demonstrate an inconsistency in set theory, you would have derive two contradictory theorems using ONLY the axioms of set theory. > > > > Is it possible to define the complete infinite Binary Tree in ZFC and to show that there are never more than ℵ0 infinite paths distinguishable by nodes at any level? Is it further possible to show that the sequence 1, 2, 4, 8, ... of nodes has the limit ω? > > > Not a contradiction in set theory though cause it doesn't state at any finite level, there is aleph_1 paths. There is no infinite level. Nodes are existing only at finite levels. What are paths if not sequences of nodes at finite levels? Regards, WM
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| From | "Shobe, Martin" <martin.shobe@yahoo.com> |
|---|---|
| Date | 2018-10-02 19:00 -0500 |
| Message-ID | <pp10rn$cck$1@dont-email.me> |
| In reply to | #424760 |
On 10/2/2018 5:07 AM, transfinity01@gmail.com wrote: > Every natural number that is followed by natural numbers belongs to a finite initial segment of |N. Yes. >Since all natural numbers n_d that can be defined and identified in mathematical discourse are followed by aleph_0 natural numbers, the set N_def of all those n_d is finite, not fixed though. No. [snip nonsense] Martin Shobe
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| From | transfinity01@gmail.com |
|---|---|
| Date | 2018-10-03 03:09 -0700 |
| Message-ID | <f7d34407-6490-4eff-8e00-9f89a85ba41c@googlegroups.com> |
| In reply to | #424808 |
Am Mittwoch, 3. Oktober 2018 02:01:01 UTC+2 schrieb Shobe, Martin: > On 10/2/2018 5:07 AM, transfinity01@gmail.com wrote: > > Every natural number that is followed by natural numbers belongs to a finite initial segment of |N. > > Yes. > > >Since all natural numbers n_d that can be defined and identified in mathematical discourse are followed by aleph_0 natural numbers, the set N_d of all those n_d is finite, not fixed though. > > No. Please find a natural number that requires N_d to be not finite. Regards, WM
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| From | "Shobe, Martin" <martin.shobe@yahoo.com> |
|---|---|
| Date | 2018-10-03 21:12 -0500 |
| Message-ID | <pp3su1$kts$1@dont-email.me> |
| In reply to | #424848 |
On 10/3/2018 5:09 AM, transfinity01@gmail.com wrote: > Am Mittwoch, 3. Oktober 2018 02:01:01 UTC+2 schrieb Shobe, Martin: >> On 10/2/2018 5:07 AM, transfinity01@gmail.com wrote: >>> Every natural number that is followed by natural numbers belongs to a finite initial segment of |N. >> >> Yes. >> >>> Since all natural numbers n_d that can be defined and identified in mathematical discourse are followed by aleph_0 natural numbers, the set N_d of all those n_d is finite, not fixed though. >> >> No. > > Please find a natural number that requires N_d to be not finite. You would think that a single element could be sufficient to make something infinite. Martin Shobe
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| From | transfinity01@gmail.com |
|---|---|
| Date | 2018-10-04 06:52 -0700 |
| Message-ID | <301083b6-4a55-4a39-a4c5-c03c2df12d44@googlegroups.com> |
| In reply to | #424897 |
Am Donnerstag, 4. Oktober 2018 04:12:22 UTC+2 schrieb Shobe, Martin:
> On 10/3/2018 5:09 AM, transfinity01@gmail.com wrote:
> > Am Mittwoch, 3. Oktober 2018 02:01:01 UTC+2 schrieb Shobe, Martin:
> >> On 10/2/2018 5:07 AM, transfinity01@gmail.com wrote:
> >>> Every natural number that is followed by natural numbers belongs to a finite initial segment of |N.
> >>
> >> Yes.
> >>
> >>> Since all natural numbers n_d that can be defined and identified in mathematical discourse are followed by aleph_0 natural numbers, the set N_d of all those n_d is finite, not fixed though.
> >>
> >> No.
> >
> > Please find a natural number that requires N_d to be not finite.
>
> You would think that a single element could be sufficient to make
> something infinite.
I know that the set |N \ {1, 2, 3, ..., n} is said to be infinite for every n in |N. That shows that even sets without elements can be infinite.
Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-10-04 07:58 -0700 |
| Message-ID | <68b92dc9-55b5-4f4d-8331-f822e37edded@googlegroups.com> |
| In reply to | #424925 |
There is no mathematical induction of the
form from natural numbers to the set of natural numbers.
This is NOT mathematical induction:
/* no such mathematical induction schema,
an invention by WM */
0 in M
forall n(n in M => n+1 in M)
-----------------------------
|N in M
You are highly confused and halucinating. The mathematical
induction only says:
/* the usual mathematical induction */
0 in M
forall n(n in M => n+1 in M)
-----------------------------
forall m(m in M)
For example, we can use the above induction schema to
prove that [n,omega) your "final" segments are all infinite.
Here is a proof:
Proof: Inducton base: [0,omega) is infinite by definition.
Induction step. We have already by induction hypothesis
that [n,omega) is infinite, now how about [n+1,omega) is
it also infinite. Yes, we can find a bijection f : [n+1,omega) ->
[n,omega), where f(x) = x - 1.
Q.E.D.
So all that we have proved is that for every n, [n,omega) is
infinite. But thats where mathematics stops. There is no
further induction step, that would then deduce that
[omega,omega) = {} would be infinite. Which induction schema
should this be? Even transfinite induction cannot do that.
Thats just nonsense.
For to apply transfinite induction we would need to have
apply the following induction schema, this is transfinite
induction up to omega+1:
/* this would be transfinite induction
up to omega+1, i.e. for domain omega+1 */
0 in M
forall a(a<omega & a in M => a+1 in M)
forall a(a<omega & a in M) => omega in M
----------------------------------------
forall a(a in M)
Am Donnerstag, 4. Oktober 2018 15:52:46 UTC+2 schrieb transf...@gmail.com:
> Am Donnerstag, 4. Oktober 2018 04:12:22 UTC+2 schrieb Shobe, Martin:
> > On 10/3/2018 5:09 AM, transfinity01@gmail.com wrote:
> > > Am Mittwoch, 3. Oktober 2018 02:01:01 UTC+2 schrieb Shobe, Martin:
> > >> On 10/2/2018 5:07 AM, transfinity01@gmail.com wrote:
> > >>> Every natural number that is followed by natural numbers belongs to a finite initial segment of |N.
> > >>
> > >> Yes.
> > >>
> > >>> Since all natural numbers n_d that can be defined and identified in mathematical discourse are followed by aleph_0 natural numbers, the set N_d of all those n_d is finite, not fixed though.
> > >>
> > >> No.
> > >
> > > Please find a natural number that requires N_d to be not finite.
> >
> > You would think that a single element could be sufficient to make
> > something infinite.
>
> I know that the set |N \ {1, 2, 3, ..., n} is said to be infinite for every n in |N. That shows that even sets without elements can be infinite.
>
> Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-10-04 14:13 -0700 |
| Message-ID | <385afa1f-2fe5-4029-a9c8-3df8101298e6@googlegroups.com> |
| In reply to | #424925 |
How would this show that? Again there is no
induction of a predication "infinite" by the
following schema:
/* no such mathematical induction schema,
an invention by WM */
0 in M
forall n(n in M => n+1 in M)
-----------------------------
|N in M
or you can also write it as follows, using |N = ∪n, namely
the fact that |N can be view as an infinite union:
/* no such mathematical induction schema,
an invention by WM */
0 in M
forall n(n in M => n+1 in M)
-----------------------------
∪n in M
Similarly for infinite intersection. You cannot
use mathematical deduction, for omega as in PA,
to deduce properties of an infinite intersection
as a **whole**. In a prove of
∩ [n,omega] = ∅
We prove something about the elements of the
infinite intersection, and since there are no
such elements, we know the result is empty.
The mathematical induction schema goes from
zero element and successor elements to forall
elements, but not to some complete set.
Even using some element to set bijection
like n <-> [0,..,n-1}, this doesn't give you
your Mückenheimerisches Induktions Axiom...
Am Donnerstag, 4. Oktober 2018 15:52:46 UTC+2 schrieb transf...@gmail.com:
> Am Donnerstag, 4. Oktober 2018 04:12:22 UTC+2 schrieb Shobe, Martin:
> > On 10/3/2018 5:09 AM, transfinity01@gmail.com wrote:
> > > Am Mittwoch, 3. Oktober 2018 02:01:01 UTC+2 schrieb Shobe, Martin:
> > >> On 10/2/2018 5:07 AM, transfinity01@gmail.com wrote:
> > >>> Every natural number that is followed by natural numbers belongs to a finite initial segment of |N.
> > >>
> > >> Yes.
> > >>
> > >>> Since all natural numbers n_d that can be defined and identified in mathematical discourse are followed by aleph_0 natural numbers, the set N_d of all those n_d is finite, not fixed though.
> > >>
> > >> No.
> > >
> > > Please find a natural number that requires N_d to be not finite.
> >
> > You would think that a single element could be sufficient to make
> > something infinite.
>
> I know that the set |N \ {1, 2, 3, ..., n} is said to be infinite for every n in |N. That shows that even sets without elements can be infinite.
>
> Regards, WM
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| From | bursejan@gmail.com |
|---|---|
| Date | 2018-10-04 14:24 -0700 |
| Message-ID | <5756fa0c-2ee8-4ddb-af19-acb6e17a039d@googlegroups.com> |
| In reply to | #424953 |
WM = la mouche dans la bouteille
You need to get to the next level, for example
whats a variable in mathematics...
La philosophie est un combat contre l'ensorcellement
de notre entendement par les ressources de notre
langage. Son but est de montrer à la mouche l'issue
par où s'échapper de la bouteille à mouches. Elle
conduit à la découverte de quelque pur non-sens où
l'entendement se fait des bosses en courant à l'assaut
des frontières du langage. Le monde est mesuré par
le langage, dont les limites sont logiquement
énonçables ; on ne peut que montrer l'indicible et
le secret. La philosophie n'est pas à une doctrine,
c'est une activité. Elle n'est pas une fin en soi,
mais un instrument qui aide à comprendre les limites
du langage, qui sont comme une bouteille à mouches.
Elle montre l'issue ; une fois sortie de la bouteille
à mouches, la philosophie ne sert plus à rien.
http://www.philo5.com/Les%20philosophes/Wittgenstein.htm#_01
Am Donnerstag, 4. Oktober 2018 23:13:51 UTC+2 schrieb burs...@gmail.com:
> How would this show that? Again there is no
> induction of a predication "infinite" by the
> following schema:
>
> /* no such mathematical induction schema,
> an invention by WM */
>
> 0 in M
> forall n(n in M => n+1 in M)
> -----------------------------
> |N in M
>
> or you can also write it as follows, using |N = ∪n, namely
> the fact that |N can be view as an infinite union:
>
> /* no such mathematical induction schema,
> an invention by WM */
>
> 0 in M
> forall n(n in M => n+1 in M)
> -----------------------------
> ∪n in M
>
> Similarly for infinite intersection. You cannot
> use mathematical deduction, for omega as in PA,
> to deduce properties of an infinite intersection
>
> as a **whole**. In a prove of
>
> ∩ [n,omega] = ∅
>
> We prove something about the elements of the
> infinite intersection, and since there are no
> such elements, we know the result is empty.
>
> The mathematical induction schema goes from
> zero element and successor elements to forall
> elements, but not to some complete set.
>
> Even using some element to set bijection
> like n <-> [0,..,n-1}, this doesn't give you
> your Mückenheimerisches Induktions Axiom...
>
> Am Donnerstag, 4. Oktober 2018 15:52:46 UTC+2 schrieb transf...@gmail.com:
> > Am Donnerstag, 4. Oktober 2018 04:12:22 UTC+2 schrieb Shobe, Martin:
> > > On 10/3/2018 5:09 AM, transfinity01@gmail.com wrote:
> > > > Am Mittwoch, 3. Oktober 2018 02:01:01 UTC+2 schrieb Shobe, Martin:
> > > >> On 10/2/2018 5:07 AM, transfinity01@gmail.com wrote:
> > > >>> Every natural number that is followed by natural numbers belongs to a finite initial segment of |N.
> > > >>
> > > >> Yes.
> > > >>
> > > >>> Since all natural numbers n_d that can be defined and identified in mathematical discourse are followed by aleph_0 natural numbers, the set N_d of all those n_d is finite, not fixed though.
> > > >>
> > > >> No.
> > > >
> > > > Please find a natural number that requires N_d to be not finite.
> > >
> > > You would think that a single element could be sufficient to make
> > > something infinite.
> >
> > I know that the set |N \ {1, 2, 3, ..., n} is said to be infinite for every n in |N. That shows that even sets without elements can be infinite.
> >
> > Regards, WM
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| From | "Shobe, Martin" <martin.shobe@yahoo.com> |
|---|---|
| Date | 2018-10-04 19:00 -0500 |
| Message-ID | <pp69in$4g5$1@dont-email.me> |
| In reply to | #424925 |
On 10/4/2018 8:52 AM, transfinity01@gmail.com wrote:
> Am Donnerstag, 4. Oktober 2018 04:12:22 UTC+2 schrieb Shobe, Martin:
>> On 10/3/2018 5:09 AM, transfinity01@gmail.com wrote:
>>> Am Mittwoch, 3. Oktober 2018 02:01:01 UTC+2 schrieb Shobe, Martin:
>>>> On 10/2/2018 5:07 AM, transfinity01@gmail.com wrote:
>>>>> Every natural number that is followed by natural numbers belongs to a finite initial segment of |N.
>>>>
>>>> Yes.
>>>>
>>>>> Since all natural numbers n_d that can be defined and identified in mathematical discourse are followed by aleph_0 natural numbers, the set N_d of all those n_d is finite, not fixed though.
>>>>
>>>> No.
>>>
>>> Please find a natural number that requires N_d to be not finite.
>>
>> You would think that a single element could be sufficient to make
>> something infinite.
>
> I know that the set |N \ {1, 2, 3, ..., n} is said to be infinite for every n in |N.
Good. For once you are correct. (As are those who say it.)
> That shows that even sets without elements can be infinite.
Back to the usual being wrong. The empty set (the only set without
elements) is not infinite.
Martin Shobe
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