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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Newsgroups | sci.math |
| Subject | Re: Déjà vu |
| Date | 2017-01-09 17:18 -0500 |
| Organization | Aioe.org NNTP Server |
| Message-ID | <db678007-6ff8-e7fe-12ae-43380fc1d015@att.net> (permalink) |
| References | (13 earlier) <75ee80ae-6449-4a1b-ab8f-6e199fb50e05@googlegroups.com> <1eb23cf1-3e29-c29c-e650-862d50b8fb83@att.net> <1ac56b66-fea1-4d27-b60c-a9baa9e2dcec@googlegroups.com> <8117b64f-d8ef-2104-f381-5432b75416bf@att.net> <9b8e7dfd-fa18-45ae-8feb-f52037d5cd64@googlegroups.com> |
On 1/9/2017 1:08 PM, WM wrote:
> Am Montag, 9. Januar 2017 18:34:41 UTC+1 schrieb Jim Burns:
>> On 1/7/2017 12:22 PM, WM wrote:
>>> Am Samstag, 7. Januar 2017 16:20:22 UTC+1
>>> schrieb Jim Burns:
>>>> You replace the limit set of a sequence of sets with
>>>> with a set with endpoints equal to the limits of
>>>> of the sequences of endpoints of the set sequence.
>>>
>>> Yes. lim [a_, b_n] = [lim a_, lim b_n].
>>
>> You struggle over what a particular letter-sequence means,
>
> No, I show that two different meanings are confused
> in set theory.
"are confused". Passive voice. "Are confused" by whom?
You introduced another definition for "limit" and
now you have confused yourself.
Here, I have an idea: use the standard definition for
the limit of an increasing sequence of sets: union.
'Bye with the confusion.
>> Define the _least upper bound_ of an increasing sequence
>> of sets A_n as a set B such that,
>> for all n, A_n sub B
>> and
>> for all sets C, if, for all n, A_n sub C, B sub C
>>
>> LUB [ 0, 1 - 1/n ] = [ 0, 1 )
>>
>> Is that "wrong"?
>
> I do not say that one of the two limits is "wrong".
Ah. Therefore, when you say below:
"The reason is that set theory puts union = limit,
which is wrong",
it looks as though what you mean by saying something and
not saying something "has been confused". Of course,
with the use of passive voice, we have no idea
who did the confusing.
> I only show that there are two different limits.
> I do this in order to have an example easy enough
> to understand that the union and the analytical limit
> of the sequence of FISOns differ too.
I see no good reason for you to have introduced your
analytical limit.
You want some contradiction to appear so that you can
argue against complete infinity. But giving some
different definition of "limit" and getting different results
is not a contradiction -- any more than pointing out
the fact that there is no x such that 2*x = 3 _in the integers_
while at the same time there is such an x _in the rationals_.
That's not to say that I can't think of less-than-good
reasons.
>>> The reason is that set theory puts union = limit,
>>> which is wrong.
>>
>> The least upper bound of an increasing sequence of sets
>> is the union of those sets.
>
> According to set theory the least upper bound of the
> sequence of FISONs is a set with cardinality aleph_0.
> The union of FISONs however has not cardinality aleph_0.
The least upper bound and the union are the same set.
Apparently, it "has been confused" that the same set both
has and doesn't have the cardinality aleph_0 .
> Everybody can see this here
> 1
> 1, 2
> 1, 2, 3
> ...
> The claim that all finite sets when written together
> in a single row yield a set that is larger than all,
> is simply foolish.
No set in an _infinite_ increasing sequence of sets
can be as large as or larger then all the sets in the sequence.
If it were, it would have to be the last set, but there is no
last set.
>> Every FISON is a proper subset of the union of all FISONs.
>
> No. Since the union consists only of FISONs,
> it cannot surpass all.
This is as false as the last time you said this.
There is no last FISON, so the union _must_
surpass all.
>> Also, there is a mapping from the union to a
>> proper subset of the union, what we commonly consider
>> proof that the union is infinite.
>
> The union is infinite, but not transfinite,
>> i.e., not greater than all unioned sets.
Why not use the same meaning for "transfinite" as
everyone else?
>> Also also, this is not true of any FISON. They are
>> each finite.
>
> Of course. Their whole sequence can be defined recursively
> by F(n) = F(n-1) U {n}.
I would agree with the "of course", but not because of
that recursion relation -- which looks remarkably similar
to the recursive definition for von Neumann ordinals.
Von Neumann ordinals have no problem with being infinite.
> If there are infinitely many FISONs,
> then we have infinitely many such equantions and hence
> infinitely many unions already producing all infinitely
> many FISONs. None has card aleph_0.
I'm hoping that you don't mean "of course" all FISONs
are finite because none has card aleph_0. That isn't
a reason, it's a re-statement.
> A further union,
> number omega + 1, without any further ingerdient, cannot
> surpass the all existing sets, because to surpass in
> cardinality means to have more elements.
The cardinality of omega + 1 is the same as the cardinality
of omega.
By an interesting non-coincidence, omega + 1 has a bijection
with omega which is a proper subset of omega + 1 and this
is the definition of an infinite set. Funny how that
works out.
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Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-03 07:24 -0800
Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-03 18:47 +0100
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-03 11:27 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-04 03:34 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-04 06:34 -0800
Re: Déjà vu "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-05 00:17 +0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-04 11:14 -0800
Re: Déjà vu "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-05 20:39 +0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 08:53 -0800
Re: Déjà vu "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-07 17:55 +0800
Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:07 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:13 -0800
Re: Déjà vu Simon Roberts <retenshun@gmail.com> - 2017-01-07 04:03 -0800
Re: Déjà vu "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-08 00:54 +0800
Re: 4-figure tables and geometry "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-08 00:58 +0800
Re: 4-figure tables and geometry Apollyon <adravirgo@gmail.com> - 2017-01-07 09:01 -0800
Re: 4-figure tables and geometry "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-07 12:25 -0800
Re: 4-figure tables and geometry Peter Percival <peterxpercival@hotmail.com> - 2017-01-07 20:36 +0000
Re: 4-figure tables and geometry "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-07 12:41 -0800
Re: 4-figure tables and geometry bursejan@gmail.com - 2017-01-07 16:04 -0800
Re: 4-figure tables and geometry Robert Wessel <robertwessel2@yahoo.com> - 2017-01-07 23:30 -0600
Re: 4-figure tables and geometry "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-08 21:52 +0800
Re: 4-figure tables and geometry "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2017-01-10 22:06 +0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-07 04:44 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-04 14:12 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-04 14:50 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 02:18 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-04 15:01 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 02:19 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 02:21 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 02:41 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-05 02:47 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 03:00 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 04:08 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 08:26 -0800
My GeoPosition is a point at infinity Vinicius Claudino Ferraz <boralaemcasa@gmail.com> - 2017-01-05 16:24 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-05 02:36 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 02:50 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 03:02 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 04:09 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 08:28 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 09:00 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 09:15 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-05 11:20 -0800
Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-05 21:53 +0100
vu uv datum abu.kuanysh05@gmail.com - 2017-01-05 13:06 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 16:33 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 18:41 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 02:20 -0800
Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-06 12:45 +0100
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 05:30 -0800
Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-06 15:59 +0100
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 09:11 -0800
Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-06 18:54 +0100
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 13:25 -0800
Re: Déjà vu Vinicius Claudino Ferraz <boralaemcasa@gmail.com> - 2017-01-06 13:40 -0800
Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-06 23:19 +0100
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 14:37 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:34 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:36 -0800
Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-07 12:21 -0800
Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-07 18:41 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-06 10:09 -0500
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 09:10 -0800
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-06 09:14 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-06 18:19 -0500
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 16:53 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-07 01:02 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-07 03:01 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-07 10:20 -0500
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-07 09:22 -0800
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 09:51 -0800
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 09:52 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-07 10:12 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-07 10:21 -0800
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 10:24 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-07 10:57 -0800
Re: Déjà vu genmailus@gmail.com - 2017-01-07 11:05 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-07 11:32 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-07 11:47 -0800
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 11:15 -0800
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 17:21 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-07 20:48 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-08 01:36 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-08 01:38 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-08 03:04 -0800
Re: Déjà vu Jürgen R. <jurgenr@web.de> - 2017-01-08 13:27 +0100
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-07 10:01 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 12:34 -0500
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-09 10:08 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 17:18 -0500
Re: Déjà vu genmailus@gmail.com - 2017-01-09 14:28 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 17:55 -0500
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-09 17:12 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-09 20:55 -0500
Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-09 18:08 -0800
Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-09 23:08 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 10:55 -0500
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 05:13 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 09:49 -0500
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 07:44 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 11:45 -0500
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 09:51 -0800
Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 10:33 -0800
Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 10:35 -0800
Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 13:00 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 11:05 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 18:08 -0500
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-10 17:25 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 01:48 -0500
Re: Déjà vu "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2017-01-10 23:24 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 00:34 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 11:26 -0500
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 08:55 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 12:13 -0500
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:20 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:22 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 09:23 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 13:11 -0500
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:26 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-11 13:42 -0500
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:50 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 10:58 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 11:01 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-11 11:03 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-11 11:11 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-10 00:03 -0800
Re: Déjà vu Jim Burns <james.g.burns@att.net> - 2017-01-10 10:21 -0500
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 07:29 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 07:27 -0800
Re: Déjà vu WM <wolfgang.mueckenheim@hs-augsburg.de> - 2017-01-06 09:17 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-06 09:35 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-06 13:54 -0800
Re: Déjà vu bursejan@gmail.com - 2017-01-05 03:13 -0800
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-05 08:46 -0800
Re: Déjà vu Me <franz.fritschee.ff@gmail.com> - 2017-01-05 08:51 -0800
Re: Déjà vu John Gabriel <thenewcalculus@gmail.com> - 2017-01-05 08:53 -0800
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