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Groups > sci.logic > #210427

Re: Can the empty set be the limit of a sequence of non-empty sets?

From Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups sci.logic
Subject Re: Can the empty set be the limit of a sequence of non-empty sets?
Date 2019-09-11 02:25 +0100
Organization A noiseless patient Spider
Message-ID <87impzlj3j.fsf@bsb.me.uk> (permalink)
References <7158bf04-d718-40e4-b1c1-92afe00a40f6@googlegroups.com> <878sqywjrq.fsf@bsb.me.uk> <e94c23c3-47ea-449b-8181-52ca0c32460f@googlegroups.com> <87y2ywlwb7.fsf@bsb.me.uk> <5bf8f6f2-82dd-438a-89f0-0d708a7e8966@googlegroups.com>

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Ganzhinterseher <claus.vonnesser@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)

> Am Dienstag, 10. September 2019 04:28:02 UTC+2 schrieb Ben Bacarisse:
>> Ganzhinterseher <claus.vonnesser@gmail.com> writes:
>
>> > Let's apply it to this problem: How many natnumbers can we remove from
>> > 1, 2, 3, ... without emptying this set?
>> 
>> Non-answer number 1.
>
> It is the answer. All removable numbers must first be defined. The
> limit function is 0 for every definable number. But most numbers are
> not definable.

No it was not an answer.  The point-wise limit has nothing to do with
"removable" numbers, and you failed to even mention "definable" numbers
in your claimed answer.

Here's what is actually meant by the point-wise limit:

  Let (f_n) be a sequence of functions and B ⊆ D. The sequence of
  functions is said to be convergent in the usual sense or point-wise
  convergent on B, if a function f: B -> R exists, such that for every x
  ∈ B we have f(x) = lim_{n->oo} f_n(x).  (The f_n are functions from D
  -> R with D ⊆ R.)

See? No reference to removing anything and no reference to definable
numbers.  The function e(x) = 0 meets this definition for the limit of
the e_n.  A reminder:

  e_n(x) = 1 if x >= n, 0 otherwise

If you have some other definition of the point-wise limit function, what
is it?  It would have to exclude e(x) = 0 being the limit of the
sequence (e_n).

But definability is just a ruse.  You want to talk about anything other
than the plain fact that e(x) = 0 meets the above definition, and
waffling about words like "definable" is your favourite pass time now
that you are retired.

>> As for your question: as many as you like.  It's a silly question
>> because whether N \ E = {} (for E ⊆ N) depends one which numbers are in
>> E as much as one how many numbers are in E.
>
> Of course I meant definable numbers,

You should have said so then, but the answer remains the same: "How many
definable natnumbers can we remove from 1, 2, 3, ... without emptying
this set?"  Answer: as many as you like.  It remains a silly question
for the reason given.

-- 
Ben.

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Thread

Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-08 09:49 -0700
  Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-08 11:23 -0700
    Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 13:17 -0700
      Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-10 20:31 -0700
        Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:40 -0700
          Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-11 23:12 -0700
            Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 06:45 -0700
  Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-08 21:14 +0100
    Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 12:51 -0700
      Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-09 12:59 -0700
        Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 13:36 -0700
          Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-09 19:56 -0700
            Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 08:33 -0700
              Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-10 17:54 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 13:31 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-11 15:45 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-11 07:08 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:38 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-11 14:48 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 07:06 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-12 10:31 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-12 12:00 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:29 -0700
              Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-10 08:59 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 13:39 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-10 13:56 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 13:44 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-10 13:57 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:16 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-11 13:52 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 14:01 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-11 14:35 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 06:54 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-12 07:46 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 08:39 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-12 08:54 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 13:19 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-12 13:21 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-12 14:27 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 04:13 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-14 12:13 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 03:00 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-15 03:38 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 05:42 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-15 06:02 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 13:31 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 07:54 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 07:27 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-15 09:37 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 07:26 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:33 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 07:52 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-15 16:13 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-15 21:29 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 16:55 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-16 12:59 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-16 13:12 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-16 15:34 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-16 23:49 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-17 08:53 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 14:04 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 14:55 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 16:17 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 21:29 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 21:39 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 18:35 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 18:32 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 03:46 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 21:39 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 12:46 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 17:52 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-18 18:58 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 18:47 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 14:53 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 03:37 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 21:34 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 12:37 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-18 21:01 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-19 22:11 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-19 22:21 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-20 00:51 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 18:28 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-16 15:38 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-16 15:53 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-16 08:43 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-16 17:51 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-16 13:29 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-16 16:02 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 13:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-15 17:04 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:44 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-16 13:09 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 09:28 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-17 18:38 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 13:28 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 13:43 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 14:33 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-18 09:29 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-18 10:45 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-18 14:13 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-18 15:40 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-19 04:51 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-19 14:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-20 08:22 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-20 09:55 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-21 12:13 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-21 12:33 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-21 13:47 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-21 14:17 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-23 12:02 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-23 12:26 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 06:14 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 07:54 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-23 12:46 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-23 14:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-23 15:25 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@python.invalid> - 2019-09-24 00:37 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 07:12 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 06:17 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@python.invalid> - 2019-09-24 15:26 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-24 07:03 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 07:22 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-24 07:39 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 08:33 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 08:49 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? WM <mueckenh@rz.fh-augsburg.de> - 2019-09-24 09:05 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 08:09 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? WM <mueckenh@rz.fh-augsburg.de> - 2019-09-24 09:06 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 09:18 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 13:20 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 13:43 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-25 09:41 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-25 09:49 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-27 13:27 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-27 13:49 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-28 12:27 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-28 12:36 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-28 13:08 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-28 13:24 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-28 14:00 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-28 14:39 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-29 06:11 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-29 08:00 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-29 11:05 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-29 12:02 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-29 13:34 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-29 13:45 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-29 13:47 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-30 09:52 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-30 10:13 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-30 11:30 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-30 11:57 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-30 23:44 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-01 01:19 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-10-01 07:39 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-01 11:14 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-01 12:35 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-10-01 13:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-02 02:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-02 02:29 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-02 02:58 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-02 03:24 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-02 08:45 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-02 09:02 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-03 08:51 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-03 10:52 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-03 10:56 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-10-02 10:27 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-10-02 10:31 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-03 08:46 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-10-03 10:13 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-04 13:59 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-30 11:10 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-29 14:30 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 08:00 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-23 14:19 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 07:09 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-24 06:51 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 07:15 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-21 14:22 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@python.invalid> - 2019-09-22 03:07 +0200
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-25 20:14 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-27 13:27 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-18 20:51 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-19 04:50 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-13 12:44 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 14:28 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-13 12:52 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 14:28 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-12 15:36 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 04:38 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-14 12:17 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 05:53 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-15 06:24 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 13:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-15 13:29 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-15 13:30 -0700
      Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-09 13:08 -0700
        Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 13:44 -0700
          Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-14 18:31 -0700
            Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-15 02:52 -0700
              Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 05:29 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 16:49 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 13:30 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-15 13:33 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:40 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-16 10:46 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-16 10:48 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-16 13:06 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 09:21 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 13:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 13:47 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-15 17:09 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:47 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-16 13:10 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 09:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 13:25 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 13:34 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 14:31 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-18 09:26 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-16 02:39 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:51 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-16 12:08 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 01:34 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-16 13:27 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 09:39 -0700
            Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 02:55 -0700
  Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-08 22:38 +0100
    Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-09 13:09 -0700
    Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 13:21 -0700
      Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-10 03:27 +0100
        Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 08:14 -0700
          Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-11 02:25 +0100
            Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:16 -0700
              Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 02:15 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 07:23 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 17:03 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 13:27 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-13 00:40 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 04:49 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 06:00 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 06:24 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 06:37 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 06:39 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 06:45 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 09:40 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 14:28 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 14:51 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-14 05:14 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 02:15 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-14 05:49 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 15:29 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-14 08:38 -0700
                Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 02:11 +0100
            Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-11 15:11 -0700
              Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 02:23 +0100
                Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-12 02:08 -0700
      Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-11 15:10 -0700
        Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 07:29 -0700
  Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-11 14:00 -0700

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