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Groups > sci.logic > #210652

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 2019-09-14 02:15 +0100
Organization A noiseless patient Spider
Message-ID <87blvnispc.fsf@bsb.me.uk> (permalink)
References (8 earlier) <7e3802de-0a9e-472c-9d04-5a8bb0096f1b@googlegroups.com> <87zhj9ijrs.fsf@bsb.me.uk> <6efefb29-1d42-4c17-86bd-37099e97b354@googlegroups.com> <87pnk5hymu.fsf@bsb.me.uk> <be1ba1ee-3e30-478b-a328-40e5005a6e95@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 Freitag, 13. September 2019 01:40:30 UTC+2 schrieb Ben Bacarisse:
>> Ganzhinterseher <claus.vonnesser@gmail.com> writes:

CONTEXT (why do you keep cutting key facts?):  The e_n are a family of
functions: e_n(x) = 1 if x >= n, 0 otherwise.

>> >>   lim_{n->oo} e_n(x) = 0.
>> >
>> > That is true for potential infinity (my book) and for every definable
>> > n (there are infinitely many in set theory), followed by infinitely
>> > many undefinable natnumbers.
>> 
>> Oh!  So in WMaths the limit function is e(x) = 0.  I thought you denied
>> this.
>
> Up to every definable n this is correct.

You are being evasive!  You cut the full quote.  Why would you do that?.
You agreed that, in WMaths,

  for every x in N, lim_{n->oo} e_n(x) = 0

and that is all the definition requires for e(x) = 0 to be the limit
function.  Yet you won't say "yes" without some added mysterious
qualification.

Of course, you can change your mind.  You can retract your prior
agreement that, in WMaths, lim_{n->oo} e_n(x) = 0 for every x in N, but
you are not doing that either, it seems.  Ducking and diving is the
order of the day.

> In mathematics there are only definable n.

That your made-up WMaths, yes?  The "mathematics" that permits e ∈ S and
S \ {e} = S to be the case, yes?

>> And just to be clear, you think that in "set theory" (i.e. normal
>> mathematics) there are some x ∈ N for which lim_{n->oo} e_n(x) is not 0.
>> I won't ask you to prove this -- it's just useful for people to see your
>> beliefs clearly stated.
>
> It is easy: Since all definable natnumbers are in FISONs, the actually
> infinite set (larger than all FISONs) must contain more than definable
> numbers.

More evasion.  Please confirm that you are claiming that, in what you
call "set theory", e(x) = 0 is /not/ the point-wise limit of the
function sequence I gave.

>> Presumably there is nothing special about the functions I picked.  Can
>> you confirm that you think that in "set theory" there are no point-wise
>> limit functions because the "for every x" in the definition can never be
>> met?
>
> All limit functions are correctly described in potential infinity. The
> set of definable numbers in set theory is always finite without a last
> element, i.e., the same a the set of all natural numbers in potential
> infinity.

Ha!  That is how you answer a "can you confirm that..." question, is it?

I've come to accept that you try your hardest to equivocate on such
questions, so I must also accept that the best I can hope for is to make
your evasion clear to anyone who might come across this thread.

>> >> How can there be more?  Is there a natural number that is not in the
>> >> potentially infinite set N?
>> >
>> > In set theory there must be more. There is no potential infinity.
>> 
>> As you say, there is no potential infinity so what on Earth did you
>> think you were asking about set theory?
>
> Since all definable natnumbers are in FISONs, the actually infinite
> set (larger than all FISONs) must contain more than definable numbers.

Why are you so modest?  You have discovered a universal truth that goes
far beyond definablility.  It's equally true that all natnumbers that
are greater than or equal to 1 are in FISONs, so the actually infinite
set must contain more than numbers that are greater than or equal to 1.

And you can apply it to other sets as well.  Consider the finite initial
subsets of the even numbers (FISENs).  All even numbers are in FISENs,
so the actually infinite set of even numbers must contain more than even
numbers, despite it being the set from which the FISENs are drawn!

It's just a dishonest word game.  Shame on you.

>> Mathematics (what you call set theory) proves statements like
>> 
>>   for every x ∈ N, lim_{n->oo} e_n(x) = 0.
>
> It also proves...

I need to jump in here.  You know that this means you are agreeing that
e(x) = 0 is the limit function in mathematics as well as in WMaths, yes?
I hope you can see how well you hiding your true opinions.  You suggest
further up that it's not the limit function (in "set theory"), and here
you seem to suggest it is!

<cut>
-- 
Ben.

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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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