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| 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 15:29 +0100 |
| Organization | A noiseless patient Spider |
| Message-ID | <87zhj7gdcy.fsf@bsb.me.uk> (permalink) |
| References | (10 earlier) <6efefb29-1d42-4c17-86bd-37099e97b354@googlegroups.com> <87pnk5hymu.fsf@bsb.me.uk> <be1ba1ee-3e30-478b-a328-40e5005a6e95@googlegroups.com> <87blvnispc.fsf@bsb.me.uk> <78f9593a-8a35-42e4-aa6f-03feaba1be21@googlegroups.com> |
Ganzhinterseher <claus.vonnesser@gmail.com> writes:
> Am Samstag, 14. September 2019 03:15:30 UTC+2 schrieb Ben Bacarisse:
>> 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.
>
> Yes, we had that already. They look like the following graph:
>
> _________________----------------------------
>
> We cannot repeat everything because the contributions get too long and
> will not be read by onlookers.
Indeed, but that is one line defining a set of functions that are later
referenced. Study how I do it and you will see that I keep important
context without the posts getting too long. You cut material in order
to introduce changes as you need them. For example, your "up to"
introduced below and the dishonest change when you magically made my "E"
change from a set to a sequence. I need to keep the definitions visible
to prevent such trickery.
<cut>
>> You agreed that, in WMaths,
>>
>> for every x in N, lim_{n->oo} e_n(x) = 0
>
> Yes, but every such x is not the last one. Therefore we can only say
> "up to every x the function is zero".
Don't be silly. WMaths has sets like N x {0} and functions like e(x) =
0, and it can prove facts about every member of a set. Every x in N is
mapped to 0 by e(x) and every x in N has lim_{n->oo} e_n(x) = 0. e(x)
is the limit function.
>> 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.
>
> Look, the function f(x) = 1/x has limit 0. That is a firm, existing number or point.
>
> But the limit function e(x) = 0 does not exist for all x because there
> are not all x in pot. inf.
>
> Therefore we can only say what I said above: up to every x or n.
That won't wash. If e(x) is not the limit function, then the examples
in your book are wrong too. If e(x) is the limit function you should
admit that it is. You simply won't settle the matter either way because
you can't. You don't want to admit you book does reflect your made-up
WMaths, but you don't want e(x) = 0 to be the limit of (e_n).
>> > 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.
>
> A clear statement. Think better about it.
I did not say it was not clear. I said it was evasive and it was:
clearly evasive. Why? Because I asked you (twice now) to confirm that
according to you the limit is not e(x) = 0 in "set theory". Instead of
"yes" or "no" you post the above evasive nonsense. Will you confirm (or
deny) that you do indeed think that e(x) = 0 is not the limit function
in "set theory" (AKA ordinary mathematics), or will post something else
that is a bot related but not a yes or a no?
>> 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.
>
> It is the limit for all definable numbers. But most numbers are
> undefinable.
Again, an evasive answer. I think it means no, you do not think that
e(x) = 0 is the limit function in standard analysis. Note that I don't
care why you think it, I want the world to know that you deny it.
>> 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,
>
> All definable even numbers!
The editing here is so dishonest I won't reply. If anyone really does
read this, they need to look at the parent article to see what I said
rather, than what you have edited to suit your own ends.
>> 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 told you above what that means.
And again, you cut the text of yours that shows I am right. Anyone who
cares can go and look at what I was responding to when I said "I need to
jump in here".
> This is the alternative with definition of endsegment E(n) = {n, n+1,
> n+2, ...}:
In the past you have even lied about what a trailing ... means. Why
don't you use closed forms like E(n) = { k | k ∈ N /\ k >= n } (to
borrow how you write this in your book)? I think I know why. You like
notation that shows sets are sequences, evolving and growing, not sets
that just are as a result of some property possessed by all elements.
> ∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { } (*)
This is true. In fact, ∩_{1<=k<=n} E(k) = E(n). The intersection of
them all is lim_{n->oo} E(n) = {}.
> But
>
> ∀n ∈ ℕ: E(1) ∩ E(2) ∩ E(3) ∩ ... ∩ E(n) ∩ ... ∩ <dark> = { } (**).
>
> Since (*) contains already all natural numbers, the addition in (**)
> must be different from all natural numbers: <dark>.
Silly. For one thing, the "for all n" is daft because the formula that
follows it does not depend on n, but more importantly, if
<dark> ∩ E(1) ∩ E(2) ∩ E(3) ∩ ... = {}
then
E(1) ∩ E(2) ∩ E(3) ∩ ... = {}
because <dark> contains (according to you) no numbers that are in any
E(k).
> Set theorists deny this.
Of course. It's a silly thing to write.
> They claim that every endsegment E(n) is followed by infinitely many
> endsegments, but there are not infinitely many endsegmnets following
> upon every endsegment E(n). That means the intersection of those
> following endsegments <dark> which are producing the empty
> intersections in (**) is empty. That means they are not always
> there. That is what I'd call in German hirnrissig. Don't know whether
> hair-brained has sufficient power to translate it.
I can't follow this waffle. Mathematicians claim that a number can only
be in the intersection of a family of subsets of N if it is in every one
of those subsets.
For anyone who cares, the trouble you have is that you can only think of
infinite things as processes evolving over time. The intersections here
are made (in your mind) by chipping away finite sets from an infinite
granite block of numbers. Mathematics, on the other hand, defines
things that are, complete, once and for all, with no reference to time
or action. You just prove that for any k, k ∉ E(k+1) to show that the
intersection is empty.
--
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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