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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Newsgroups | sci.logic |
| Subject | Re: Some results about unit fractions |
| Date | 2023-04-16 22:30 +0100 |
| Organization | A noiseless patient Spider |
| Message-ID | <87sfczsef4.fsf@bsb.me.uk> (permalink) |
| References | (8 earlier) <6b5e7753-cf00-468a-9fbc-bba1261034den@googlegroups.com> <87h6tiuhhf.fsf@bsb.me.uk> <a1758f59-1323-4ab6-80fb-36034bc6e6fdn@googlegroups.com> <87sfd0u0vc.fsf@bsb.me.uk> <31df6707-2b15-4f26-bc8d-c099dd5f319fn@googlegroups.com> |
WM <askasker48@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)
> Ben Bacarisse schrieb am Sonntag, 16. April 2023 um 02:28:11 UTC+2:
>> WM <askas...@gmail.com> writes:
>
>> For the record, your argument started with a false premise:
>>
>> You: "If ℵ₀ unit fractions are smaller than all x in (0,1], ..."
>>
>> Me: "But no unit fractions are smaller than all x in (0,1].
>
> Then not ℵ₀ unit fractions are smaller than all x in (0,1]. Fine. Then
> NUF(x) = ℵ₀ only for an x > 0.
>
>> You: ".. then you cannot distinguish them. If two of them, p and
>> q, are distinct, then you have p > q > 0 and p is not in the set of
>> ℵ₀ unit fractions smaller than every x > 0."
>> Me: "No unit fraction is smaller than every x > 0."
>
> Fine. I got the contrary impression from your arguing.
So here's the hole you got yourself into and are trying to pretend I
didn't say what I said:
Me: Mathematics says that NUF(x) = ℵo for x > 0.
You: Yes, for every definable x, usually called eps, this is true.
Me: Speculation about something in (0,1] for which NUF(x) =/= ℵo can be
ruled out
You: No.
Me: If you were a mathematician, you would formally characterise everything
in (0,1] and prove ∃x in (0,1] with NUF(e) =/= ℵ₀.
You: Simple.
It is at this point you started an argument with a false premise. So
start over and try again to do this "simple" thing: characterise
everything in (0,1] and prove ∃x in (0,1] with NUF(e) =/= ℵ₀.
I'll wait... Meanwhile, mathematics characterises everything in (0,1]
with axioms and proves that ~∃x in (0,1] with NUF(e) =/= ℵ₀ so if you
can do what you said was "simple" you will have proved conventional
mathematics inconsistent. That must be worth a few minutes typing.
> But then some sit at x > 0.
> That is also what mathematics proves:
> ∀n ∈ ℕ: 1/n - 1/(n+1) = 1/(n(n+1)) > 0
> all are there sitting at different points of the real line.
Yes. You cling to this trivial fact like a drowning man to an oar. But
you can't get from it to "so therefore there is a first" nor to "so
NUF(x) 'increases' by 1" nor to anything that contradicts the equally
trivial fact that NUF(x) is two-valued.
> Alas we cannot find any real point where unit fractions sit as long as
> there are not yet infinitely many.
Use mathematics not words. Your current metaphor soup includes "sit"
(equals?) "as long as" (nothing changes in my scenario) "not yet" (time
has nothing to do with it.
> That proves dark unit fractions.
You can't even say what a dark number is much less prove anything about
one. Meanwhile, in mathematics, we characterise the set (0,1] (see the
axioms of the reals) and prove that for any x in (0,1], NUF(x) = ℵ₀.
It's a simple proof. There is nothing else in (0,1] other than the
reals for which NUF is ℵ₀. This is why you will fail to do what you
said was "simple" (see above).
> Or do you want again to change your position?
Please cite the two positions of mine that you think are different.
Yes, I know, you never comply with requests to back up these claims,
but I feel I must ask in case you have some evidence.
Now let's address your other embarrassing claim: the third of the great
unproven (and never to be proven) "theorems" of WMaths:
∃x in (0,1] with |UF(x)| ∈ N. (NF(x) = {1/n < x with n ∈ N}.)
You say you can't show such a x. You say you can't put any bounds on
such an x. But neither can you prove that such as x exists.
Nonetheless you make the claim. Do you want again to change your
position? I need to know if I can cite it along with the other junk
"theorems" of WMaths.
--
Ben.
Back to sci.logic | Previous | Next — Previous in thread | Next in thread | Find similar
Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 07:06 -0700
Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-12 07:42 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 07:49 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 08:26 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 08:27 -0700
Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-12 23:55 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-13 09:44 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-12 16:11 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 09:37 -0700
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Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-17 12:02 -0700
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Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-18 05:05 -0700
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Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-21 03:41 -0700
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Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-21 13:08 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-22 06:45 -0700
Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-22 15:30 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-23 06:31 -0700
Re: Some results about unit fractions Gus Gassmann <horand.gassmann@gmail.com> - 2023-04-22 06:48 -0700
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Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-23 15:23 -0400
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Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-23 06:57 -0700
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Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-15 11:31 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-16 01:28 +0100
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Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-17 12:23 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-17 13:17 -0700
Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-04-18 02:49 +0100
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-18 04:58 -0700
Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-18 05:06 -0700
Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-18 05:07 -0700
Re: Some results about unit fractions Mostowski Collapse <bursejan@gmail.com> - 2023-04-18 06:54 -0700
Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-19 05:17 -0700
Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-04-18 04:32 -0700
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Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 14:24 -0700
Re: Some results about unit fractions Python <python@invalid.org> - 2023-04-12 23:44 +0200
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-13 10:01 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 08:20 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 08:30 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 09:39 -0700
Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-04-12 09:57 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-12 15:55 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-12 14:17 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-12 18:32 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-13 09:48 -0700
Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-04-13 18:50 -0400
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 07:15 -0700
Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-14 07:27 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 07:39 -0700
Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-14 08:36 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 09:38 -0700
Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-14 09:45 -0700
Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-04-14 09:56 -0700
Re: Some results about unit fractions Julio Di Egidio <julio@diegidio.name> - 2023-04-14 10:08 -0700
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