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Re: Some results about unit fractions

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From Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups sci.logic
Subject Re: Some results about unit fractions
Date Sun, 02 Jul 2023 01:50:50 +0100
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Fritz Feldhase <franz.fritschee.ff@gmail.com> writes:

> On Saturday, July 1, 2023 at 7:32:38 PM UTC+2, Transfinity wrote:
>
>> [...] In an exchange which is defined as lossless at the outset,
>> there is no loss admissible.
>
> Agree. JB is talking nonsense here.

I find this reply surprising.

All of the infinity-critical mob simply object to what happens "in the
limit".  Infinite operations produce results that can't come from any
number of finite operations.

Infinite sums and products yield values never attained by any of the
finite sums.  Infinite intersections can be empty where no finite
intersections are even finite.  And infinite compositions of
permutations can result in orderings that are lossy.

WM's silly matrix is designed to complicate the issue, but there are
very much simpler examples.  Let s(i, j) be the permutation that swaps
the ith and jth elements of a sequence.  The infinite composition of the
lossless swaps s(k, 2k) (for all k in N) is an ordering which, when
applied to the infinite sequence n_i = i, gives the sequence e_i = 2i
with no odd numbers in it.  The infinite composition of all s(k, k+1)
applied to n_i gives the sequence 1, 2, 3, ... with 0 nowhere to be
found.

The result of infinite operations (which are formally limits) do not
preserve all properties of the results of finite operations.

-- 
Ben.

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Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 01:34 +0100
  Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-20 08:34 -0700
    Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:09 -0700
      Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:18 -0700
      Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-21 07:17 -0700
        Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-21 16:52 +0200
          Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-22 05:48 -0700
            Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 13:20 -0700
    Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-22 00:51 +0100
      Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-22 05:58 -0700
        Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 01:05 +0100
          Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 17:17 -0700
            Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:26 +0100
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-23 09:01 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 01:59 +0100
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-06-26 04:42 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 14:42 +0100
                Re: Some results about unit fractions JVR <jrennenkampff@googlemail.com> - 2023-06-26 15:22 -0700
                Re: Some results about unit fractions Python <python@invalid.org> - 2023-06-27 01:14 +0200
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 08:12 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 07:59 -0700
          Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-23 08:53 -0700
            Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 09:52 -0700
            Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 02:05 +0100
              Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-26 08:05 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-29 01:34 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-29 05:31 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-29 16:37 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:18 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:21 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 13:52 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-29 19:15 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-30 14:27 +0100
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:03 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:06 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:09 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:15 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:21 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:26 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 02:05 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 09:04 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:56 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-30 16:47 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:15 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 10:20 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 02:13 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:59 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:34 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 09:55 -0700
                Re: Some results about unit fractions Python <python@invalid.org> - 2023-07-02 19:10 +0200
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 13:01 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 10:27 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 14:14 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-06-30 11:49 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-06-30 20:30 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-01 10:26 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 16:18 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 17:37 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 12:55 -0400
                Re: Some results about unit fractions Transfinity <transfinity01@gmail.com> - 2023-07-01 10:32 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 15:42 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:17 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 13:00 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 16:24 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:05 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:28 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 17:30 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 14:44 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 18:49 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 17:07 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-02 06:20 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 04:04 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:39 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:33 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:27 -0700
                Re: Some results about unit fractions Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-07-02 01:50 +0100
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:50 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:19 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 12:58 -0400
                Re: Some results about unit fractions Transfinity <transfinity01@gmail.com> - 2023-07-01 11:16 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-01 15:16 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-02 08:14 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-02 18:44 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-03 06:31 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-03 11:32 -0400
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:46 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-04 19:12 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-04 16:25 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-04 22:14 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-05 18:13 -0700
                Re: Some results about unit fractions Jim Burns <james.g.burns@att.net> - 2023-07-06 12:45 -0400
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-03 09:50 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:51 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-04 13:35 -0700
                Re: Some results about unit fractions Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-03 10:07 -0700
                Re: Some results about unit fractions WM <askasker48@gmail.com> - 2023-07-04 11:53 -0700

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