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Groups > comp.lang.c++ > #81367

Re: rational numbers

From Bart <bc@freeuk.com>
Newsgroups comp.lang.c++
Subject Re: rational numbers
Date 2021-09-21 11:12 +0100
Organization A noiseless patient Spider
Message-ID <sicb5v$gnl$1@dont-email.me> (permalink)
References (16 earlier) <siahjp$k2p$1@dont-email.me> <siaifp$8u1$1@dont-email.me> <sianpk$lq5$1@dont-email.me> <siarfn$ud5$1@dont-email.me> <sic28b$m8a$1@dont-email.me>

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On 21/09/2021 08:39, David Brown wrote:
> On 20/09/2021 22:38, Bart wrote:

>> But to talk with some knowledge about how Print might be better
>> implemented in any language, you really need to have tried implementing
>> Print within a language, and specifically implementing it as a built-in
>> feature
> 
> No one cares about how easy or hard it is to implement.

You're changing the goalposts. You said my opinion wasn't an informed 
one, when I was talking about the deficiences of both cout and printf 
approaches.


> A BASIC-style print statement is fine
> for BASIC-style languages - typically designed to be quick and simple
> for easy tasks, but unsuitable for bigger work or more complex work, or
> programs that don't fit into the simple sequence of start program, read
> files and/or keyboard, print to screen and/or files, stop program.

What can 'cout' or 'printf' do that an easier-to-use and better designed 
Print can't do? This is an example bit of C++ posted a couple of days ago:

CMT:

     std::cout << sizeof(__int64) << "\n";
     std::cout << sizeof(__m128) << "\n";

     std::cout << foo_64.is_lock_free() << "\n";
     std::cout << foo_128.is_lock_free() << "\n";


I might be missing something, but is there any reason why something like:

     println sizeof(__int64);
     println sizeof(__m128);

     println foo_64.is_lock_free();
     println foo_128.is_lock_free();

wouldn't cut it? Too sensible? Too uncluttered? Might leave too many 
people thinking, where's the catch? Because all that extra crap in C++ 
must do something important, right?


> But for a language that supports multiple types, formatting,
> translations, redirected outputs, systems without a console, etc., then
> a simple print statement won't do.  It is both too much, and too little.

You're making this up aren't you?

Simple Print doesn't mean an inability to do anything. It means being 
able to do most of it, but in a simpler manner with a lot less typing!

> In fact, /no/ single solution will do everything.

But it might do 90% of it.

> When you think you
> have "/the/ answer" to a coding or programming language problem, you are
> almost guaranteed to be wrong - and you, Bart, think you have all the
> answers.

Some things are just no-brainers.

> So a good, serious programming language does not provide a "print"
> statement.

Yeah. And the better ones also do away with mutability. And global 
variables (see new 'pen' language). And loops. And of course goto.

>> Here, anyone can judge for themselves (although I doubt they'll be that
>> open minded in a C++ group):
>>
>>    20 print i, sqr(i)
>>
>>    std::cout << i << " " << sqrt(i) << std::endl;
>>
>> The first line is from decades-old BASIC. The second line, which also
>> needs iostream and math.h includes, is from latest C++.
>>
> 
> The first version is easist for a quick and dirty script.

Most of my uses of Print are quick and dirty:

* Because I add and remove such statements extensively for debugging, so 
the total number of Prints written are much greater than than the number 
of static Print statements in a finished program

* I also use it a lot for large numbers of throwaway programs, test 
programs, code posted on forums, etc, in a variety of languages.

C's printf is poor in that regard, but I think C++'s cout might just pip 
it. However Zig's print facilities I think are even worse; once you've 
figured out how to do it once, you have to keep that example locked away 
for future reference!


> The second
> is better for more serious programming.

So give me an example of serious programming where:

   println X

is no good at all, and you're better off with:

   std::cout << X << "\n";

> Oh, and if your "sqr" is a language built-in function for square roots,
> then that demonstrates another reason why serious languages avoid
> built-in functions.  The name is wrong, and changing the library is
> vastly easier than changing the language.

SQR comes from BASIC (most languages use 'sqrt'). Many also have such 
abilities built-in, because it's convenient.

In mine, sqrt is an operator. You don't need to include or import 
anything; it's just there. And usually mapped to an x64 'sqrtsd' 
instruction, but that's up to the backend.

Now look at the abs() function, and you realise why it is BETTER to have 
such things properly built-in, and not just a bunch of templates. In C, 
you have these variations:

   abs(x)       // these need stdlib.h
   labs(x)
   llabs(x)
   fabs(x)      // these need math.h
   fabsf(x)

Maybe there's some more, I don't know. I just have 'abs', and it works 
on any suitable type, because it's a unary operator like 'negate'.

> And there you have it.
> 
> With your personal language and tools, if you want to change the way the
> spacing or formatting works, you change the language and the
> compiler/interpreter.  With real languages, the programmer changes the
> code they write to change the formatting.

You say you like Python.

Python also injects implicit spaces and implicit new lines. But that's 
OK, even though it is a PITA to figure out how to suppress them.

But C++, where it is a PITA to have to add explicit spaces and newlines, 
is also fine.

The only place it isn't fine, apparently, is my language, where I have 
implicit spaces and explicit newlines!

There /is/ a simple way to suppress spaces, but if you don't know what 
it is, then instead of writing:

   print "ABC","DEF"             # ABC DEF

you have the option to just split the print into two:

   print "ABC"; print "DEF"      # ABCDEF

Because of how it works. In Python, you HAVE to go and look this up, as 
splitting a print will just insert a newline instead of a space.

(Space suppression between my print items uses: ",," instead of ",". 
When that gets too ugly, then you use formatted print.)


> Contrary to some experts' views, I have nothing against BASIC.  I
> learned to program in BASIC, in several dialects - the "B" stands for
> "Beginners'".  But then I grew up, and understood that while languages
> like BASIC can undoubtedly be good for a few hundred line programs, they
> are rarely a good choice for more serious work.

I want to port an algorithm which is expressed in both language A and 
language B, into a new language.

Suppose A and B were C++ and BASIC; which do you think would be simplest 
to work from?

The chances are that it will be BASIC, since most of its features exist 
also in many other languages.

With C++, especially if written by Bonita Montero, it would likely mean 
first implementing a dozen C++ libraries that it will depend on, and 
disentangling a mess of arcane syntax.

You shouldn't really write off a language for language for being too simple.

It actuality, that simpler language, more likely to use mostly simple, 
universal features, might be something like Lua or Python. Or even C, 
provided the author hasn't gone mad with macros.

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Thread

rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-16 14:59 +0200
  Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-16 16:40 +0300
    Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-16 18:24 +0200
      Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-16 17:05 +0000
        Re: rational numbers Manfred <noname@add.invalid> - 2021-09-16 19:58 +0200
        Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 09:21 +0200
          Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-17 10:34 +0200
            Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 15:55 +0200
              Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-17 17:49 +0200
                Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 18:22 +0200
          Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-17 22:07 +1200
            Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-17 13:32 +0200
              Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-18 09:15 +1200
            Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-17 14:06 +0000
      Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-16 20:41 +0200
        Re: rational numbers Bart <bc@freeuk.com> - 2021-09-16 21:11 +0100
          Re: rational numbers Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-09-16 21:26 +0100
            Re: rational numbers Bart <bc@freeuk.com> - 2021-09-16 21:54 +0100
            Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-16 23:07 +0200
              Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-16 23:27 +0200
      Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-16 23:12 +0300
        Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-17 09:50 +0200
          Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-17 11:15 +0200
            Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-17 19:19 +0200
              Re: rational numbers James Kuyper <jameskuyper@alumni.caltech.edu> - 2021-09-17 19:00 -0400
              Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-18 11:39 +0200
                Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-18 11:56 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-18 11:01 +0100
  Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-17 05:36 +0000
    Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-17 09:55 +0200
      Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-17 11:16 +0000
        Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-17 18:33 +0200
        Re: rational numbers Tim Rentsch <tr.17687@z991.linuxsc.com> - 2021-10-06 13:06 -0700
    Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-17 14:03 +0000
      Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 17:12 +0200
        Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-17 17:16 +0200
          Re: rational numbers Manfred <noname@add.invalid> - 2021-09-17 18:59 +0200
            Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-17 17:13 +0000
              Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 10:17 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-19 14:07 +0000
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 15:58 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-19 21:53 +0000
      Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-18 09:34 +1200
        Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-18 12:00 +0200
          Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-18 14:54 +0000
            Re: rational numbers Bart <bc@freeuk.com> - 2021-09-18 17:36 +0100
              Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-18 23:29 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 01:09 +0100
                Re: rational numbers red floyd <no.spam.here@its.invalid> - 2021-09-18 23:45 -0700
              Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-18 22:48 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 00:46 +0100
                Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-19 08:06 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 10:26 +0100
              Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 10:23 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 12:04 +0100
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 16:01 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-19 17:39 +0100
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-20 05:25 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 10:37 +0100
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-22 04:58 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 11:26 +0100
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-22 23:13 +1200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 13:45 +0100
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-24 21:37 +1200
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-22 15:29 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-23 07:26 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-19 21:54 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 00:31 +0100
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-20 08:33 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 16:11 +0100
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-20 18:08 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 18:39 +0100
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-20 19:49 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 19:04 +0100
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-20 21:35 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-20 21:38 +0100
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-21 10:28 +1200
                Re: rational numbers Bo Persson <bo@bo-persson.se> - 2021-09-21 09:08 +0200
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-21 09:39 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 11:12 +0100
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 15:45 +0300
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 14:37 +0100
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 17:09 +0300
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 16:26 +0100
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-21 18:04 +0200
                Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-21 11:51 -0700
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-22 11:09 +0200
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 15:38 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 15:36 +0000
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-21 15:49 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 16:21 +0000
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 09:21 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 17:45 +0100
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 17:02 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 18:16 +0100
                Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-21 11:53 -0700
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 20:48 +0100
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 20:23 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 23:29 +0100
                Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-21 13:47 -0700
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 20:11 +0300
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 18:33 +0100
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 20:43 +0300
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 18:59 +0100
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 21:20 +0300
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 20:32 +0100
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 20:24 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-21 18:52 +0000
                Re: rational numbers Bo Persson <bo@bo-persson.se> - 2021-09-21 18:34 +0200
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-21 01:16 +0300
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-21 00:39 +0100
                Re: rational numbers Manfred <noname@add.invalid> - 2021-09-22 23:45 +0200
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-22 23:51 +0200
                Re: rational numbers Manfred <noname@add.invalid> - 2021-09-23 18:42 +0200
                Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-23 21:52 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 00:17 +0100
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-23 02:03 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 11:18 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-23 10:26 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 12:21 +0100
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 12:40 +0100
                Re: rational numbers Richard Damon <Richard@Damon-Family.org> - 2021-09-23 08:05 -0400
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 15:02 +0100
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-24 08:48 +1200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 23:05 +0100
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-23 23:47 +0000
                Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-23 16:56 -0700
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-24 01:58 +0100
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 01:40 +0000
                Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-23 19:35 -0700
                Re: rational numbers "daniel...@gmail.com" <danielaparker@gmail.com> - 2021-09-24 09:07 -0700
                Re: rational numbers "daniel...@gmail.com" <danielaparker@gmail.com> - 2021-09-24 09:21 -0700
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-23 14:58 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 17:02 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-23 16:21 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 18:31 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-24 09:12 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-24 12:10 +0100
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 11:23 +0000
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-24 15:19 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-24 17:25 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-25 09:27 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-25 11:07 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-25 10:14 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-25 11:53 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-25 11:23 +0000
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-25 12:34 +0000
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-25 15:37 +0300
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-25 15:46 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-25 15:19 +0000
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-25 17:16 +0000
                Re: rational numbers Christian Gollwitzer <auriocus@gmx.de> - 2021-09-27 23:51 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-27 23:41 +0100
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-23 10:26 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-23 14:04 +0000
                Re: rational numbers Manfred <noname@add.invalid> - 2021-09-23 17:47 +0200
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-23 17:07 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-23 17:08 +0000
                Re: rational numbers Manfred <noname@add.invalid> - 2021-09-23 19:30 +0200
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-24 10:06 +1200
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-22 05:06 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 10:51 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 10:54 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 11:59 +0100
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 11:04 +0000
                Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-22 14:17 +0200
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-22 14:32 +0100
                Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-22 16:23 +0200
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-22 15:18 +0300
                Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-22 16:16 +0200
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 15:15 +0000
                Re: rational numbers "Alf P. Steinbach" <alf.p.steinbach@gmail.com> - 2021-09-22 17:57 +0200
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-22 16:05 +0000
                Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-22 14:13 -0700
                Re: rational numbers HorseyWorsey@the_stables.com - 2021-09-23 09:01 +0000
                Re: rational numbers James Kuyper <jameskuyper@alumni.caltech.edu> - 2021-09-23 12:08 -0400
                Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-23 10:55 -0700
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-22 20:46 +0300
                Re: rational numbers "daniel...@gmail.com" <danielaparker@gmail.com> - 2021-09-22 14:42 -0700
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-23 09:15 +0300
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-22 14:04 +0000
                Re: rational numbers Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2021-09-22 07:18 -0700
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-23 07:31 +0000
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-23 11:05 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-23 08:28 +0000
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-24 00:51 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-24 04:37 +0000
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 07:46 +0000
                Re: rational numbers "daniel...@gmail.com" <danielaparker@gmail.com> - 2021-09-24 08:59 -0700
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-24 22:49 +0300
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-25 00:55 +0000
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-24 12:17 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-27 05:25 +0000
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-27 11:37 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-28 04:49 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-23 11:29 +0100
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-24 04:38 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-24 11:15 +0100
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 10:19 +0000
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-27 05:34 +0000
                Re: rational numbers scott@slp53.sl.home (Scott Lurndal) - 2021-09-23 14:07 +0000
                Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-23 14:50 +0000
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-20 05:20 +0000
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-24 21:45 +1200
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-25 16:15 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-27 05:36 +0000
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-27 11:19 +0300
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-27 21:27 +1300
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-27 15:49 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-28 04:53 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-28 10:16 +0100
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-29 12:10 +0000
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-29 14:34 +0100
                Re: rational numbers Bart <bc@freeuk.com> - 2021-09-29 15:54 +0100
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-28 13:23 +0300
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-29 10:34 +1300
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-29 12:18 +0300
                Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-29 22:46 +1300
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-29 13:07 +0300
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-10-02 22:57 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-29 12:16 +0000
                Re: rational numbers Paavo Helde <myfirstname@osa.pri.ee> - 2021-09-29 20:15 +0300
                Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-30 04:46 +0000
            Re: rational numbers Ian Collins <ian-news@hotmail.com> - 2021-09-19 11:03 +1200
      Re: rational numbers Juha Nieminen <nospam@thanks.invalid> - 2021-09-19 10:12 +0000
  Re: rational numbers Siri Cruise <chine.bleu@yahoo.com> - 2021-09-23 07:38 -0700
    Re: rational numbers alessandro volturno <alessandro.volturno@libero.it> - 2021-09-24 09:45 +0200
      Re: rational numbers Branimir Maksimovic <branimir.maksimovic@gmail.com> - 2021-09-24 07:50 +0000
      Re: rational numbers David Brown <david.brown@hesbynett.no> - 2021-09-24 10:58 +0200
        Re: rational numbers Siri Cruise <chine.bleu@yahoo.com> - 2021-09-24 02:48 -0700

csiph-web