From: "Grein, Christoph" <christoph.grein@eurocopter.com>
To: comp.lang.ada@ada.eu.org
Subject: Re: Anybody in US using ADA ? One silly idea..
Date: Tue, 4 Feb 2003 10:13:59 +0100 (MET)
Date: 2003-02-04T10:13:59+01:00 [thread overview]
Message-ID: <mailman.14.1044350541.3911.comp.lang.ada@ada.eu.org> (raw)
> "Grein, Christoph" <christoph.grein@eurocopter.com> wrote in message
> news:mailman.10.1044267682.3911.comp.lang.ada@ada.eu.org...
> > > > Do you know, an integer is definitely a real number.
> > >
> > > You sure? How about a simple theorem that any two distinct
> > > real numbers have another real number between them? Either
> > > this theorem doesn't hold (and the whole math goes out
> > > the window) or the integers are most definitely not reals.
> > >
> > > Which will it be?
> >
> > Where is there the contradiction? Integers can be embedded in reals as a
> subset.
>
> Operations available for the type and how they behave.
> The theorem above was an example. Let's see:
>
> F(X, Y) = A
>
> such that for any given, finite X and Y where X < Y it
> produces A that satisfies the requirement that X < A < Y
>
> Trivial to do for real numbers. Impossible for integers.
> Which means that, at least in this respect, integers are
> not a subset of reals. To be more precise, you could
I'm out of words with this statement...
Why on earth do you think that each and every trait of a superset is going to
hold in subsets? That's a very peculiar definiton of "subset", to say at least.
> argue that they are a subset or real *values* but that's
> not the same thing.
>
> You could also define an operation F that takes two
> integers and returns a generic real but that would also
> mean that integers do not posess a property critical
> to the definition of the real numbers.
next reply other threads:[~2003-02-04 9:13 UTC|newest]
Thread overview: 228+ messages / expand[flat|nested] mbox.gz Atom feed top
2003-02-04 9:13 Grein, Christoph [this message]
2003-02-05 6:50 ` Anybody in US using ADA ? One silly idea AG
2003-02-04 13:26 ` Dmitry A. Kazakov
-- strict thread matches above, loose matches on Subject: below --
2003-02-03 10:13 Grein, Christoph
2003-02-05 5:44 ` AG
2003-02-04 16:05 ` Chad R. Meiners
2003-01-17 6:08 Grein, Christoph
2003-01-16 11:10 Grein, Christoph
2003-01-16 16:13 ` Stephen Leake
2003-01-16 16:53 ` Victor Porton
2003-01-03 1:18 Alexandre E. Kopilovitch
2002-12-31 18:37 Anybody in US using ADA ? Mr Bill
2002-12-31 18:55 ` John R. Strohm
2003-01-01 3:20 ` Marin David Condic
2003-01-02 17:57 ` Anybody in US using ADA ? One silly idea Warren W. Gay VE3WWG
2003-01-02 18:29 ` Vinzent Hoefler
2003-01-02 22:02 ` Warren W. Gay VE3WWG
2003-01-02 20:36 ` Bill Findlay
[not found] ` <ujn2va.go3.ln@beastie.ix.netcom.com>
2003-01-03 1:44 ` Bill Findlay
2003-01-09 2:21 ` faust
2003-01-03 2:56 ` Marin David Condic
2003-01-03 4:11 ` sk
2003-01-03 4:43 ` Bill Findlay
2003-01-03 6:01 ` Robert C. Leif
2003-01-07 17:47 ` Kevin Cline
2003-01-07 19:49 ` tmoran
2003-01-09 5:15 ` Kevin Cline
2003-01-03 13:16 ` Marin David Condic
2003-01-03 18:28 ` Bill Findlay
2003-01-04 15:17 ` Marin David Condic
2003-01-09 16:36 ` faust
[not found] ` <roliva.8b4.ln@beastie.ix.netcom.com>
2003-01-09 4:32 ` Hyman Rosen
2003-01-03 20:07 ` tmoran
2003-01-03 23:06 ` Martin Dowie
2003-01-09 16:22 ` faust
2003-01-04 7:07 ` Robert C. Leif
2003-01-04 17:49 ` Steve
2003-01-05 3:07 ` Robert C. Leif
2003-01-07 12:38 ` Richard Riehle
2003-01-09 16:36 ` faust
2003-01-03 9:24 ` Kevin Cline
2003-01-03 10:11 ` John R. Strohm
2003-01-03 13:23 ` Marin David Condic
2003-01-03 18:40 ` John R. Strohm
2003-01-04 9:05 ` Kevin Cline
2003-01-04 16:34 ` John R. Strohm
2003-01-03 19:40 ` Kevin Cline
2003-01-03 22:34 ` Ted Dennison
2003-01-04 8:53 ` Kevin Cline
2003-01-04 11:48 ` Dmitry A. Kazakov
2003-01-04 18:15 ` Robert A Duff
2003-01-04 20:18 ` Hillel Y. Sims
2003-01-05 14:13 ` Dmitry A. Kazakov
2003-01-05 15:45 ` James S. Rogers
2003-01-06 14:13 ` Dmitry A. Kazakov
2003-01-06 1:20 ` Hillel Y. Sims
2003-01-06 14:14 ` Dmitry A. Kazakov
2003-01-06 19:07 ` Randy Brukardt
2003-01-07 12:33 ` Dmitry A. Kazakov
2003-01-08 4:24 ` Hyman Rosen
2003-01-08 13:55 ` Dmitry A. Kazakov
2003-01-08 18:43 ` Wes Groleau
2003-01-08 21:54 ` Ted Dennison
2003-01-09 5:05 ` Hyman Rosen
2003-01-06 1:37 ` Robert C. Leif
2003-01-06 14:13 ` Dmitry A. Kazakov
2003-01-06 19:13 ` Pascal Obry
2003-01-07 12:02 ` Dmitry A. Kazakov
2003-01-07 3:00 ` Hyman Rosen
2003-01-07 12:10 ` Dmitry A. Kazakov
2003-01-08 3:41 ` Hyman Rosen
2003-01-08 13:19 ` Dmitry A. Kazakov
2003-01-09 4:23 ` Hyman Rosen
2003-01-10 13:51 ` Dmitry A. Kazakov
2003-01-13 17:05 ` Hyman Rosen
2003-01-15 17:04 ` Dmitry A. Kazakov
2003-01-15 17:23 ` Hyman Rosen
2003-01-15 18:19 ` Bill Findlay
2003-01-15 19:02 ` Hyman Rosen
2003-01-15 19:11 ` Bill Findlay
2003-01-15 22:51 ` chris.danx
2003-01-15 23:39 ` Bill Findlay
2003-01-15 23:57 ` chris.danx
2003-01-16 0:32 ` Bill Findlay
2003-01-16 5:23 ` Richard Riehle
2003-01-16 17:11 ` Hyman Rosen
2003-01-16 17:50 ` Richard Riehle
2003-01-16 17:57 ` Frank J. Lhota
2003-01-16 18:26 ` Wes Groleau
2003-01-17 8:27 ` Anders Wirzenius
[not found] ` <h0770b.5e3.ln@beastie.ix.netcom.com>
2003-01-17 17:32 ` Warren W. Gay VE3WWG
2003-01-17 17:31 ` Warren W. Gay VE3WWG
2003-01-16 0:19 ` Richard Riehle
2003-01-16 0:16 ` chris.danx
2003-01-16 0:46 ` Bill Findlay
2003-01-16 1:19 ` Jeffrey Carter
2003-01-16 2:44 ` Richard Riehle
2003-01-16 0:24 ` Bill Findlay
2003-01-16 10:34 ` Jean-Pierre Rosen
2003-01-16 18:20 ` Dmitry A. Kazakov
2003-01-16 18:59 ` Hyman Rosen
2003-01-17 4:09 ` Richard Riehle
2003-01-17 14:36 ` Hyman Rosen
2003-01-17 16:28 ` Dmitry A. Kazakov
2003-01-17 17:23 ` Hyman Rosen
2003-01-17 19:02 ` Richard Riehle
2003-01-17 20:02 ` Hyman Rosen
2003-01-25 1:40 ` Richard Riehle
2003-01-26 4:57 ` Hyman Rosen
2003-01-18 12:31 ` Dmitry A. Kazakov
2003-01-18 22:53 ` Hillel Y. Sims
2003-01-19 6:18 ` Kevin Cline
2003-01-19 12:34 ` Dmitry A. Kazakov
2003-01-21 2:10 ` Hillel Y. Sims
2003-01-21 9:25 ` Dmitry A. Kazakov
2003-01-21 18:55 ` Kevin Cline
2003-01-23 11:00 ` Dmitry A. Kazakov
2003-01-23 16:27 ` Hyman Rosen
2003-01-25 11:53 ` Dmitry A. Kazakov
2003-01-26 6:32 ` Hyman Rosen
2003-01-27 10:11 ` Dmitry A. Kazakov
2003-01-27 15:08 ` Hyman Rosen
2003-01-28 8:27 ` Dmitry A. Kazakov
2003-01-28 15:48 ` Kevin Cline
2003-01-28 16:29 ` Dmitry A. Kazakov
2003-01-28 17:14 ` Hyman Rosen
2003-01-29 8:28 ` Dmitry A. Kazakov
2003-01-28 17:11 ` Hyman Rosen
2003-01-29 8:37 ` Dmitry A. Kazakov
2003-01-29 15:44 ` Hyman Rosen
2003-01-29 21:34 ` Mark Biggar
2003-01-29 22:54 ` Hyman Rosen
2003-01-30 9:03 ` Dmitry A. Kazakov
2003-01-30 14:59 ` Hyman Rosen
2003-01-30 16:32 ` Dmitry A. Kazakov
2003-01-30 17:58 ` Hyman Rosen
2003-01-31 8:31 ` Dmitry A. Kazakov
2003-01-31 15:02 ` Hyman Rosen
2003-01-31 16:12 ` Dmitry A. Kazakov
2003-01-31 17:11 ` Hyman Rosen
2003-02-03 9:59 ` Dmitry A. Kazakov
2003-02-03 13:26 ` Hyman Rosen
2003-02-03 16:12 ` Dmitry A. Kazakov
2003-02-03 17:00 ` Hyman Rosen
2003-02-04 9:54 ` Dmitry A. Kazakov
2003-02-04 14:50 ` Colin Paul Gloster
2003-02-04 15:56 ` Hyman Rosen
2003-02-05 12:53 ` Dmitry A. Kazakov
2003-02-05 15:22 ` Hyman Rosen
2003-02-05 7:02 ` Amir Yantimirov
[not found] ` <en04h-1k4.ln1@beastie.ix.netcom.com>
2003-02-04 9:48 ` Dmitry A. Kazakov
2003-02-04 10:10 ` Colin Paul Gloster
2003-02-04 13:12 ` Dmitry A. Kazakov
2003-02-04 14:33 ` Colin Paul Gloster
2003-02-04 15:22 ` Dmitry A. Kazakov
2003-02-04 16:47 ` Hyman Rosen
2003-02-04 15:10 ` Hyman Rosen
2003-02-05 12:53 ` Dmitry A. Kazakov
2003-02-05 15:35 ` Hyman Rosen
2003-02-04 7:04 ` AG
2003-02-03 12:34 ` Dmitry A. Kazakov
2003-02-05 4:38 ` AG
2003-02-04 10:08 ` Dmitry A. Kazakov
2003-01-30 8:09 ` Dmitry A. Kazakov
2003-01-30 15:01 ` Hyman Rosen
2003-01-30 16:33 ` Dmitry A. Kazakov
2003-01-30 17:12 ` Stephen Leake
2003-01-31 8:51 ` Dmitry A. Kazakov
2003-01-31 15:04 ` Hyman Rosen
2003-01-30 18:01 ` Hyman Rosen
2003-01-31 8:38 ` Dmitry A. Kazakov
2003-01-31 15:11 ` Hyman Rosen
2003-01-31 16:27 ` Dmitry A. Kazakov
2003-01-31 17:25 ` Hyman Rosen
2003-02-03 9:59 ` Dmitry A. Kazakov
2003-02-03 13:11 ` Hyman Rosen
2003-02-03 14:40 ` Hyman Rosen
2003-02-04 10:11 ` Dmitry A. Kazakov
2003-02-04 6:34 ` AG
2003-02-03 12:58 ` Dmitry A. Kazakov
2003-01-27 16:04 ` Kevin Cline
2003-01-19 3:42 ` Hyman Rosen
2003-01-19 12:34 ` Dmitry A. Kazakov
2003-01-19 14:13 ` Hyman Rosen
2003-01-20 8:43 ` Dmitry A. Kazakov
2003-01-16 19:08 ` Hyman Rosen
2003-01-17 16:28 ` Dmitry A. Kazakov
2003-01-17 4:03 ` Richard Riehle
2003-01-17 16:28 ` Dmitry A. Kazakov
2003-01-21 5:53 ` Richard Riehle
2003-01-21 6:24 ` tmoran
2003-01-16 19:09 ` Larry Kilgallen
2003-01-15 22:48 ` Robert A Duff
2003-01-16 18:20 ` Dmitry A. Kazakov
2003-01-25 16:05 ` Robert I. Eachus
2003-01-25 20:33 ` Richard Riehle
2003-01-27 13:29 ` Wes Groleau
2003-01-27 16:29 ` Hyman Rosen
2003-01-28 13:24 ` Robert A Duff
2003-01-28 17:16 ` Hyman Rosen
2003-01-28 18:44 ` Robert A Duff
2003-01-28 20:04 ` Hyman Rosen
2003-01-07 13:51 ` Richard Riehle
2003-01-08 3:51 ` Hyman Rosen
2003-01-06 16:33 ` Georg Bauhaus
2003-01-06 16:23 ` Wes Groleau
2003-01-06 4:20 ` Kevin Cline
2003-01-06 14:16 ` Dmitry A. Kazakov
2003-01-06 16:08 ` Wes Groleau
2003-01-06 17:26 ` James S. Rogers
2003-01-07 13:36 ` Wes Groleau
2003-01-07 18:40 ` David C. Hoos
2003-01-07 21:29 ` James S. Rogers
2003-01-07 3:14 ` Hyman Rosen
2003-01-07 13:40 ` Wes Groleau
2003-01-08 4:30 ` Hyman Rosen
2003-01-04 18:04 ` Ted Dennison
2003-01-04 20:20 ` Hillel Y. Sims
2003-01-05 2:47 ` Ted Dennison
2003-01-09 16:24 ` faust
2003-01-09 15:04 ` Ted Dennison
2003-01-10 14:23 ` faust
2003-01-11 5:44 ` Ted Dennison
2003-01-11 5:48 ` Ted Dennison
2003-01-06 4:39 ` Kevin Cline
2003-01-06 9:49 ` Ted Dennison
2003-01-03 0:07 ` Robert C. Leif
2003-01-03 2:51 ` Marin David Condic
2003-01-03 18:13 ` Warren W. Gay VE3WWG
2003-01-04 15:30 ` Marin David Condic
2003-01-07 12:58 ` Richard Riehle
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