Re: Motion on interval flavors
Dear prof Kulisch,
I am quite puzzled by your attitude to Kaucher/modal IA.
It seems to me that you, and probably other
participants in this forum, are not aware
with the history of the acceptance of negative numbers!
I make the analogy with negative numbers because
improper (Kaucher/modal) intervals are just
like negative numbers (as their radii are negative).
There is a lot in internet about the history of the acceptance
of negative numbers, see e. g.:
http://en.wikipedia.org/wiki/Negative_number
(section "history")
This section finishes like this:
In A.D. 1759, Francis Maseres, an English mathematician, wrote that negative
numbers "darken the very whole doctrines of the equations and make dark of the
things which are in their nature excessively obvious and simple". He came to
the conclusion that negative numbers were nonsensical.[14]
In the 18th century it was common practice to ignore any negative results
derived from equations, on the assumption that they were meaningless.[15]
Are we living in the 18th century? Indeed, negative numbers were not
real numbers before mathematicians accustomed to use them.
Regards,
Svetoslav
PS. Here are some other links to "The History of Negative Numbers":
http://nrich.maths.org/5961
http://logica.ugent.be/albrecht/thesis/HPM2008.pdf
http://www.ma.utexas.edu/users/mks/326K/Negnos.html
http://www.basic-mathematics.com/history-of-negative-numbers.html
http://logica.ugent.be/centrum/preprints/Numberline-ScienceAndEducation-rev.pdf
A BBC film:
http://www.bbc.co.uk/iplayer/episode/p003hyd9/In_Our_Time_Negative_Numbers/
On 6 Jul 2012 at 15:56, Ulrich Kulisch wrote:
Date sent: Fri, 6 Jul 2012 15:56:50 +0200
From: Ulrich Kulisch <ulrich.kulisch@xxxxxxx>
To: John Pryce <prycejd1@xxxxxxxxxxxxx>
Copies to: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
Subject: Re: Motion on interval flavors
> Am 20.06.2012 07:49, schrieb John Pryce:
> > I'm not very happy with the name "set-based" intervals, but calling them
> > "standard" intervals is no longer appropriate, as well as clashing with the
> > main meaning we give to "standard" (as a noun and also an adjective). Any
> > better name welcomed.
> >
> > Regards
> >
> > John Pryce
> >
>
> I see two kinds of set-based intervals, the closed and bounded intervals
> of IR and the closed intervals of \overline{IR}. What about calling the
> first cb-intervals and the second c-intervals.
>
> Kaucher or modal intervals are not really intervals. They are abstract
> entities. Why not calling them i-intervals for inverse or improper
> intervals or m-intervals.
>
> Best regards
> Ulrich
>
> --
> Karlsruher Institut f"ur Technologie (KIT)
> Institut f"ur Angewandte und Numerische Mathematik
> D-76128 Karlsruhe, Germany
> Prof. Ulrich Kulisch
>
> Telefon: +49 721 608-42680
> Fax: +49 721 608-46679
> E-Mail: ulrich.kulisch@xxxxxxx
> www.kit.edu
> www.math.kit.edu/ianm2/~kulisch/
>
> KIT - Universit"at des Landes Baden-W"urttemberg
> und nationales Grossforschungszentrum in der
> Helmholtz-Gesellschaft