Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

Re: Motion 31: V04.2 + V.Lefevre + M.Hack = V04.3



Am 03.02.2012 10:48, schrieb Jürgen Wolff von Gudenberg:
Hi
  just some comments on notation. See below

Am 01.02.2012 15:01, schrieb Vincent Lefevre:
On 2012-01-31 21:43:40 +0000, John Pryce wrote:
§3.1: Is the notation compatible with the ISO 80000-2:2009 standard?
http://en.wikipedia.org/wiki/ISO_31-11 says: R* = R \ {0}

I wasn't aware. I've used R* myself for years.

In France, R* is a well-known notation for R \ {0}, ditto for the
other fields (for rings, it is ambiguous since depending on the
context, it can mean the ring without 0 or its group of units).

An alternative is \overline{R} (with mathbb).

Yes, this is the notation I generally see. It is used here:

   http://en.wikipedia.org/wiki/Extended_real_number_line

and here:

   http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html

where it is said:

   "Although the notation for this set is not completely standardized,
   \overline{R} is commonly used."

I think we didn't choose that at the start because Ulrich's liking
for \overline{IR} to mean all closed intervals is a little
incompatible. It's a macro, so trivial to change globally.

I don't see it as incompatible. \overline{IR} is also the set of
all closed intervals whose *bounds* are in \overline{R}, so that
I think that's fine.
There was some discussion about this question early in July 2009. The use of R* for R\{0} was not mentioned during this discussion. I remember that at the end of the discussion we agreed to use \overline{R} for the extended reals. However, in later mails R* was used again. I think we should switch back to \overline{R}.

Best wishes
Ulrich

--
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik (IANM2)
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 - Universität des Landes Baden-Württemberg und nationales Großforschungszentrum in der Helmholtz-Gemeinschaft