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.