RE: [P-1788]: Re objective == infinity
I think the confusion is between
* the notion of a closed set, which is well-defined and understood the same way in all math classes, and
* the high-school notions of closed, open, and semi-closed intervals which in different textbooks may be interpreted differently for infinite intervals.
If a textbook defines a closed interval as an interval that contains endpoints, then
* [0, infinity) is not a closed interval, but
* it is a closed set.
-----Original Message-----
From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Ralph Baker Kearfott
Sent: Sunday, September 30, 2012 11:59 AM
To: N.M. Maclaren
Cc: Arnold Neumaier; stds-1788
Subject: Re: [P-1788]: Re objective == infinity
The confusion might be the distinction between closed sets and compact sets. I didn't see any inconsistencies between my analysis and topology courses, but I probably didn't go to the same school or use the same reference material as you.
Baker
On 09/30/2012 09:48 AM, N.M. Maclaren wrote:
> On Sep 30 2012, Arnold Neumaier wrote:
>>
>> The conventions about closed intervals are very standard, and don't vary with the field. This stuff is taught to all math students in the first semester.
>
> I was taught different ones in analysis and topology, and it is
> probably still done in some places. Even if not, conventions change
> over time, and I don't care which I use as long as I know which it is.
>
> One of the things I learnt fairly early in my career is that virtually
> NO convention is invariant across all areas and across periods of many
> decades, but I do have a rather wider range of experience than most
> people. But there is a consequential point, the failure of which used
> to send me up the wall (and occasionally still does):
>
> PLEASE, when writing papers or documents to be read by people from
> very different areas or over a long period, either define terms or
> provide references to their definition.
>
>
> Regards,
> Nick Maclaren.
>
--
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Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA
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