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Re: "natural interval extension"



Frederic & P1788

On 8 Dec 2015, at 08:18, Frederic GOUALARD <Frederic.Goualard@xxxxxxxxxxxxxx> wrote:
> Le 2015-12-08 08:21, Svetoslav Markov a écrit :
>> The term  "natural interval extension" meaning replacement
>> of all real quantities and operators by interval
>> ones has been introduced by Moore.
>> So I find great the suggestion by Michel to rename this
>> term "Moore Interval Extension" in tribute to R Moore.
> 
> Giving a new, additional, name to an existing procedure is one thing (and Michel's suggestion is a great one). Redefining a term whose use is already pervasive in the interval literature with a new meaning is a horse of a completely different color.
> 
> If we had to name in the standard what has often been called "natural interval extension" so far, I would applaud Michel's suggestion to use "Moore Interval Extension".
> 
> I have strong reservations to redefining "natural interval extension" to something entirely different, even if proposing in parallel a new name for the old procedure. That is calling for a great deal of confusion in the future...

I feel rather vexed by this discussion, because this terminology has lain "hidden in plain sight" for some six years. 

As I recall, there was a time when the only standard text we had was Level 1 of the set-based flavor (of course flavors didn't exist then). I put that definition in right at the start. It has basically never changed. Surely there must have been some discussion of it then? Maybe someone less lazy than me will look at the record to see if I recall right.

A.If one thinks of "interval extension" as being a property of a *function*,
  I maintain that the definition in 1788 is the most "natural".

B.If one thinks of it as being a property of an *expression*, then the one
  that's "common in the literature" is sort of natural. Or it would be, if
  the books/articles making the definition made clear that many different
  expressions can define the same function. But they don't. Even Warwick
  Tucker's book, which I find exemplary in most ways, is vague, as Michel
  Hack pointed out on 7 Dec. (WT promised me to make it clearer in a future
  edition.)

I haven't a good solution to the problem. Personally as a real-analysis guy I see A as the "right" meaning, but I see the confusion that might be caused. Could we keep the main 1788 text unchanged but insert a footnote about it as a corrigendum?

Regards

John Pryce