Re: Guillaume's alternative definition(s) of "com"
Vincent
On 18 Feb 2013, at 10:07, Vincent Lefevre wrote:
> On 2013-02-16 15:40:11 +0000, John Pryce wrote:
>> The dac, together with the bounded input(s), suffices to prove that
>> all the intermediate values, as well as the output, are
>> mathematically bounded, by compactness. (A continuous function on a
>> compact set is bounded.)
>>
>> I think this was my reason for saying that com should describe what
>> actually happens at Level 2, rather than what ideally happens at
>> Level 1. Namely, I claim that your i2+o2 can never produce more
>> informative results than what such a compactness argument can
>> produce using i1+o1. And that there is no other good reason to move
>> to i2 and/or o2.
>
> I agree. This is what I said in our private discussion in November:...
Thanks for circulating that. It's "obvious when you see it" but easy to forget why it's obvious. It needs spelling out in a Note to the main text somewhere.
John