Le 24-mai-05, à 01:10, Patrick Leahy a écrit :
>
> On Mon, 23 May 2005, Hal Finney wrote:
>
>>> I've overlooked until now the fact that mathematical physics
>>> restricts
>>> itself to (almost-everywhere) differentiable functions of the
>>> continuum.
>>> What is the cardinality of the set of such functions? I rather
>>> suspect
>>> that they are denumerable, hence exactly representable by UTM
>>> programs.
>>> Perhaps this is what Russell Standish meant.
>>
>> The cardinality of such functions is c, the same as the continuum.
>> The existence of the constant functions alone shows that it is at
>> least c,
>> and my understanding is that continuous, let alone differentiable,
>> functions
>> have cardinality no more than c.
>>
>
> Oops, mea culpa. I said that wrong. What I meant was, what is the
> cardinality of the data needed to specify *one* continuous function of
> the continuum. E.g. for constant functions it is blatantly aleph-null.
> Similarly for any function expressible as a finite-length formula in
> which some terms stand for reals.
>
>
You reassure me a little bit ;)
PS I will answer your other post asap.
bruno
http://iridia.ulb.ac.be/~marchal/
Received on Tue May 24 2005 - 06:40:46 PDT