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
itself to (almost-everywhere) differentiable functions of the
What is the cardinality of the set of such functions? I rather
that they are denumerable, hence exactly representable by UTM
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
and my understanding is that continuous, let alone differentiable,
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.