On Nov 23, 2007 7:15 AM, Mathieu Bouchard <matju@artengine.ca> wrote:
On Sat, 17 Nov 2007, Uur Güney wrote:It's not because it's a continuum, that it has infinite dimensions. Real
> An example of sound producing mechanism is
> plucked and vibrating string (or vibrating membrane) It is a continuum
> and so has infinite dimensions.
numbers form a continuum, but have only 1 dimension.
The set of all possible continuous functions over a given finite interval,
forms a continuum that has infinitely (countably) many dimensions. This
continuum also happens to include some simple (Fourier-compatible)
discontinuities as well. (Including all possible discontinuities is
another story.) Physical sounds can be understood to have no
discontinuities, as several factors tend to "low-pass" the sound enough to
remove discontinuities.