On 01/22/2014 09:00 PM, Virgil wrote: > In article <email@example.com>, > "Michael F. Stemper" <firstname.lastname@example.org> wrote: >> On 01/22/2014 03:05 PM, Virgil wrote: >>> In article <email@example.com>, >>> firstname.lastname@example.org wrote:
>>>> If the question was: "How can *we* define a number?, then the answer could >>>> only be: "A number can be identified by a finite string of symbols taken >>>> from >>>> an uncountable alphabet". >>> >>> There are tribes which deal with at least small numbers but who have no >>> alphabets or written language, and some whose numberings are not even >>> expressed in words. >>> >>> So while ONE answer coud be WM's, his is not even the only answer in use. >> >> I don't think that his is viable, because the symbols are taken from an >> uncountable alphabet. I'd think that the alphabet would need to be finite. > > Or at least countable (our idea of countable, not WM's)!
That's surprising. Everything that I've read on the subject of languages (which is admittedly limited) specifies finite alphabets.
Is there someplace that would give a simple overview of what changes when you extend the theory to include infinite alphabets?
-- Michael F. Stemper If you take cranberries and stew them like applesauce they taste much more like prunes than rhubarb does.