On Saturday, May 3, 2014 12:48:09 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Friday, 2 May 2014 23:20:55 UTC+2, Zeit Geist wrote: > > > Can you please provide a Countable List > > Every list is countable. > > > of ALL Finitely Definable Real Numbers? > > Remember, this List must have a Finite Definition. > > I use set theory. All finite expressions in all possible (non-formal and formal) languages form a countable set. This is undisputed except by extreme-matheologians who wish to create uncountably many languages or uncountable alphabets. I do not argue with them. >
But there are Uncountable many Languages. Just pick one.
> A real number is defined by (at least) one or (frequently) more of those expressions. Therefore all real numbers form a subset of the set of all finite expressions. According to ZF set theory a subset of a countable set is countable. >
But how do you know that that countable subset is Finitely Definable?