On Friday, 2 May 2014 23:20:55 UTC+2, Zeit Geist wrote: > On Friday, May 2, 2014 1:18:07 PM UTC-7, muec...@rz.fh-augsburg.de wrote: > > > On Friday, 2 May 2014 21:12:01 UTC+2, Dan Christensen 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.
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.