On Dec 13, 3:56 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > No? Nearly every real number is undefinable. The measure of definable > reals is 0. If most reals are non-definable, why must all reals of > every Cantor list always be definable? If all reals of the list are > definable, then they belong to a countable set. Then we cannot prove > uncounatbility. Or can we prove that the set of definable reals is > uncountable - because it is countable but there are, somewhere else, > undefinable "reals"? > > Regards, WM
Cantor's list do contain non definable reals. Actually some diagonals of Cantor's are non definable. The bijective function between all definable reals and the set N of all naturals is NON definable set!
Note: definable is short for "definable by parameter free finite formula"