
Re: Why do we need those real nonconstructible numbers?
Posted:
Nov 8, 2017 8:16 AM


If the a_n are rational numbers, they might come from a finite process,
it can even be the case that the partial sums, s_n = sum_i=1^n a_n, which will be
then rational numbers again, might converge, and then there will be a limit n>oo s_n,
which is not necessary a rational number anymore, it can be a transcendental number,
https://math.stackexchange.com/q/37121/4414 (elementarysettheory) (cardinals) (transcendentalnumbers) the transcendental numbers are uncountable.
Am Mittwoch, 8. November 2017 14:10:57 UTC+1 schrieb burs...@gmail.com: > But SUM a_n where a_n is an arbitary infinite sequence > is not a finite description. > > Am Mittwoch, 8. November 2017 13:44:58 UTC+1 schrieb WM: > > Am Mittwoch, 8. November 2017 12:58:14 UTC+1 schrieb burs...@gmail.com: > > > Nope, transcendental numbers don't have a finite > > > description. > > > > "SUM 1/2^n!" is a finite description. > > > > > They are the rest of all real line > > > > > numbers that are not rational numbers or > > > algebraic irrational numbers, and as such they > > > > > > are uncountable. > > > > All finite descriptions belong to a countable set. Everything beyond is unmathematical nonsense, delusions of unmathematical minds. > > > > Regards, WM

