
Re: Why do we need those real nonconstructible numbers?
Posted:
Nov 9, 2017 4:01 AM


Am Donnerstag, 9. November 2017 08:38:59 UTC+1 schrieb bassam king karzeddin: > whereas the absolute (Pi) exists exactly in the perfect circle that doesn't exist in any imaginable reality
It does not exist in reality. But it exists in imagination. And its circumference can be approximated as closely as we like (in ideal mathematics  not in reality).
To accept it as a number or value or lenght is questionable. But a rather convincing argument is this: If it exists on the real line, then it must be a point, because if only adding any positive eps like 10^1000000000000 gives a number that provably is not the limit of so many sequences (Vieta, Wallis, GregoryLeibniz, Euler, Ramanujan, Borwein,... see for instance GU03.PPT in https://www.hsaugsburg.de/~mueckenh/GU*/) > > Had the Greek recognized this simplest fact, then never they would have raised their three famous impossible constructions for sure
These constructions are not impossible. They are only impossible with the tools allowed by Plato. (See for instance the Quadratrix, loc cit p. 40)
Regards

