So from a theoretical computer science perspective we have two algorithms for root 2, N(ewton) and V(edic). For any k the finite sequences Nk and Vk are maybe different, but "converging". So then there are two representations of a computable real (root 2). We then have that equality of computable reals is undecidable. So we cannot finitely prove that these are the same number. So whether root 2 is "real" and well defined depends on whether we assume ( or allow) the existence of a Platonic space that can solve this undecidable problem. I shall await to see what future lectures say.
Thank you. It is undoubtedly my first time to really understand the method by Newton. Never too late. :)
Thankyou. 💕
So from a theoretical computer science perspective we have two algorithms for root 2, N(ewton) and V(edic). For any k the finite sequences Nk and Vk are maybe different, but "converging". So then there are two representations of a computable real (root 2). We then have that equality of computable reals is undecidable. So we cannot finitely prove that these are the same number.
So whether root 2 is "real" and well defined depends on whether we assume ( or allow) the existence of a Platonic space that can solve this undecidable problem.
I shall await to see what future lectures say.
Thx. 💕