Re:How many real numbers exist? New proof moves closer to an...
by ummonk on Monday July 19, 2021 @06:35PM
(#27888072)
> It is in its canonical form (i.e. as a numbers, not something that represents it), which is what I said.
This isn't a coherent sentence. A real number is a cauchy sequence of rational numbers. There is no one canonical sequence that defines Pi.
> No I don't. I could pick two atoms floating through space somewhere and say "This distance, right now."
> I could also say: "The distance traveled by this particle in a second."
That process of picking out and localizing the atoms (which are not localized to specific points) would entail performing a measurement with a macroscopic apparatus. At that point, the configuration of the apparatus can be encoded.
This isn't a coherent sentence. A real number is a cauchy sequence of rational numbers. There is no one canonical sequence that defines Pi.
> No I don't. I could pick two atoms floating through space somewhere and say "This distance, right now." > I could also say: "The distance traveled by this particle in a second."
That process of picking out and localizing the atoms (which are not localized to specific points) would entail performing a measurement with a macroscopic apparatus. At that point, the configuration of the apparatus can be encoded.