alt Hacker NewsNumerical issues totally exist but the reason has nothing to do with the fact that Cauchy sequences don't exist on a computer imo.
Numerical issues totally exist but the reason has nothing to do with the fact that Cauchy sequences don't exist on a computer imo.
The abstract formulation is different from the concrete implementation. It is precisely b/c the abstractions do not exist on computers that the abstract analysis does not automatically transfer the necessary analytical properties to the digital implementation. Cauchy sequences & Dedekind cuts are abstract & do not exist on digital computers.