Xenomortis wrote:dudiobugtron wrote:PM 2Ring wrote:As Xenomortis said, "if you think you've all the reals, I have Cantor's diagonal argument as backup".
Any program that purportedly generates all the reals has to do so in some sequence, i.e., it creates a list of reals. And any list of reals is susceptible to Cantor diagonalization.
Any countably infinite list of reals is susceptible to Cantor diagonalisation. An uncountably infinite list containing all of the reals wouldn't be, though. If the program only does countably infinite steps, then sure it won't generate all of the reals. However, it may be able to generate all of the reals after doing O(|R|) steps.
How do you propose to get an uncountable list?
We are talking about a computer; it calculates things step by step. The term "uncountable" doesn't fit in anywhere.
All you need is some parallel processing. Uncountably infinitely many processes running in parallel, that is.