On 5/4/2014 10:34 AM, Virgil wrote: > In article <email@example.com>, > firstname.lastname@example.org wrote: > >> Do you agree that Cantor proved the uncountability of all real numbers > > Of the set of all real numbers as defined by the real number field, yes, > twice! >
What, wouldn't you have it thrice, as to the nested intervals, antidiagonal, and expansion space bits?
Yes you'd mentioned here for the expansion space then constructing the zero and one bits, another counterexample was put forward from here, the same.
This line function has its place in the real numbers, there are still features to understand of it.
Given that's already the real analysis of all continuous functions, finding about more about it than that, has that if logic weren't incomplete there wouldn't be much reason to expect extra features. What with physics then finding the numbers a bit off, here again it's plain that the line function has extra feature than the classical, here for countable additivity, and also the polydimensional.
The polydimensional here is the explanation I give for how numbers are as they are and how concrete numbers have these features in the large and small. Then these are usually as effects of Shannon and Nyquist. As well then for attenuation in the general and so on, this is for the extra-standard in the probability and the mechanics.