On Thursday, May 2, 2013 7:55:37 AM UTC-4, WM wrote:
> I think it is a matter of taste. Some say that SUM1/n! is a number, > > other do not. But it is not important here to take position. > > > > > A function is not a number... An > > > expression can be evaluated into a number. But 8 is a number 2*4 is an > > > expression 4+4 is an expression 2^3 is an expression they are all > > > different expressions/calculations leading to same value.- > > > > Yes. And the point here is that Cantor's argument is only valid for > > decimal expansions and is only supplying decimal expansions. (The > > original argument applies binaries.) > > > > Since 1/9 has no decimal expansion, it cannot be the anti-diagonal of > > a Cantor-list. > > > > Regards, WM
First a comment about naming numbers. It seems to me if Pi is admitted into the set of reals, then 1/9 can be accepted, we just need to name it. hey one-ninth seems to work. Ad if we accept this, then it is just a question of naming the irrationals. We can name whole sets of them, e.g., x*Pi for x any real number.
But what really strikes me about this whole discussion is that it doesn't matter. It seems to be like arguing whether Euclidean or spherical geometry is correct. As the saying goes: if it works use it.
So my questions for WM are not whether you mathematics is correct, but I want to know: * what useful tools can we get out of it? IS it a useful system? * Can you construct it into a Formal system (ala Hilbert)? Does it have internal consistency?
For example (since somewhere in this discussion you claimed to be a professor of physics) can this help in calculating the physics of a black hole (IOW, some how avoid the singularity)?? The mathematics of infinite reals seems to work for nearly every physics problem. Would yours do any better?
I'm hope these questions bring the discussion away from teh heat and into the light. ed