[N0B0DY]

"Pat, that example is incorrect since there are INFINITELY many 9's, thus mutliplying by ten must yield 9.9999..."

I took this from the Shout Box if that is okay. I was wondering what mathematical means you would propose, Neutralino, for the quantum jump above, if we know that numbers exist between numbers continuously, there doesn't seem to be a case whereby we could justifiably make that arbitrary discrete jump.

I think pursuing this might lead to a simplified QM understanding because we have a fubar mix of continuity and discretness, in the sense that we can use either one as each other to satisfy both: an infinite number of discrete units continuing forever; one absolute unit; an eternal continuation of one unit; and the absolute decimal point.

If we multiply .999... by 10, then we multiply 1.000... by 10, we get 9.999... and 10.000... Are we therein not in the identical boat?

[AntonioLao]

Infinite series are good and useful as far as they are proven to be convergence and laid the foundation for the mathematics of infinitesimal calculus: differential and integral. But the fact is there are more divergence series than there are convergence. That is why the theory of limits is only applicable to an uncountable real domain of applicability. It's applicability to the complex imaginary domain is questionable since infinity is defined in complex analysis as the largest complex imaginary number at the north pole of Riemann complex sphere.