On Jan 25, 3:59 pm, VK <schools_r...@yahoo.com> wrote: > > Or maybe that's more-or-less what you were saying in your last > > paragraph. Maybe all we're disagreeing about is whether or not > > "math" (in the sense of sci.math) can encompass computational results. > > I think yes; possibly you think no. > > It can - by using symbols instead of real values, as I said. Other > words instead of using exact finite surrogate values and real > calculations - by using AI-based algorithms for string manipulations. > > Other words for the conventional discrete math > e + pi - e = 3.1415926535897927(0) > so results into some finite rational number > (with possible discrepancy in last significant digits by OS and OS > versions) > and > e + pi - e == pi is false > It is absolutely irrelevant if we have 8, 16, 16 millions or googol > significant digits after comma. We simply cannot accomplish the first > necessary step in the algorithm: "let's take e..." within the frame of > the discrete math and any real calculations. > > Instead all abstract math emulators like Mathematica are using symbols > and string manipulations so > e + pi - e > comes to > strSymWrdE + strSymWrdPi - strSymWrdE = strSymWrdPi > just like string "A" with strings "B" and "C" added will be "ABC"; and > "ABC" being left and right trimmed results in string "B" > - of course it is simplified to a profanity sample, the real mechanics > is much more complicated than that.
Yes, I understand all this. By "computational results" I didn't mean symbolic manipulation on a computer, I meant numerical results calculated on a computer -- specifically, in this case, demonstrating that e^(e^(e^e)) is not an integer by calculating its value numerically to sufficient digits. To me, that is on-topic at sci.math. (From a "pure math" perspective we would of course rather do it symbolically, so the OP's question has an indisputable relevance here in any case.)