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# /sci/ - Science & Math

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 >> Anonymous Thu Sep 12 13:55:01 2019 No.10967475 [View] File: 239 KB, 1080x1143, yelp.jpg [View same] [iqdb] [saucenao] [google] [report] >>10967431What do you mean by "applications". Practical applications are interested in getting rationals.>And scalars aren't real (in the physical sense), since they lack dimension.>realNothing we have words for "is real" if you ask long enough - certainly not in the sense of materialist realism.>Then what does 'y' equal? Remember the goal is to avoid using 'i', and deal purely with realsThey were talking about constructing C given R and you can do that by formally* looking at the ring R[X] or finite sequences of polynomials** and taking the quotient w.r.t. the ideal X*X+1.*in the sense that you can operate with those things in a computably enumerable way**sequences of X functioning as basis, and sequences of X's being nicely enumerable, i.e. you can write stuff down and compute and even teach a computer how to do itThat is to say, you consider the totality of polynomials with coefficients in R and X*X=-1.So e.g. -7 + 2 * X + 5 * X * X + 8 * X * X * X * X * Xand by above ideal rule, this above polynomial is judged to be equal to-7 + 2 * X + 5 * (-1) + 8 * (-1) * (-1) * Xi.e. this above polynomial is judged to be equal to-13 + 10 XWorking in the ring of polynomials and with the above ideal rule amounts to just working with what's otherwise called the complex numbers. Executing the rule of replacing all instances of X*X with -1 is formally and thus computationally completely unproblematic. Sidenote-7 + 2 * X + 5 * X * X + 8 * X * X * X * X * Xis also-7 X^0 + 2 * X^1 + 5 * X^2 + 0 X^3 + 0 X^4 + 8 * X^5so the representation{-7, 2, 5, 0, 0, 8}for polynomials suggests itself. This way you're also done with "X" and algebra w.r.t. complex arithmetic is reduced to arithmetic and reduction rules with list:{-7, 2, 5, 0, 0, 8} becomes the pair (-7+(-1)*5+0, 2-(-1)*0+8), i.e. (-13, 10)If you already believe in R, then complex arithmetic are just very simple functions on lists of reals (the polynomials)
 >> Anonymous Wed Jul 31 13:55:14 2019 No.10852528 [View] File: 239 KB, 1080x1143, fascist.jpg [View same] [iqdb] [saucenao] [google] [report] http://www.cis.upenn.edu/~jean/math-basics.pdfJust saw this got an update, maybe you're interested
 >> Anonymous Wed May 1 07:24:56 2019 No.10606664 [View] File: 239 KB, 1080x1143, fascist.jpg [View same] [iqdb] [saucenao] [google] [report] I've a PhD in physics, but in the last years my free time is largely devoted to math foundations.Otherwise I work in computer vision / Bayesian inference.
 >> Pair bonding in humans  Anonymous Wed Apr 10 14:43:07 2019 No.10541690 [View] File: 239 KB, 1080x1143, 1554154691940.jpg [View same] [iqdb] [saucenao] [google] [report] What do we know?

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