Pi is transcendental and no number except pi itself, can be subtracted from pi to yield a whole number.
Quote from: QwazyWabbit on September 29, 2008, 03:19:27 PMPi is transcendental and no number except pi itself, can be subtracted from pi to yield a whole number.The transcendence has nothing to do with that.Let n in Z := {...-2, -1, 0, 1, 2, ...}. pi - (pi - n) = n
Quote from: math on September 30, 2008, 09:24:01 AMQuote from: QwazyWabbit on September 29, 2008, 03:19:27 PMPi is transcendental and no number except pi itself, can be subtracted from pi to yield a whole number.The transcendence has nothing to do with that.Let n in Z := {...-2, -1, 0, 1, 2, ...}. pi - (pi - n) = n It has everything to do with it.Associative law reveals:pi - (pi - n) = (pi - pi) - n = 0 - n and is not equal to n except when n = 0 so your equation is flawed.But you have effectively subtracted pi from itself. My assertion is correct. However, the the flaw of my original statement is one of not being more formal with regard to precision and significant figures.9, the integer is exact. pi, the symbol is exact. C = pi * D is exact.3.14159265358 as an approximation of pi is precise but inexact. C = 3.14159265358 * D is precise but inexact.Subtracting 0.14 from pi to approximate 3 is inexact and imprecise in comparison with 9, the integer.Doing something like 3^2 (1 + pi - pi) would have been exact but mostly useless obfuscation but of course, the whole clock is useless obfuscation. I was merely pointing out the nature of the lack of mathematical rigor in the equation for 9 o'clock.