Math

Dedekind Cut confusion on the square root of 2
Hi, I'm trying to formally prove that S = { x in Q : x < 0 or x^2 < 2 } is the square root of 2, in the Dedekind Cut sense. This is claimed without proof all over the place, e.g. in the Wikipedia article "Construction of the real numbers". By definition, S^2 = { xy : x,y >= 0 are in S } U { x in Q : x < 0 }.... 12 Jan 2010 08:10

zero variety?
Hi Can the empty set be regarded as an abstract algebraic variety? ... 12 Jan 2010 18:35

Exactly why the theories of relativity are complete nonsense- the basic mistake exposed!
Arindam Banerjee wrote: On Jan 4, 9:18 am, "Arindam Banerjee" <adda1...(a)bigpond.com> wrote: Since no self-respecting person has responded negatively to my paper showing that Einstein's theories of relativity are nonsense, I take it that my objections are perfectly valid as they have now passed internatio... 7 Jan 2010 10:10

differentiability of convex functions
Let f: R^n -> R be defined as f(x) = max{<a, x>: a \in A}, where A is a compact subset of R^n. Then f is a convex function hence differentiable (I mean total differentiable i.e. Frechet-differentiable) everywhere but a countable number of points. I wonder if there is any sufficient condition on A that guarantees th... 17 Jan 2010 18:26

CONTINUUM SUM DEBUNKED??? :(
Hi. I think I *may* have found a proof that it is Impossible to, in general, give a method or procedure for producing consistent solutions to difference equations of analytic functions, at least in a sufficiently "natural" way. F(x+1) - F(x) = f(x) for F(x). The proposed proof: -- Suppose f(x) = sum_... 9 Jan 2010 16:18

Integral operator cannot take constant values
Why the integral operator K: L^2 (0,1) -> L^2(0,1) defined by: Kx(t) = Integral[ (1+ts)exp(ts)x(s) ds from s=0 to s=1] _cannot_ take constant values? i.e why the constant functions do not belong to the range of K. ... 9 Jan 2010 11:52

Help sought: Does anyone recognize this series in physical systems?
Help sought: Does anyone recognize this series in physical systems? ------------------------------------------------------------------- Interesting little pattern spotted. 2 x (1) 2 x (2x1, 2x3) 2 x (2x1, 2x5, 2x3) 2 x (2x1, 2x7, 2x5, 2x3) The convention is that the first column doubles wha... 7 Jan 2010 12:26

Computing Julia set of exp(z) to really high resolution
Hi. I was wondering: Is there any way at all to draw the Julia set for the complex exponential exp(z) to high resolution? Note that if one affixes a small finite "bailout", the resulting plot is very "bubby", and doesn't show much structure. The actual Julia set is a collection of infinitely thin hairs or someth... 6 Jan 2010 09:23

Rational Number Square To Two Discovered. By Aiya-Oba
(a/b)^2 = 2 Where a, is 44721359550, and b, is 31622776604. - Aiya-Oba (Philosopher) Such thant, ( 44721359550/31622776604)^2 = 2 = (1.414213562)^2 = 2 Q E D. Pythagoras is vindicated. -Aiya-Oba ... 16 Jan 2010 18:21

Anti-Einsteiniana: Natural Philosophy Alliance?
W. H. Newton-Smith, THE RATIONALITY OF SCIENCE, Routledge, London, 1981, p. 3: "For vewed sub specie eternitatis scientists (even physical scientists) are a fickle lot. The history of science is a tale of multifarious shiftings of allegiance from theory to theory. Newtonian mechanics had its hour of flourishing wit... 8 Feb 2010 08:53