Math

Galileo's Paradox
GALILEO'S PARADOX 1 2 3 4 5 ................. 1 4 9 16 25 ............... There is a paradox because the 1:1 Correspondence suggests the sets are equal in size, by extension from the finite case, and yet clearly the second set is contained in the first set. That an infinite set can be put into 1:1 ... 29 Dec 2006 12:45

Convergence in Measure Question
Hello. This question is #38 in chapter 2 of Folland. Suppose f_n -> f in measure and g_n -> g in measure. Show that f_n g_n -> fg in measure if u(X) < infinity, but not necessarily if u(X) = infinity. I tried fooling around with |f_n - f| |g_n - g| >= |f_n| |g_n - g| + |f| |g_n - g| = (|f_n| + |f|) |g_n - g|, ... 12 Oct 2006 01:50

Group Theory
Let G be a group such that the intersection of all its subgroups which are different from (e) is a subgroup different from (e). Prove that every element in G has finite order. How do you show this is true? ... 5 Oct 2006 15:57

Cantor Confusion
Cantor's proof is one of the most popular topics on this NG. It seems that people are confused or uncomfortable with it, so I've tried to summarize it to the simplest terms: 1. Assume there is a list containing all the reals. 2. Show that a real can be defined/constructed from that list. 3. Show why the real fr... 9 Feb 2007 19:20

Pi berechnen: Ramanujan oder BBP
Am 21 Sep 2006 06:02:36 -0700 schrieb Hans Mull: Hallo! Da ich ein leidenschaftlicher Pi-Auswendiglerner bin, nahm ich mir vor kurzem bor, ein Programm, zu schreiben, das eine ausreichen genaue Ann?herung an Pi in (relativ) kuzer Zeit berechnen kann. Nun wei? ich nicht, welchen Algorithmus ich daf?r ve... 22 Sep 2006 10:42

Euclidean Spaces
I am totally stuck on this problem: Suppose k >= 3, x, y belongs to R^k, |x - y| = d > 0, and r > 0. Prove: (a) If 2r > d, there are infinitely many z belonging to R^k such that |z - x| = |z - y| = r. (b) If 2r = d, there is exactly one such z. (c) If 2r < d, there is no such z. How must these statements ... 12 Sep 2006 14:27

Am I a crank?
Hi, I like mathematics and play with it in my spare time, perhaps excessively. I would like to prove something as yet unproved, but doubt I ever really will. I just read an article about mathematical cranks and began questioning myself. I know its a very odd question and perhaps awkward, but I'm really curiou... 2 Oct 2006 18:24

Any coordinate system in GR?
The offhand claim is sometimes made that GR, which I take it means the formal machinery of GR, treats all coordinate systems equally. Is this true? Aside from questions about smoothness, it seems to me there is at least some other implicit condition on permissible coordinate systems. Consider a 1-dimensional ma... 22 Sep 2006 19:38

Prime numbers
What's everyone's opinion of the site www.primenumbersformula.com? Is the author for real, or just a crank? ... 12 Jul 2006 22:36

An uncountable countable set
An uncountable countable set There is no bijective mapping f : |N --> M, where M contains the set of all finite subsets of |N and, in addition, the set K = {k e |N : k /e f(k)} of all natural numbers k which are mapped on subsets not containing k. This shows M to be uncountable. Regards, WM ... 14 Nov 2006 20:41