Math

Questions on Green's Theorem
With the given problem: F = (-yi + xj)/(x^2 + y^2), show that int_C(F.dr) = 2*Pi for every positively oriented simple closed path that encloses the origin. We can't compute it directly because C is arbitrary. But what motivates us to consider a smaller circle: C_1 where it is a positively oriented circle with ce... 11 Jun 2010 19:16

Posting Msgs with Math Symbols?
I use Tbird for mail, is there some way to post msgs with math symbols? ... 11 Jun 2010 19:16

Cute observation ...
This isn't new, this isn't deep, and it isn't a mystery, but I sometimes use this to get kids interested in proof. For prime p>3, p^2-1 is a multiple of 24. It's not hard to prove, but it's a good one to get kids thinking about how we can know something is always true without just checking every number. Jus... 13 Jun 2010 05:04

Big Bang is a amorphous, a nonentity, process whereas Atom Totality is a "something that is building" Chapt 3 #153; ATOM TOTALITY
I like using Wegener's Continental Drift theory for an example of how a true theory removes a fake theory of a "static Earth". I like it because it shows that true science usually divides the scientists of that community. Divides them into bandwagons of those who cling onto the old past and falsehoods. And the Co... 10 Jun 2010 15:42

maybe I need to combine this chapter with "Dirac new radioactivities" Chapt 3 #152; ATOM TOTALITY
Mike Dworetsky wrote: Reality check: would this numerology have given the same answer 5-6 billion years ago when the CMB was closer to 5 K? Or was e different back then? What about 10 billion years ago when it was even hotter? I may have to combine this chapter with "new radioactivities" for I ... 10 Jun 2010 17:55

Very vicious differential problem
a > 0, b real. y' = ysin(y)/(1+x^a) lim (for x -> infty) y(x) = b Existence and uniqueness of C^1 solutions is the matter. This seems even harder than the previous. ... 10 Jun 2010 23:27

Solving a first order ODE
Hi, I have the differential equation y'(x) = sqrt[ (B-y)/y) ] Is there a general method, or infact any method I can use to solve this? Thank you, Ashley ... 11 Jun 2010 03:48

Need help with proof of Cantor's Theorem using Dedekind cuts
Hi, I am looking for a proof that the cardinality of the real numbers (represented as Dedekind cuts) is greater than that of the natural numbers -- so, not the usual diagonal proof. Either that or a sketch outline of how to proceed, or even suggestions on how to begin. Any help would be appreciated. Dan ... 10 Jun 2010 05:37

Cosmic Blackbody Microwave Background Radiation proves Atom Totality and dismisses Big Bang Chapt 3 #151; ATOM TOTALITY
II. Cosmic characteristics and features; support Chapter (3) uniform blackbody 2.71 K cosmic microwave background radiation and Dark Night sky: Olber's Paradox fully answered I no longer remember in which edition that I had the Blackbody Cosmic Microwave Background Radiation as the top supporting piece of evide... 10 Jun 2010 04:33

half operator problem -- wondering if this is a discussed topic
I tried some Google searches, but don't know what keywords to use. Here's the problem: given a function f mapping the reals into the reals, find g mapping the reals into the reals such that f(x) = g(g(x)) for any real x. For f(x) = ax+b this is easy. For f(x) = x^b for any real b this is easy. For f(x) = ... 14 Jun 2010 01:56