Recent content by galoisjr

Oh and btw the answer is obviously no and can easily be seen by drawing your basic coordinate axes and arbitrarily choosing two intersecting sets in which neither is a subset of the other... Which seems to imply that a scientific theory can never be proven no matter how much data there is to...

Ok nvm this answer was obvious... I over complicated it.

I was just reading an article the other day about the debate in public schools about teaching evolution as an absolute truth as it has been taght for the past umteen years. Not saying that I'm a proponent of creationism or even that I'm not, but there are some serious flaws in teaching it as the...

I was originally an applied math major and about 2 years ago doubled up with a major in physics... Being an applied math major, I have had quite a few courses in mathematical modeling, and there was always something that bugged me about quantum physics. I figured that I would figure it out once...

Thank you Don Antonio. And you're right. The book that my class used in college just mentioned them. However, I did read a little of Artin's book and I don't remember seeing anything about them, but I most likely overlooked it. I really enjoyed the book by Rotman. It is a very well organized...

Ok, to start off I have been examining the structure of polynomials. For instance, consider the general polynomial P(x)=\sum^{n}_{k=0}a_{k}x^{k} (1) Given some polynomial, the coefficients are known. Without the loss of generality...

I just found the second sheet of paper that seems to convey my reasoning for why i think that the twin prime conjecture must be true. Traditionally when thinking about the density of the primes, we use the pi(x) function. However, this function gives densities in blocks of numbers of an...

I was just saying that if it could be shown that there exists some k in the set of integers bounded above by n! such that my conjecture holds then it would be a sufficient proof of the TPC. What I was trying to say is that k is arbitrary in my conjecture but it needs some bound to be proof of...

I also noticed this, however I was computing them by hand. But this was my reason for introducing k.

It truly does not matter what k is limited to just that it is limited. For instance if k was limited to n! would be sufficient. I however do not think that k could be limited to just n to produce such a result. For proof of my conjecture, it does not matter what k is, just that it exists. I...

Thanks to everyone for the immediate responses. And especially to Dodo for computing the case of k = 1. If I new of some formula to find such a k then the conjecture would be quite simple to prove. This is the reason why I posted this here, so that I could gain some insight because like I...

The prime numbers are the multiplicative building blocks of the integers. Even so, their distribution escapes all methods of rationalization. As with building a pyramid, the primes are most densely distributed near zero, the point of origin, and as we move towards larger numbers the primes are...

nevermind i figured it out. the integral about the circle of radius delta doesn't approach zero for all of s

can anyone help me out?

I was reading through the first chapter of Edwards' book on the zeta function, and I'm a little confused about Riemann's original continuation of zeta to all of the complex plane... The zeta function is supposed to be defined for all s in the set of complex numbers by \zeta \left( s \right) =...