Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20120201 03:42:08
Crazy zeta function  infinity equals negative number!?Alright, ζ(0) = 1 + 1 + 1 + ... = 1/2. Miracles do happen! #2 20120201 05:45:59
Re: Crazy zeta function  infinity equals negative number!?Hi Alex23; only when the sum converges which it clearly does not for s=0. So the above definition does not hold. Look here for how an analytic continuation is used: http://mathworld.wolfram.com/RiemannZetaFunction.html In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20120203 06:27:48
Re: Crazy zeta function  infinity equals negative number!?I read the article. So the definition changes for that domain with gamma functions and what not. Last edited by Alex23 (20120203 06:28:30) #4 20120203 06:32:13
Re: Crazy zeta function  infinity equals negative number!?Hi Alex23; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20120205 22:12:04
Re: Crazy zeta function  infinity equals negative number!?To others, infinity is a concept not a number but to me there is even and odd infinity. To them 1+infinity=infinity but to me 1+infinity>infinity. They got all those values like 1/12 or etc because they play with the infinity as they like. If you have a function of 11+11+1..infinity, if you use their concept you would get sometimes S=1/2 yet you know when it is even, S=0 and when it is odd, S=1 and this function alternates 0 & 1 to the infinity. I think people need to respect the infinity, otherwise we would be haywired. I do sometimes play with the infinity and I can proof that Zeta function is not always true and converge to value 4.#7 20121216 01:08:16
Re: Crazy zeta function  infinity equals negative number!?Did you use Euler's definition that the zeta of 2n is equal to Bernoulli of 2n times 2pi to the 2n over 2 times 2n factorial times minus 1 to the n+1th power? 