Europe has long had warm winters starting say several years ago. Back in 1944 during the Ardennes offensive there was like a foot of snow. You can see for yourself the weather of Berlin, Stockholm, Warsaw, Helsinski. Not a single snow flake in Europe...
NASA says Earth's greenhouse effect makes Earth 33 C hotter than the Moon. All of that warming can be explained by Earth having 1 bar of pressure compared to the Moon having no pressure. Going from the Moon to Earth is like going from the top of the troposphere to sea level, roughly speaking...
So far, tested my strong conjecture, which is a strengthening of Bertrand's postulate, to 655 million less 1, where the smallest difference has increased from 1 to 527. As for n being powers of 2, so far, tested using Mathematica to the exponent being 700 where the difference has increased from...
If it's so easy to prove, I wouldn't have considered it worthy of being a conjecture. :wink: When n is prime, my conjecture reduces to Bertrand's postulate when n is prime. It's what happens when n is composite that makes my conjecture interesting. :cool: I won't publish anything unless I'm...
Some sources refer to values of functions as height. I suppose it's easier for some people to comprehend. :tongue:
Any possible way to depict graphically what the Riemann zeta function looks like? Or would this be too complex to do, no pun intended :tongue:?
Starting at 22:50 of the given link, there's a pretty cool computer depiction of Riemann's zeta function. :cool: Can anyone make a comment as to how realistic this particular depiction might be?
In other words, most of the points on the line where the real part is 0.5 do not have height 0? Also, could the Reimann zeta function evaluate to negative values?
The Riemann hypothesis states, whenever the Riemann zeta function hits 0, the real part of the input must be 0.5. Does any input with real part being 0.5 make the function hit 0? Also, assuming the hypothesis is true, would it suffice to prove that if the input's real part is not 0.5, then the...
Interestingly, it appears that, for any k > 0, the number of primes in the range (2k , 2k + 2 \times k2) \geq k. The difference between 2k + 2 \times k2 and the kth prime above 2k appears to be a non monotonically increasing function of k and that only when k = 1 do these two values equal each...
Therein lies a twist. How can people ever know if the universe is flat? People once thought Earth is flat, yet Earth is round. Scientists now think the universe is flat, but how can they be sure they are right? No instrument in the world, no matter how accurate, can ever determine if something...
An infinite series can either converge or diverge. By the same token, in my opinion, the universe could be considered either finite or infinite depending on how it expands. Just my 2 cents. :tongue:
http://en.wikipedia.org/wiki/Series_%28mathematics%29
I formulated my original first conjecture into a weak conjecture and a strong conjecture. The weak one is the same as my original first conjecture. The strong one is that, for any n > 1, the number of primes in the range (n , n + how many prime factors n has × the sum of n's prime factors) \geq...
There is also a Firoozbakht's conjecture, which is of the same nature as Cramér's conjecture. :cool:
http://en.wikipedia.org/wiki/Firoozbakht%E2%80%99s_conjecture
Legendre's conjecture and Oppermann's conjecture are of the same nature.
http://en.wikipedia.org/wiki/Legendre%27s_conjecture...
If numbers are not real and part of the universe, then why are there rules in them? For example, http://en.wikipedia.org/wiki/Pythagorean_theorem
Numbers therefore are discovered, not invented. :biggrin: