Curios

Could you please elaborate a little more. What exactly do you mean by P? Is it the number of primes up to a number N? That graph look very similar to the Log-factorial graph: http://en.wikipedia.org/wiki/Image:Log-factorial.PNG

I have not checked this thread in a long time but what I meant by: "I need the exact solutions to some calculations and not an estimate to the solution such as X^99 or an approximation of Pi or e." is that I'm not trying to calculate either Pi or e (the exact value for them cannot be calculated anyways). I'm trying to find the roots to a massive number. Anyways thanks for the help and the links.

I wanted to ask if anyone knows about a software or powerful online calculator that is able to perform calculations with a solution (a real number in this case) in the range of 300-400 digits. I’m currently working on a problem that involves primes and need such a calculator to test few results. I need the exact solutions to some calculations and not an estimate to the solution such as X^99 or an approximation of Pi or e. I hope someone can help. Thanks

Alright. It is clear that the cable or rod is made out of atoms and that the speed at which these atoms readjust to the "new" location is the speed of light. But if you were to look at the whole scenario in a bigger picture you would then see the cable expand at the instant it was pulled (nothing to do with rigid) because the pull at the other end is not instantaneous. What I mean is the instant the cable was pulled it was displaced at that end by a certain value, but at that instant the other end did not have a chance to displace because it controlled by the speed of light. So the cable would look like it expanded. Can this happen though?

I've got a question that kind of bugged me the other day. Maybe you guys can help. From what I know, information cannot be communicated at speeds faster than the speed of light because of obvious reasons.... But this scenario had me thinking What if a ridged non deformable cable was set between to neighbouring planets in space and was pulled at one end causing an instant pull at the other end of the cable. Could it be possible that this pull or "information" had traveled faster than light? I thought that maybe the flaw had to do with the wave-like pull traveling through the cable at speeds slower than that of light. But what if you have a rod instead of a cable? The reason I got a little more confused is because pulling the cable at the one end by some amount is going to displace the other end by the same amount. (Action & reaction) But will this reaction be instantaneous? Am I missing something?

What's wrong Tom Mattson? Don't tell me you're letting the trivial debate get under your skin. Please dont give any favours out to anyone but yourself. Appreciated

Quote from Matt Matson: "The physical universe plays no role in deciding mathematical truths" What if a system is 100% faultless and makes a mistake? It simply can not happen. If it did happen, then all mathematical theorems and laws of nature will fail. The physical universe is the ultimate test to mathematical constructs. They cannot contradict each other and both be correct. The point I’m trying to explain is that a system with 99.999% certainty still contains a small amount of uncertainty while a system with 100% certainty has 0 uncertainty.

Because we happen to live on earth.

I think there is a slight difference between 0.99 and 1 or 0.999 and 1 etc… Take an example of a system that succeeds 99.999% of the time to do whatever task and fails the remaining 1*10^-3%. This effectively means that the system will fail once every 100,000 attempts. This sounds a bit faulty since you guys are debating 0.999 and not 0.999 but a system or law of nature that succeeds 99.999% keeps that very slight possibility of failure while a 100% successful system eliminates anything other than success. This may sound stupid but there is a difference because that 0.0001% failure exits in a 99.999% successful system while the 100% leaves no margin for debate! (Failure wise) An example of this is a quantum fluctuation whereby the possibility of you randomly chosen (by nature) to be tunneled through a concrete wall to another room exits! although very small. The very nature of that small probability existing allows me to debate it, while otherwise I wouldn’t be able to. Another example I can think of is a trans-planetary missile that is 99.999% accurate. When launching that missile to Pluto for example, a tolerance between where it is aimed and where it will hit exists and is certain. I have to admit that reading your posts reminded me when I got worried about birth control pills because I thought they were 99% effective (actually 99.99%) and thought the law of large numbers will get me! Hence my 1st post.