cosine

I would think that PM them on the server would not be any better. It would b like saying that I can't give you the codes to the U.S. nuclear missles on the mssage board, but I could through SFN's PM. The code by the way is 12345.

Well hey, nice proof! Btw, what was your goal?

Hey, it help me alot if you could give me an equation solved for a complex [math]z[/math] in the complex plane union with infinity (sorry I don't know the latex for that). I'm looking for an equation of the form z = an expression made of the 3 complex numbers that determine it. I've been trying to find something like this for a few days, any help is appreciated. Edit: By the way this is in Mobius geometry. The name aludes me of the plane, but basically the plane is the union of the complex plane and the point at infinity. Again, thanks for any help.

This is a biconditional, right? Edit: Yep!

Thanks for the info Dave. But I'm curious if you guys saw my suggestion on the paid subscription thread. Is it a reasonable idea to open up the arcade for donations to the server?

You could have the paid feature enable the arcade again. That way the forum stays the same. And thats a nice incentive for people who appreciate SFN.

Dr. Pei Wang at Indiana State University is currently doing a lot of interesting research on Artificial Intelligence by talking about NARS, Non Axiomatic Reasoning Systems. Computers use PAS, Pure axiomatic systems, where all knowledge is known for any question, and if a PAS can't answer the question, it is the questioner's fault for not asking a good question. Humans use NARS, where knowledge can be insufficient for a problem it has to solve. PAS is purely deductive. NARS are more inductive. I recommend that you check out Pei Wang's paper: Cognitive Logic vs. Mathematical Logic Interestingly, as Pei Wang has learned about NARS, he has built a computer demonstration using NARS, which is also on his website: Pei Wang's Publications And here is a thread currently on the General Mathematics Forum where I talked a little about it some more: http://www.scienceforums.net/forums/showthread.php?p=223366#post223366

Sorry, only an undergrad, but here's some new stuff I've been reading: http://www.cogsci.indiana.edu/farg/peiwang/PUBLICATION/ Dr Pei Wang of Indiana State University has been research NARS, Non Axiomatic Reasoning System, to work on how the human mind's logic system works. There is even an interactive program he's made using NARS.

I like your idea of how it could be fixed later on as to only take a percentage of Earth markets... although I have to laugh at myself on this because when this happens, companies will try to improve technology, but to the point of being able to send their "earth work" jobs to the future colonies! And when this happens, haha... well we'll have to deal with it over time. All I can say to that is it seems that there is no ideal body politic, and it takes careful balancing and rebalancing to handle change in humanity. You are making it seem like that all institutions that exist now are the only ones that will in the future. I would be more than suprised if companies around the world were sending things into space and there wasn't an international space politics body. I mean, there are alot of safety factors alone that need to be considered. Like what happens when an Austrailian company's moon nuke accidentily falls on to Germany? There are many possible other unifying bodies as well, which you mentioned, such as the UN, or a treaty protocol like the Kyoto Treaty. And I wouldn't start throwing public money to wealthy business men yet. The industry needs to be able to exist without public funds for there ever to be a possibility of it being a private industry. If it needs public funds then why not keep it public property? The labor problems I'm envisioning is private companies pulling all of their jobs out of the U.S. and sending them to a cheaper third world country, as well as companies doing whatever they can to cut costs, which could easily include a cut in quality. Quality is something I don't want tampered with when such things are getting launched into potentially dangerous positions about the heads of humanity.

Thats a nice proof.

I suggest that anyone interested in A.I. check out the work of Pei Wang (and other works he may reference). He is doing work on Non-Axiomatic Reasoning Systems. He talks alot about Human Logic vs. Mathematical logic, among MANY other relevant topics. http://www.cogsci.indiana.edu/farg/peiwang/papers.html

Would you like a complex C? In that case: ln(-3) = ln(-1) + ln(3) = i*pi + ln(3) Hope this helps.

I didn't know about the second question you gave' date=' but as to this question: You give: [~(pvq)v((~p)^q)'] Which I would first do: [(~p^~q)v(~p^q)] In both cases ~p must be true, and either q or ~q would satisfy, so you have ~p^(qv~q) Now it depends if you accept the law of the excluded middle. If you do, (meaning that you accept that q must be true or not true), then it follows that the expression is equivalent to ~p Hope this helps.

I figured since this is a thread on limits, perhaps a little something should be said about the rigorous definition of limits. [math]lim_{x-->a} f(x) = L[/math] Means that for any [math]e > 0[/math] there exists a [math]d > 0[/math] such that [math]|f(x) - L| < e[/math] and [math]|x - a| < d [/math]

Thankyou for strengthening the rigor

Hm, yes, this is neccessary, given the hypothesis! Awesome observation! Given that, I believe a proof could follow this way... I don't know if the original poster wanted to see one though, so I present a spoiler space: [hide]Since any collection of 11 numbers is > 1, then let A = the product of the smallest 11 numbers. By hypothesis, A > 1. Let B = the product of all the other numbers of the collection. Then the question asks to proove if AB > 1. We know that A > 1. Since A is the smallest 11 members of the set, it follows that B > A, so B > 1. Thus, AB > 1. This being what we wanted to proove.[/hide]

Ecoli's post was extremely thorough here, I wish there was a karma system in place for posts like that. Its a primer!

84... I think I'm gonna live longer. Yeah as soon as I put in my weight of 215 at 5' 11" the guy came up like a pear, and I was like... wtf? I guess I did every other answer "right" though...

Sorry' date=' what's broughty? The value you've given is an approximation. Pi is a trascendental number, meaning that it is not rational, nor is it a rational root of any rational number (meaning that it can't be expressed as [math']a^{b}[/math] where [math]a[/math] and [math]b[/math] are rational, nor can it be expressed as the root of any polynomial equation). If you would like an easy excercise in deriving pi, trying taking the circle formulas you know, [math]C = 2 \pi r[/math] and [math]A = \pi r^{2}[/math], and trying to say, approximate C or A of a given circle, and then solve the equation for pi. The most straight foward way to do this is to put a regular polygon around or inside the circle and increase the number of sides of the polygon in order to better approximate the circle (or you could do both polygons around and inside the circle and then take the average of the two for a slightly better approximation). Then once you have an Area or Circumfrence, divide that by [math]r^{2}[/math] or [math]2r[/math] respectively. Have fun! (By the way, this method of approximating the circle with regular polygons is attributed to Archimedes and is known as the "Archimeden method".)