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[Note: this is a paste from another forum. Feel free to ignore-I don't mean to be spamming!] I am trying to understand Godel numbering, and any help would be much appreciated. For fun, I was just trying to make some Godel numbers for functions (is this even allowable?) to try to investigate properties of these functions with arithmetical proofs on the Godel numbers. So I had a few questions: 1. I can use induction on Godel numbered statements, right? 2. Is it fine to number functions? 3. If it is fine, how do I represent operations arithmetically. For example, how could I arithmetize something like g(f(x))?

How many unique games of chess can be played?? A quadrillion, maybe a googol (10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000) well it's more than that. A close estimation of the number was found in 1950 by the, "father of information theory", Claude Shannon. He estimated the lower bound on the game-tree complexity of chess to be about 10120. In his paper "Programming a Computer for Playing Chess " he explains: With chess it is possible, in principle, to play a perfect game or construct a machine to do so as follows: One considers in a given position all possible moves, then all moves for the opponent, etc., to the end of the game (in each variation). The end must occur, by the rules of the games after a finite number of moves (remembering the 50 move drawing rule).Each of these variations ends in win, loss or draw. By working backward from the end one can determine whether there is a forced win, the position is a draw or is lost. It is easy to show, however, even with the high computing speed available in electronic calculators this computation is impractical. In typical chess positions there will be of the order of 30 legal moves. The number holds fairly constant until the game is nearly finished as shown [...] by De Groot, who averaged the number of legal moves in a large number of master games. Thus a move for White and then one for Black gives about 103 possibilities. A typical game lasts about 40 moves to resignation of one party. This is conservative for our calculation since the machine would calculate out to checkmate, not resignation. However, even at this figure there will be 10120 variations to be calculated from the initial position. A machine operating at the rate of one variation per micro-second would require over 1090 years to calculate the first move! Later Dutch computer scientist Victor Allis estimated it to be closer to 10123 This is a huge number. For comparison note that some have estimated that the total number of atoms in the observable universe is somewhere around 1079 to 1081

Interested in Fractals, Mandelbrot sets. There is a language called Julia! that is one of the latest packages to make the world of Fractals accessible. Documentation: http://docs.julialang.org Julia Set Examples: http://mathemartician.blogspot.de/2012/07/julia-set-in-julia.html

This has puzzled me for quite a while now, and I can't seem to find a clear answer to this. When writing mathematical texts (in LaTeX, say), people often use the symbol epsilon, e.g. denoting some small positive variable. However, some people use the epsilon-version with a straight back (similar to the \in symbol), while others use the one with a curly back (the reversed 3). Why?? Why use one instead of the other? Why is one of them better? And why have two different ways to write it?

Fellow Math Lovers I'm really excited that my chess teacher and friend, Dan Heisman, has joined the Chess.com family. For those who don't know, he is a highly respected chess author of 10 books, and winner of numerous awards. Anyway, I've organized a little tournament to introduce people to Dan. First prize will be a FREE chess lesson with him - an $85 value. http://www.chess.com/tournament/win-a-free-lesson-with-dan-heisman-open Hope you can join!

If I had an equation that said del dot u = 0 (1) And then I had another equation that used a term (u dot del) u Then wouldn't that term just equal 0? http://pages.cs.wisc.edu/~chaol/data/cs777/stam-stable_fluids.pdf I'm trying to understand this here paper, and the Advection term in the Navier-Stokes Equation. http://en.wikipedia.org/wiki/Advection#The_advection_equation But why is it that even though it says del dot u is 0, the u dot del term is not set to 0? Are vector dot products not commutative?

I'm in 7th grade, and i love math, but i'm not that good at math, yet still i'm good for my grade and always willing to help if possible. Is anyone willing to give help of any sort? Thanks, -7thSense-

So now i am in 8th grade and o need help with math state test. And im going for honors/AP math in high school. All the"nomial" numbers, area of 3d shapes (also pyramids and tetrahedrons etc) and imaginary numbers. Help? Keep in touch though thr messages. I'm checking them now since almost all are deleted. And i'll keep postimg on this forum so track it if youre willing to hlp. Thanks:) -7thsense-

I am a Civil Engineering student, and I have just finished the "last math class of my life" - Ordinary Differential Equations. I'm starting to miss math. I was wondering if anyone would have recommendations as to how I can continue the journey of math once my formal education in it has concluded.

An old one, but for those who haven't seen it before: What's wrong with the following reasoning? a = b aa = ba aa - bb = ba - bb (a+b)(a-b) = b(a-b) a+b = b b+b = b 1+1 = 1 2 = 1 By the way, someone should convince erik to implement LaTeX support in these forums :/

Like i said, I'm in 7th Grade. The state assessments start tomorrow. Any suggested topics I should review and anyone willing to give a quick little review? We covered things like basic areas of 2d and 3d figures, perimeters, surface areas, graphing/data, algebra/solving+substituting for variables, stuff like that. There is also a MAP (Measure of Academic Perception) test that will begin in about a month or so, and they have completely random topics. The way it works is you start with a question, and if you answer it right, it goes to a harder question, if you get it wrong, it goes to an easier one. There will be things such as radical numbers, quadratic equations, slops/coordinates, and other seemingly (for me) complicated topics. Any help out there? Thanks so much, -7thSense-

I would like to invite you to the sequel of a sequel, a no holds barred tournament. You can bring out whatever you can find to help you in this tournament, be it chess engines, grandmaster friends, entire chess schools, psychic powers ... anything! Fritz Friendly! - III

We need two more players to complete our roster for the pending Team Match with The Power of Chess. http://www.chess.com/groups/team_match.html?id=57006 If you are rated over 1900 and can join that would be a HUGE help -- BUT, first come first served!!

Does anyone know how to prove that for any invertible function f(x), mapping R→R, there is at least one function g(x) such that g(g(x))=f(x), or find a counterexample?

So you've probably heard the expression "be there or be square". The other day, someone told me to "be there or be a rhombus with a right angle". Then I was thinking of how to express the word square in really complicated terms. A few hours ago, I came up with this: Be there or be the limiting polygon of the simplest polygonal Sierpinski set that contains the topological equivalent of all one dimensional figures, including the fractal cantor brush and all spiders having up to aleph null appendages (i.e. shape around the Sierpinski carpet (square)). Someone else I know got this: Be there or be a quadrilateral that can be inscribed in the inversion of a line not through the point of inversion and which subtends equal arcs in the inversion (cyclic quadrilateral with equal angles) There are probably more complicated ways of saying square, but as of not, I don't know of any. Goal is to make the most "insider talk" that only few people can understand. Any creative ideas?

It is (relatively) common knowledge that addition is not closed under irrational numbers: pi+(-pi)=0, pi and -pi are irrational, 0 is rational. However, suppose we are talking about the sum of roots of prime numbers. A proof that sqrt(p)+sqrt(q) where p and q is short: Assume sqrt(p)+sqrt(q) is rational, it can be expressed as a/b. Then p+q+2Sqrt(pq) is a^2/b^2, also rational. The (p+q) and the 2 are ignorable, and pq is not a perfect square, so sqrt(pq) is irrational. However, I don't know how such a proof would be done with say sqrt(2)+sqrt(3)+sqrt(5). Squaring this would give only more square roots. Using the fact that sqrt(2)+sqrt(3) is irrational doesn't seem to help either. It there a quick way of proving that the sum of roots of primes is irrational if not 0? Is there a counter example? Thank you!

PROBLEM OF THE WEEK http://www.math.purdue.edu/pow/Problem No. 14 (Fall 2009 Series)A set F is called countable if either F is finite or there is a one-to-onecorrespondence between the elements of F and the natural numbers.Two sets A and B are called almost-disjoint if A intersection B is finite. Prove or disprove: There are uncountably many pairwise almost-disjointsets of natural numbers (positive integers). In more formal language:Does there exist an uncountable set F such that each element of F is aset of natural numbers and each two elements of F are almost-disjoint?

Is there a solution for , I wonder...?!

Integral of [e^t/(e^(2t)+4)] How do I do this intgeral???

Is there a trick to factorising the quadratic: ax(to the power of four) + bx³ + cx² + dx + e My actual problem is: z^4 + 2z^3 - 4z^2 - 2z + 3. All help appreaciated! :)