Mathematics

Although the set of real numbers and the set of natural numbers each contain an infinite numbers of elements, the set of reals has a higher cardinality than the set naturals. Why is that?

I've been trying to figure this out for a while. In the F-Zero games the cars are able to travel over 1000 km/h, which would obviously end the race much faster if it was a real sport. The games only depict each race as lasting 3 laps, so obviously that wouldn't be a long enough race to satisfy the audience. Now, let's consider these factors: -Each car is driving at over 1000 km/h. -The track is at least 500 meters. -The race is 30 laps long. With those factors in mind, what total time would the race accumulate?

Suppose a>9 is odd and b is the cycle length of a as defined below. Then I conjecture that if (a - 1) / b = 2 ^ c for some positive integer c then a is prime. Cycle length: a is an odd number > 9 and Od is the odd part function, Sloane's A000265. Let a(0) = 1 and a(n) = Od(a(n-1) + a) for n > 0. If a(n) = 1 for 0 < n < N/2 - 1 then the cycle length is the smallest such n, otherwise it is a/2 - 1. For more information see A179382. Example: 11 = 5*2^1+1 11 (1,3, 7, 9, 5) 97 = 24*2^2+1 97 (1,49, 73, 85, 91, 47, 9, 53, 75, 43, 35, 33, 65, 81, 89, 93, 95, 3, 25, 61, 79, 11, 27, 31) if c = 1 that's OEIS A001122 if c = 2 that's OEIS A155072 if c = 3 …

hello everyone, this is my first post. I have decided to refresh my math, all by myself, following some old high school books. anyway I like to understand what I study, but with this example I have severe difficulties understanding it. I attempted solving the example without looking at it, but I failed miserably, entering in an endless loop of wrong assumptions, since this book seems to be written only as a textbook to be accompanied by live lessons, it lacks several explanations of what's being done, IMO. "in a class of 25 students, 7 students play basket, 13 play soccer, 9 none of the above. how many students play both basket and soccer?" the demonstration fol…

From the Wikipedia article on Pythagorean means, a geometric construction... where [math]a[/math] and [math]b[/math] are two numbers represented as line segments. Their arithmetic, geometric, harmonic, and quadratic means are shown expectedly. Now, the harmonic mean is a sector of the line segment from endpoints of A and G. What is the significance of that angle, i.e. is it a right angle? Because otherwise I can see H taking on any other value. Also, the Wikipedia article also gives the following properties for the Pythagorean means: [math]M(n,n,...,n)=n[/math] [math]M(bx_1,...,bx_n)=bM(x_1,...,x_n)[/math] [math]M(...,x_i,...,x_j,...)=M(...,x_j,...,…

Hey all, I'm working on a project right now and Im going to skip right to the point. I count occurrences for probabilistic training. Sometimes my program generates a string like this 'eres your stuff' Should I leave it the way it is, which is approximately 80% grammatical, or should I prettify it? Should I even waste my time on prettifying its output? Another question is this. If I make a variable for strength that counts every sequence of occurrences, certain sequences are going to emerge as more probable, namely, sequences of 1 or 2 occurrences. I don't want to arbitrarily assign a number, but I'm thinking that if I add one occurrence, the most probable one…

Let's say I want to group numbers between 1 and 50 with 4 columns: 1 2 3 4 1 2 3 5 1 2 3 6 ... 2 3 4 5 2 3 4 6 ... 47 48 49 50 To find the total possible combinations,we do: 50*49*48*47 __________ 1*2*3*4 This formula gives the maximum possible combinations. My question is,what would the formula be to find maximum of how many combinations of these numbers include number 1 and 2(for example)?

Hi!!! I need some help... I want to write a code in matlab for the backward euler method. How can I solve the equation to determine y^(n+1)??? Are newton's method, fixed point iteration, fsolve, fzero equal???

Hi all, thanks in advance for any help. This is the question: Solve the following recurrence relation by forward substitution and then verify the result by mathematical induction: T(n) = 2T(n/7) for n > 1, n is a power of 7 T(1) = 1 My answer: T(7) = 2T(7/7) = 2T(1) = 2 T(14) = 2T(14/7) = 2T(2) = 2^2 T(21) = 2T(21/7) = 2T(3) = 2^3 T(28) = 2T(28/7) = 2T(4) = 2^4 (I'm not sure if going up in 7's is correct) Solution for recurrence relation: T(n) = 2^log n T(1) = 2^log 1 = 2^0 = 1 T(2n) = 2T(2n/2) = 2T(n) = 2^1 x 2^log n = 2^ log 2n Check answer for T(14) = 2^2 2^log n = 2^log 14 = 2^7^2 (two to the power of 7 squared) = 2^7lo…

Richard Feynman on The Pleasure of Finding Things Out said something about how when he was tutoring his cousin about algebra and said that his cousin was to find the value of 'x'. Feynman went on to the answer and then his cousin said 'but you did it with arithmetic, you have to do it in algebra'. The following was then about how algebraic rules were invented so kids could pass a class even though they didn't know what they were doing and that it didn't matter how you got the answer so long as your answer is correct. My question is, apart from the 'traditional' rules of algebra, in what other ways could you 'do' algebra and also what did it mean when it was said that…

Hi, I am trying to apply Hidden Markov Model to improve my detection accuracy. In my program, there are two states, 1 and 0. I used Bayes detector to generate the probability for each instance to be in class 1 and 0. For example, I have a sequence Actual states: 1 1 1 1 0 0 0 0 probability in class 1: 0.5 0.6 0.7 0.8 0.9 0.2 0.3 0.4 0.5 0.5 probability in class 0: 0.2 0.3 0.4 0.5 0.5 0.5 0.6 0.7 0.8 0.9 I tried to "use probability in class 1" as the "seq" and "Actual states" as "states" in function hmmestimate ([estimateTR, estimateE] = hmmestimate(seq,states) But it seems that "seq" must be integers, and I do not understand what is the requirement for the inp…

Hello everyone, I want to make sure I understand the Cartesian product of two sets. Let A = {1, 2} B= {3, 4} Then A X B = {(1,3),(1,4),(2,3),(2,4)} Is that correct? Thanks

why pi is used in math?i mean why always 3.14....

Hi all, In my work we have to run tests whose input parameters are in 3 dimensions, forming lines across a grid, like so: What I want to know is, what is the best way of quantifying the spread of these lines? If I were to use the extreme points to plot a cuboid I think that would overestimate the parameter space over which the experiments were run. I have also considered calculating the convex hull, using the extremes but I feel this might also lead to the same problem, albeit with a smaller overestimation. I need to demonstrate that the lines are well spaced out from one another, perhaps by the angles between the lines. Is there already a way of quantify…

i got a question from a class teacher,nobody in the class or in the higher class can do it,because,number system is not in our syllabus.but i wanna know,let a=<3^n+2n+1>,where n can be any of positive numbers.the question is for which values of n;a can be a perfect square?oh,can anyone tell me about a book of number system where i can learn by ownself?

I'm doing work for math class (high school level), and we're currently on linear systems of equations. Simple linear systems like: ...as taken from my text. Some of several methods we're expected to use are elementary substitution and elimination (there are more efficient ways, but these are the focus for now). What's peculiar is that for some of the problems, it takes me 3 or 4 attempts to finally get a working answer when using these methods. I'm not sure why, but I often derive an answer which only solves one or two of the equations, rather than all the equations in the system. This is pretty strange, since whenever this happens, I can never pick out what I di…

I twist my outer Obloid shape 90 degrees, No matter how I think, including using logic and lateral thinking, I can not make my shape fit. I have come to you, the maths department of forum, for your help. NO ONE, seems to understand my lateral thinking.

Hello everyone, For as long as I have known about the constant [latex]e[/latex], I have been in awe of its many uses and at times strange properties. Now I know its definition as a limit and as a series, but I have never quite understood just what makes [latex]e[/latex] so special, beyond the fact that it helps us solve problems. So my question is: what makes [latex]e[/latex] so significant to the overall study of mathematics? I hope that makes sense. I look forward to others perspective on this. Thanks

If 1 dimension has length. 2 dimensions has area. 3 dimensions has volume. what does 4 dimensions have?

Dear all, I'm interested in learning more about the foundations of math. Any reading suggestions? Thanks, kmerfeld

I'm doing my thesis now about Knowledge Management (KM) readiness assessment in organization. I'm thinking to use fuzzy logic for doing the statistic, and my lecturer advised me to use Fuzzy Multi-Criteria Decision Making (FMCDM). By the way, my research steps are: arrange the questionnaire using Likert scale, then weighted it using FMCDM method. But even I've read many many papers about FMCDM, I still couldn't find and still stuck about how to weight the scaled questions using this method? I hope you all can help me to solve my problems.

Hello everyone, I want to prove that for postive integers x, y, y is not equal to x+y. I want to do this using the WOP. Here's what I have done so far: Suppose for some postive integer x, there exists a y st y y+x. By the WOP, there exists a smallest x0 st y=x0+y. Now I think I may have to apply the WOP again, but am not sure. Any advice? Thanks a lot, Kevin P.S. A little help using special BBC code. I'd like to use LaTex but when I try to do the not equal sign it shows up as: [latex]\ne [/latex] How do I get rid of the < br > ?

Just curious as to whether there is an exact formula to calculate pi using algebra.....Disregarding c/d or any approximation such as 22/7. Is there any relation to primes and while im asking is there any formula for finding an Nth term prime. I.E. a pattern showing where a prime will crop up. Im currently trying to formulate an equation that finds pi using only numbers 1-4. Where a = 1, b = 2, c = 3 and d = 4; something like; (d/c) * ((d/c) + (c/b) * ((d/c) / (c/b)))); Makes something within 2 decimal places, obviously this is just random and at some point must happen but im curious whether a formula along these lines already exist and can prove pi in purely …

The little I know about primes is that there is no any 'Systematic Formula' for obtaining prime numbers in either ascending or descending order.And the whole world is in a delima as wheter there is a limit to primes or NOT.That is whetther there is a HIGHEST PRIME NUMBER. I have Good, Better and Best formulae for generating Prime Numbers systematically. TRY THE GOOD ONE: P=7d-4 Where: P=prime number(Needed) d=odd number(Chosen) Example: At d=5, it means; P=7(5)-4=35-4=31 there are a few exceptions for the Good formula. Questions and contributions are welcome

On reading this exchange (part of a long thread on definition of religion) - something occurred to me. Do the rules governing regular 3-d solids change in non-euclidean space? http://en.wikipedia.org/wiki/Platonic_solid http://en.wikipedia.org/wiki/Archimedean_solid http://en.wikipedia.org/wiki/Euler_characteristic etc...