Mathematics

I sincerly wish to only hear out others opnions. I have no desire to re-hash old topics of mine. With the moderators approval I ask the following, with out any intention of further reply. Is there a diffrence between the space of Zero and the value of Zero?

I just need to get this stuff out of my head and this is probably a better place to do it than in(yet another) notebook. A + A' = B f(x) + r(x) = B f(x) != r(x) or f(x) = r(x) - Dependent on base and x. Mixed base series possible consisting of only palindromic numbers. ie. 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33... and no, I have no idea what use any of this would ever be. I keep thinking cryptography, but not sure how that would go. Is non-palindrome forming mixed base possible? Unknown at present.

this is a cool idea i found over at xkcd forums. for a number n, if n is composite, break it into its prime factors. if n is prime, place '<' '>' around the number and determine the n'th prime its is. then the first 20 numbers are... 1 <> 2 <<>> 3 <><> 4 <<<>>> 5 <><<>> 6 <<><>> 7 <><><> 8 <<>><<>> 9 <><<<>>> 10 <<<<>>>> 11 <><><<>> 12 <<><<>>> 13 <><<><>> 14 <<>><<<>>> 1…

I'm looking for an algorithm that can help identify abnormal trends in time-series metrics. The best I've been able to find so far is ARIMA (a completely new concept for me). We offer several services which we monitor active usage against, for any given time of day (typically updated once a minute). Here's a example of one of our services: What I'm interested in is gradual degradation that doesn't get noticed until ... well, it gets noticed. For example, if we zoom in to 12/6 we see: So what I'm specifically interested in here is the trend downward `@17:30~`. Likewise another good example would be: Here we can see the abnormalities on 12/1 and 12/4 during peak. Ar…

This article explains why the cardinality of a set must be either Aleph0 or |ℝ|. In "Cardinality of the set of binary-expressed real numbers" I have shown that binary numbers cannot fill the unit real interval in spite of infinity of digits. In general, the members of a discrete set can only occupy isolated points in a continuous space leaving empty intervals behind. So, the fundamental difference between a continuum and a discrete set is the continuity, not the number of elements. Continuity and discreteness are collectively exhaustive and mutually exclusive. The cardinality of discrete set is aleph0, that of cintinuous set is |ℝ|. Because a set must be continuous or d…

i have lot of doubts regarding polynomials and numerical method .. can someone help me understand some basics of it ... ? how do i dissassemble this sofa of polynomial properly ? and how does numerical method help ? can i have an example of a simple problem where i can utilize numerical method ???

Cardinality of the set of binary-expressed real numbers This article gives the cardinal number of the set of all binary numbers by counting its elements, analyses the consequences of the found value and discusses Cantor's diagonal argument, power set and the continuum hypothesis. 1. Counting the fractional binary numbers 2. Fractional binary numbers on the real line 3. Countability of BF 4. Set of all binary numbers, B 5. On Cantor's diagonal argument 6. On Cantor's theorem 7. On infinite digital expansion of irrational number 8. On the continuum hypothesis You can read the article in the pdf below or the link below Cardinality of the set…

for a dv volume cylinder we get dv=2*pi*r*dr*L but why to multiply this r with dr.please make it understand

I am a new member have a problem, the subject of which has interested me for years. The solution for a in the hyperbolic function (for a catenary) y = aCosh(x/a), sometimes with +c added as a 'curve shifter'. I have managed in the past by iterative trial and error if y & x are known, but very time consuming, ineligant, sometimes unsuccessful. The Casio calculator I use has a "solver", which is useful when it can find an answer, but often can't. I have a new all singing & dancing HP 50G with several solvers, which is far to complicated for me to use at all! The problem is me. I do not understand why sometimes a cannot be found? Surely every Cosh curve…

Hello! Well, It's another math question that I want to know the answer of. This is not homework, I just want to know how to solve this. Unfortunately I have no idea what to do so if you can solve this one for me I would really appreciate it because I just need to look at your equations to understand how to solve this, would be good if you wrote a few words aswell, as an explanation. Here it goes: Put together two parabola sections to a roller coaster with a steady shift in P. What are the equations of the parabolas. Just a tip; They are asking for the equations of the curves on the image, There are two curves that meet in the coordinate P Regards!

Can a point can exist in 0 dimensions and if so, does it mean it's wrong to say 0 dimensions is nothing. It seems logical to say nothing has no dimensions. But if a point can exist in 0D then is no dimensions the same thing. If we look at the geometric progressions from 3D to 0D, solid, sheet, line, point. Could we then say nothing has -1 dimensions. Why isn't the empty set included? Is the nomenclature of dimensions chosen for a mathematical reason. How would it alter maths if a point was said to exist in 1 dimension ie all dimensions were renamed as n+1? Doesn't it make more sense to say a point exists in 1 dimension, the first being existence, the secon…

I love science, and while I gather that I don't have to be better at math per se, as tough as it is for me, I would really like to be a dope mathematician. I'm pretty good at finding free educational materials including books online, if I'm understanding correctly if I want to brush up on my skills and really get a deeper understanding of mathematics I should revisit the basics first with arithmetic, algebra, and elementary geometry. After the basics I should go for some trigonometry and both integral and differential calculus. For my work with computers I should also revisit discreet mathematics. From there I won't be anywhere close to a master but I'll be in fit…

according to euler, the infinite series 1+2+3+4+5.... = -1/12. the "proof" is a bit complex, but basically revovles around letting the series 1-1+1-1+1-1 = 1/2 here's my problem with this. let S = 1 +1/2 +1/3 +1/4 +1/5 +1/6 ... multiply S by 2. 2*S = 2 +1 +2/3 +1/2 ++2/5 +1/3 ... subtract S 2*S -S = 2 + 2/3 +2/5 +2/7 +2/9 ... subtract S again 2*S -S -S = 1 +2/3 -1/2 +2/5 -1/3 +2/7 -1/4 +2/9 -1/5 0 = 1 +1/6 +1/15 +1//28 +1/45... which aproaches a finite value greater than 0.

I was reading a book on timeseries and all the obvious candidates were there but the fourier was briefly mentioned. Now i dont have a great deal of knowledge of calculus or geometry but i was just curious as to identifying the coefficients. I have what i think is the general formula but the guide i used starts using complex numbers as proof and seems to overcomplicate the equation. Apart from the coefficients do you think the transform would have use in a timeseries? I'm talking straight X and Y discrete data, from which there is no obvious or absolute "periods", although i would like to know if it could dissect that part for me. Regards,

Hello, I have been looking around lately for literature about a specific topic but have not found anything directly relevant to what I am looking for, so I was wondering if anyone had any "keywords" regarding this topic for me to try out. Basically if we have a polyhedron, and we were to join it to another polyhedron along an edge or face, does this change its euler characteristic? I would like to find some kind of proof that the euler characteristic stays the same no matter how many joined polyhedra you have, even with the joining possibly occuring sometimes between edges, other times between faces, maybe also between completely different polyhedra. Does anyone k…

If a two dimensional object that is 2 x 2 inches has four square inches and a 2 inch cube has 8 cubic inches how many would a four dimensional object that is 2 inches on each side hold? Would it be proper to assume it would have 16 cubic inches or would it contain another measurement like 16 tesseracts?

Hello, My knowledge of abstract algebra beyond linear vector spaces is very limited. My problem is inspired from the (not very well-known) triangular inequality between angles of a tetrahedron (see for example http://convexoptimization.com/wikimization/index.php/Fifth_Property_of_the_Euclidean_Metric): [latex] \left| \widehat{x,y}-\widehat{y,z} \right| \leq \widehat{x,z}\leq\widehat{x,y}+\widehat{y,z} [/latex] where x,y,z are three vectors and [latex]\widehat{x,y}[/latex] is the angle formed by the vectors x,y. I am looking for a way to abstract this into some algebra of vertices. Say a vertex is the tuple [x,y], we would need to define some "addition" opera…

Hi all, I am currently operating a piece of equipment that essentially collects particles and separates them based on their size. Essentially you have 8 stages, and each stage has a differing size of particles it collects. For example: Stage----Size of Particles (D) (um)-----Mass Collected (M) (mg) 1-------------0.1 - 0.2------------------------------1 2-------------0.2-0.5------------------------------0.1 3-------------0.5 - 1--------------------------------1 4-------------1 - 2----------------------------------0.5 5-------------2 - 4-----------------------------------1 6-------------4 - 5----------------------------------0.5 7-------------5 - 9------------------------…

Howdy all! I have yet another question, this time in the realm of mathematics. For a project I'm doing at work I need to create an optimal sampling method for a drill cone and so the basics of the problem are like this: We have 3 cones nesting inside one another or a cone with 3 "layers". They all have the same base angle [latex]\alpha[/latex] but different radii and heights. If we use V as the volume of the bottom cone, then middle cone is 2V and the outer (largest) cone is 9/4V. Based on this I need to calculate percentages of the total height of the entire cone for the following: h3 - from the top of the outer cone to the top of middle cone h2 - from the top o…

Hi. By its definition, the distance from a parabola to its focus and directrix are the same. Well, this is not a directrix as I knew; it is at the opposite side : Question is -- are the lengths of the paths Q1 - P1 - F and Q2 - P2 - F and Q3 - P3 - F The same ?

I make use of computer a LOT in my math studies. My PC helps me to reduce errors, research questions if I'm having difficulty, crunch numbers, create geometric figures, graph data and functions, and interact with a lot of smart, like-minded people like you. Anyway, can any of you think about the down-side of computers in math studies? Jagella

I wont pretent to fully understand the hpothesis itself because of lack of knowledge of complex numbers (though i have basic understanding of imaginary numbers i dont understand the "critical line" or why infinite 0's sit on it). However i grasp the concept of the zeta function and how generally exponents create a convergence. I specifically want to know how using the pattern 1-(1/2^s) + 1-(1/3^s) + 1-(1/5^s) + 1-(1/7^s) etc relates to the zeta function. The example i have doesnt clarify how the zeta function and this prime pattern relate exactly so any information would be gladly accepted. (Also any examples of complex numbers that sit on this critical line). …

On Fermat’s last theorem This theorem states that for any n except 2, the equation X^n+Y^n=Z^n is not true for any positive integer triplet X, Y and Z. Fermat’s “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” has fascinated mathematicians from 1637 but no one has found what his proof was. Let us try to understand this theorem better. Please read the article at On Fermat’s last theorem http://pengkuanonmaths.blogspot.com/2015/07/on-fermats-last-theorem.html or On Fermat’s last theorem https://www.academia.edu/13665056/On_Fermat_s_last_theorem

Hi, Hope this is in the right place, apologies if not. I've recently started a Maths & Physics Degree and am just about to embark on my first Maths module. I've been toying with the idea of getting myself a graphics tablet to use on my assignments alongside the Windows Maths Input Panel. I'm not planning on using it day to day as i find it easier to scribble with a pen and paper but thought it would save me quite a bit of time when writing up assessments etc. I just wondered if this is something any of you guys have experience of and if it was a viable idea. Additionally if you have used these before do you have any recommendations? Thanks in advance, …

I'm not sure I understand exactly the product in category theoretic terms. The book I'm using gives a very concrete example that is easy to understand. However, I'm not sure I get it generally. How does it work for the product of the reals? What's X in that case? What are f1 and f2?