Mathematics

As an addition to all current field axioms. "For every A in S there exists a z1 and a z2 constituting A. Such that any A in operation of a binary expression of mulitpilcation or divison is only representing z1 or z2. Such that z1 and z2 for all A's other than zero equal A. Such that z1 for zero equals zero. Such that z2 for zero equals 1. "

I am getting on in years and since retirement I have been giving Fermat's Last Theorem some thought. I believe most people are attempting to solve this puzzle in the wrong way. There may be NO good reason why (say) A^3 + B^3 = c^3 should not have a whole number solution. However there is a very simple reason why the relevant "wrong sum" A+B=C cannot logically be deduced. Please note, I am not saying it cannot exist - only that there is a simple reason that it cannot be deduced. The reason applies to all powers>2. Perhaps this was Fermat's starting point!? I should be interested if this thought gets any response. More later - perhaps a conjecture if not quite a…

Complet text of the proof All wholes numbers in the next are given in the prime base [math]n[/math]. Here are the known positions, repeatedly discussed on the mathematical forums. Thus, let (1°) [math]A^n+B^n = C^n[/math], where prime [math]n > 2[/math] and [math]A, B, C[/math] have no common factors. Let for the moment the number [math]ABC[/math] is not divided by [math]n[/math]. Then: (2°) [math]C^n-B^n=(C-B)P[/math], where [math]C-B=a'^n, P=a''^n[/math], [math]C^n-A^n=(C-A)Q[/math], where [math]C-A=b'^n, Q=b''^n[/math], [math]A^n+B^n=(A+B)R[/math], where [math]A+B=c'^n, R=c''^n[/math], [this follows from the simple lemma: if the numbers […

If we assume that (-1) (-1)=-1 and (-2)(-2)=-4 but know that (0) (0)=0 Then (1+-1) (1+-1) must equal 1-1-1-1 =-3 and not the sum of (0) (0) which it should equal 0 unless we have assumed otherwise but have not. Likewise (-1+2) (-1+2) =(-1)(-1) must equal -1+-2+-2+4=-7 and not the product of (-1+2) (-1+2)=(-1)(-1) which should equal -1, which is inconsistent and does not equal -7 if we assume that (-1)(-1)=-1. But if we assume that (-1)(-1)= 1 then (1+-2)(1+-2) should equal 1+-2+-2+4=1 likewise (1+-1)(1+-1)=(0) (0)=1-1-1+1=0 which it does

Is the quantity 1/infinity undefined? I mean the probability of selecting a number from the infinite series of whole numbers? Is it undefined?

Title says it all. I've been challenged by my teacher to do this. I am currently doing it out by hand, it it is extremely tedious and annoying. Are there other more efficient ways to do this? Thanks in advance. (P.S. I know I can put it into wolfram, I do have the answer. I just need to figure it out by hand)

Hi, I am a senior in High school. In only 4 months I have managed to self teach (from paperback books, PDF files and online courses uploaded to various platforms such as youtube)the following during my free time: Calculus 1,2,3, Differential Equations Linear Algebra Abstract Algebra Discrete Mathematics Analysis 1,2 Calculus of Variations (Optimization Calculus) Elementary Number theory Concise Introduction to Mathematical Logic It is clear to me that I am gifted. I can only imagine once I dedicate myself full time to the study of math. I am not clear what exactly to study. I am interested in Complexity Theory, Number Theory and Artificial Intelligence. I…

I never studied the curve algorithms; I just use 'em. So I really have no idea how to answer this question. Once again working in SVG. When using the cubic Bézier curve commands, I want to find out the coordinates of the actual peaks. For instance, c 3.75,20.0 5.00,-20.00 8.75,0.00 approximates (!) a one-cycle sine curve. I want to be able to figure out the curve's minimum and maximum (y-axis) values. How can I do this? Thanks!

If numbers have a beginning witch is one they necessarily have an ending If they don't ..... Is the problem in the way we address or write numbers ? Let say numbers are a circle 1 is a rayon in a circle 2 is a diameter 3 is 3 rayon dividing the circle in equal surfaces 4 is 4 rayon ..... etc In the end we are going to draw a disk But when? When are the surfaces between rayons are going to be equal to 0? One day for sure Conclusion : Infinity doesn't exist and numbers begin with 0 which is a centre in the circle And the infinity? well its calculable but how much exacly? Is it Allah (1665) that the Muslims..etc worship? And what is the obvious way to get…

Hello everyone I was wondering if there was a general formula (sum, product, ...) to define the n-th derivative of the m-th power of a function f(x) So far, I've found that for [math]n[/math] up to 3, the following should be right (if I made no mistakes): [math]\frac{d^{n}\left[f(x)\right]^m}{dx^n}=\frac{d^{n}f}{dx^n}m\left[f(x)\right]^{m-1}+\left(\frac{df}{dx}\right)^n\left[f(x)\right]^{m-n}\cdot\prod_{i=0}^{m-1}{(m-i)}+n\left[f(x)\right]^{m-n+1}\cdot\prod_{i=1}^{m-1}{\frac{d^{i}f}{dx^i}}\cdot\prod_{i=0}^{m-2}{(m-i)}[/math] Can anyone tell me if it's even possible to make such formula, and if yes, what that formula is exactly? Thanks. Function

Hey guys, tis my first entry so apologies if I seem a little nervous! My friend and I were having a healthy debate on rather silly physics theories as we do. My friend then suggested the existance of irrational dimensions. This seemed far more silly than any other but i found some proof off a website i cant remeber the address of. I would like to open this thought up to debate - irrational dimensions or at least non-integer dimensions (like 4.3rd dimension or the e'th dimension) Thanks all!! Perry.

I have been playing about with primes, But this is not a prime question, I was looking at the difference between each prime, Then the difference between that difference until I reached 1, To look for patterns. I was wondering what it is called when you take a certain amount of numbers has shown below and find the difference between the difference until you end with 1? (1 is the point of triangle). I have tried to look it up but end up with differences between everything but what I want to know, There is most probably a simple name but it escapes me at the moment. Each difference of the same number is the same colour,0 pink,1 purple, 2 blue, 4 yellow.

Hi everyone! Lately at school we've been dealing with logarithmic inequations and they seem pretty tricky. So I was wondering if anyone could add a link or just post some useful hints that would help solving these inequations. I'd appreciate any kind of help!

Is it at all possible to have the number 0.0(reoccuring)1? or for that matter any other number at the end? my idea is that the number is 0.0 with an uneding string of 0s on the end, but if it did have an end, it would end in 1. Is this possible?

Hey all, I read this article on the Riemann hypothesis: http://plus.maths.org/content/music-primes It's the first article I've read so far that actually showed me the implications the Riemann hypothesis has on prime's. Unfortunately, after reading the article I googled "Riemann harmonics" and didn't find anything. I'm not that surprised that they made the name up and I would like to read more about them; what are they called? Thanks.

In another thread, I asked how would you locate the center of a given circle, using only a compass and straightedge, and I got absolutely wonderful answers. During that thread, many solutions involved already knowing how to construct a tangent line to one of the points on the circumference of the given circle. I must confess, I don't know how to do it. So here is a related question. Using only a compass, and a straightedge, how do you construct a line which is tangent to a given circle, at a given point on the circumference? Regards

This thread concerns attempts to construct artificial general intelligence, which I often underline may likely be mankind's last invention.I am asking anybody that knows supermathematics and machine learning to pitch in the discussion below.PART ABack in 2016, I read somewhere that babies know some physics intuitively. Also, it is empirically observable that babies use that intuition to develop abstractions of knowledge, in a reinforcement learning like manner.PART BNow, I knew beforehand of two types of major deep learning models, that:(1) used reinforcement learning. (Deepmind Atari q)(2) learn laws of physics. (Uetorch)However:(a) Object detectors like (2) use somethin…

Is the fact that a Minus x Minus = Positive an axiom or is there a [simple] mathematical proof?

Numerical Noise Generator Based on Real-World Noise Simulation The goal: Create a model for Serial\Parallel Noise Generator that can be considered as a Random Number Generator, meant for the impossibility of the analysis, by using hidden variables in Chaos theory ... The idea: if group of n members have random speeches at random times a receiver from a distance can only hear noise ! I have made a new way to create probabilistic hidden variables by simply Independent Random Intersection Between Independent Systems ... note: this model is abstract, can be implemented in different ways, The papers are in the Attachments ... NNGBRWNS.pdf

is there such a definition in the content of integral account/calculation courses or in the content of calculus? I remember something like this: [math] \int^{v(x)}_{y=u(x)} f(x,y)dy [/math] if in this integral [math]f(x,y)[/math] function ( [math] \alpha \leq x \leq \beta [/math] and [math] a \leq y \leq b [/math] ) is derivable in the D region that characterized with the given inequalites in the paranthesis,then this region would be called as "regular region" but I am not sure about the exact definition could someone provide some more context about regular region (if possible)? thanks

While trying to sleep last night I discovered a new triangle. I call it the Piangle. What's a Piangle? Maybe this will make it clear. The Piangle is an unraveled circle. Imagine cutting a radius, then draw some inner circles. Next unroll each outline to the right. This is a right triangle, so by the Pythagorean theorem the length of the hypotenuse is , which is or . The Piangle is not distorted, it's just an unrolled circle. It even has the same area as its corresponding circle. Its area is 1/2*b*h = = . Proof that I discovered this: the hypotenuse = ≈ 6.3…

Imagine that you are given a smooth space of unknown geometry. What kind of constructions would you use to figure out the number of dimensions of this space?

This is absolutely brilliant. I have a book at home that is filled with little mental tricks on how to do math quickly in your brain, including the "pneumonic" method; some of the tricks are laughably easy (but impressive to those who are unsuspecting) and some take a LOT of practice. I am not even remotely close to anything even SIMILAR to what this guy does. It's absolutely amazing! I figured you guys would enjoy it too. Since I know the book tricks in general (again, it's far from easy and I'm not really anywhere close to this level) I kinda looked for where he's stalling while he's calculating and where he uses humor to hide his mental tricks --- even…

i can't quite work this one out... i think the first step is to say that we want to find complex root of this: z^{n} = a but yeah...i dunno...can someone give me a few pointers please Sarah

Hi! According to this site http://www.intmath.com/applications-integration/11-arc-length-curve.php the arc length of the curve y = f(x) from x=a to x=b is given by: length_ab = Derivative_ab( Sqrt ( 1 + (dy/dx) ^ 2 ) dx) So, we got a sine wave function which is y = A * sin (F * x + P) from x=a to x=b the length of this is length_sine = Derivative_ab( Sqrt ( 1 + (A * F * cos (F * x)^2 dx) Example of this is in first link or here: http://www.wolframalpha.com/input/?i=tell+me+the+arc+length+of+y+%3D+1.35*sin%280.589x%29+from+x+%3D+0+to+10.67 Now, my question is what is the algorithm to compute length for specified x=a to x=b. For example, l…