Mathematics

if this is true why we need any numbers beyond 0 and 1? Feels like different scaling of the natural numbers. What would be the difference between the infinite numbers between 0 and 1 or the infinite numbers between 0 and 1 000

This is a question to the mathematicians on the forum: when you're trying to solve an open problem in pure mathematics, what are the first things you do? Do you test the conjecture with a few example problems? Do you look up recent theorems related to the question, or do you just dive right in?

I've just begun the study probability and I have a very basic question. If I roll a fair dice I know I have a one in six chance of getting a "1". What is my chance of getting a "1" if I roll it twice? (It could be either on the first roll or the second roll or both. I am just concerned with getting a "1" at some point.) What is my chance of getting a "1" if I roll it ten times? (Same thing: I'm just concerned with getting a "1" (could be more than one "1") at some point.) I realize this may be too basic of a question for this forum, but I'm hoping someone will have the time to help me out with this really simple question. Thank you.

Hi All, votefavorite I am trying to measure a curved profile of a surface(2D) to determine the surface availability at different rate of testing. I have attached an image for a rough picture. Actually I have a reference geometry and performed two tests to determine the behavior. They two had different profiles at top portion. So I considered an axis for reference geometry and drew radial lines with 15deg angle difference each and marked those points as 1 (15 deg anticlockwise from vertical axis),2(30 deg anticlockwise from vertical axis),3,... and measured length of the radial …

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…

Are there any formulas for finding the LCM of at least 2 numbers? All I know is tedious methods which give you a long amount of time of computing (not always? If yes, then what is it? If no then is it still possibe that we can find a formula?

Suppose you determine a point as the centroid for a single variable function is there a method to verify that the point is indeed the centroid?

In another thread on this subject it was stated that “we can establish a one-to-one mapping between any Rm and any Rn.” There is a relationship that occurs in R3 that I believe cannot be mapped to R2. The relationship exists between the sphere center and the surface curvature. I believe that because R2 has no third orthogonal plane or axis that this relationship does not exist in R2. This is best described as a relationship that exists between the tangent to a small circle on the surface of a ball and the gross position of the ball in 3-space. The illustrations show how this relationship can be seen. Mathematically, it is expressed as an identity…

I have a scenario that im trying to quantify, and wondering if there is a scientific/mathematical way of approaching it. Scenario: Under the previous process when purchasing goods for the values of $0 to $2,000 we were required to obtain one verbal quote. Now under the new process when we purchase goods for the same values we are required to obtain two verbal quotes. Example: Under the previous process one quote was obtained for $1,200, under the new process two quotes were obtained for $1200 and $980 Is there any way to quantify the benefit to the organization by following this new process. As under the previous process it would have cost $1,200 but by se…

In every R there exists an integer zero element ( -0 ) ( -0 ) =/= 0 |0| = |-0| ( -0 ) : possesses the additive identity property ( -0 ) : does not possess the multiplication property of 0 ( -0 ) : possesses the multiplicative identity property of 1 The zero elements ( 0 ) and ( -0 ) in an expression of division can only exist as: (0)/( -0 ) 0 + ( -0 ) = 0 = ( -0 ) + 0 ( -0 ) + ( -0 ) = 0 1 + ( -0 ) = 1 = ( -0 ) + 1 0 * ( -0 ) = 0 = ( -0 ) * 0 1 * ( -0 ) = 1 = ( -0 ) * 1 n * ( -0 ) = n = ( -0 ) * n Therefore, the zero element ( -0 ) is by definition also the multiplicative inverse of…

When calculating the circumference of a circle, we use 2πr. Since π is an irrational number, then for a unit circle, for example, the circumference must be an irrational length. However, the meter was origionally based on being one billionth the distance between the N. Pole and the Equator thus making the circumference of the Earth an integer in terms of meters. The meter was later changed to be based on the speed of light to again force the value of c in a vacuum to be an integer in meters/second despite an uncertainty of 4 parts in a billion. i.e. the uncertainty then becomes the length of the meter. It is the relationship of the speed of light to the cir…

I have gotten several different and conflicting definitions from teachers over the past few years. One teacher described a graph with a decreasing y-axis value and increasing x-axis value as an indirect relationship, wihle another teacher calls this inverse relationship. What's the difference, what the correct relationship, what do the graphs look like?

Hello, I hope someone of you knows the label propagation algorithm? It is used on networks /graphs to find clusters/communities. In the first step, every node in the graph gets a unique label. In the next step, the labels of the nodes are replaced by a label that most of its neighbors have. The algorithms is described in https://arxiv.org/pdf/0709.2938.pdf on page 5. I wonder if it works only on undirected graphs or even directed graphs. If it also works on directed graphs, when is one node a neighbor of another? In other words, if two nodes A and B are connected by a directed edge A --> B, which node is neighbor of which? Is only node B a neighbor…

We wonder the primality of prime numbers and why they are located in specific locations. I discovered a way of why this is the way it is. Primes and their locations are cause by this multiplicative-odd-number series process: First the odd numer 3 is multiplied to itself and above 3 odds: 3*3=9 3*5=15 3*7=21 3*9=27 and so on... Second the next odd of 3 which is 5:(same process like above) 5*5=25 5*7=35 5*9=45 5*11=55 and so on Third, fouth and so on.This process will continue unto infinity. let's find out using the above process why 2,3,5,7 are primes below 10. 3*3= 9 5*5=25 here, the…

Hello everyone, Im new in this forum and in advance I would like to apologise for possibly posting this thread in a wrong place. I am learning mathematics and I came across this problem that I can't find a solution for: x^2 - 4^2 = 1000000 , find all possible integer solutions for x and y. Being an amateur mathematician I tried to understand this problem using system of equations technique and instead of million i used a prime number (5) as an anwser and turned this equation into difference of squares: (x+2y)(x-2y) = 5; 5 is prime, has two divisors -> 5, 1; (x+2y) = 5 (x-2y) = 1 2y - 2y = 0 (y is out) 2x = 6 x = 3…

The collatz conjecture If for any given positive integer n, a series is created such that: If the number is even, divide it by two. If the number is odd, triple it and add one. Then the Collatz Conjecture states that if the operation repeats often enough, the resulting series of integers created will always converge to 1 regardless of the size of n. Proof: If you tripple any odd number and add one the result will always be an even number. If you divide any even number by two, then half of the results will be odd while the other half will be even. Since every odd number will be changed to an even number by 3n+1 then we know a di…

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…

No number tables...no properties. No axioms change (except) when involving zero. The following projection operators allow for no further axioms...... [math]0 = \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) [/math] 0.z1 = 0 0.z2 = 1 [math] P_1 0 = (1, 0) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 1 \cdot 0.z_1 + 0 \cdot 0.z_2 = 0.z_1[/math] [math] P_2 0 = (0, 1) ~ \left ( \begin{matrix} 0.z_1 \\ 0.z_2 \end{matrix} \right ) = 0 \cdot 0.z_1 + 1 \cdot 0z_2 = 0.z_2[/math] The distributive property (all combinations of a, b, and c as zero) a * (b + c) = a *…

Axiom Let every number be arbitrarily composed of two numbers. Let the number table exist as such… 0=(0,1) 1=(1,1) 2=(2,2) 3=(3,3) 4=(4,4)…and so on Let no "ordered pair" be represented by another "further" ordered pair. Let the first number of the number chosen be labeled as z1 Let the second number of the number chosen be labeled as z2 Let multiplication exist as follows… (A x B) = ( z1forA x z2forB ) = ( z2forA x z1forB ) = ( z1forB x z2forA ) = ( z2forB x z1forA ) Let division exist as follows… (A/B) = ( z1forA/z2forB ) (B/A) = ( z1forB/z2forA )

From Wikipedia: The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science. An Origional Solution: copyright: October 19, 2017 Author: Paul Ikeda Version: V3.0.0.0 Any thoughts or quesrions?

As we all know, there exist many arguments that 0.999...=1. All of the proofs I have seen are based upon arguments drawn from mid-level mathematics. As a philosopher, this bothers me because, when proofs of a basic-level proposition depend upon mid-level arguments, there is the obvious danger that these arguments, if analysed and deconstructed in sufficient detail, will be found to be question-begging; that's to say, at some point, we may find that they have assumed the conclusion as a premise. So my question is: is there any way by which we can mount an argument that 0.999...=1 by arguing "upwards" from the axioms and definitions of arithmetic, rather than "…

This is a clear explanation w.r.t. the "Trigonometric Rule Collapser Set", that may perhaps be helpful. (See source) The above is not to be confused for u-substitution. (See why) In the sequence: x = sin t, where dx = cost dt, and 1 − x2 = 1 − sin2 t = cos2 t ....(from problem: ∫ √1- x2) ..the novel formulation dx | dt · dx occurs such that the default way of working trigonometric equations is compressed, permitting the reduction of the cardinality of steps normally employable. For example, in the video above, while evaluating ∫ √1- x2 dx, in a preliminary step, the instructor writes ∫ (√1-sin2θ/(√cos2θ) ) · cosθdθ. Using my trig collap…

Postulates 3 = ( ( 1,1,1) “placed into” (_,_,_) )= (1,1,1) 2 = ( (1,1) ) “placed into” (_,_) )= (1,1) 1 = ( (1) ) “placed into” (_) ) = (1) 0 = ( (0) “placed into” (_) ) = (0) So that ( 3 x 2 ) is… Either (1,1,1) or (_,_,_) for 3 And Either (1,1) or (_,_) for 2 (but NOT both for each, and only the opposite of each, in any binary expression) Then…. (1,1,1) placed into (_,_) then added Or (1,1) placed into (_,_,_) then added So that in binary operation by 0 ( 2 x 0 )…is (1,1) placed into (_) then added Or (0) Placed …

Super numbers are beyond all regular numeric potential. Regular numeric potential is the all finite and infinite set. 1 super number is 1 regular numeric potential, it is that which includes the more and more level of all infinite numbers. Super numbers contain opposite potential, which can open up imaginary numbers like they are real, and close prime numbers like they are not. At imaginary number linkages there is ultra super number definition of change. At prime linkages there is there is ultimate super number definition of value.

An interesting formula to brighten your weekend for all those who periodically post strange threads about pi and all things circular. What is the following limit? [math]\mathop {\lim }\limits_{k \to \infty } \pi k\left( {\exp \left( {\frac{r}{k}} \right) - \exp \left( {\frac{{ - r}}{k}} \right)} \right)[/math]