Mathematics

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]

If 50÷1 is 50 so 1 fits 50 times so I need to ask you how many times does 0 fit in 0 0 times right? So 0÷0=0?

Lotteries the in the land of the leprachaun. http://www.bbc.co.uk/news/world-europe-41549781

Ok, imagine you had an infinite deck of cards of random faces - one of those cards has a picture of you on it. The chances of course are absolutely ziltch of you ever picking out the right card - but suppose as a fluke, or miracle, you manage to pick the right card, we would say (?) the chances of you picking the right card was 1 in an infinity. Let's change the situation and the rules slightly. This time we have a second deck of cards as well as the first deck of cards. In the second deck of cards, you have an infinite amount of blank cards. In the first pack, still an infinite amount of faces. This time you are not looking for your face specific…

Hi, another question for you fine folks. Just getting into the use of sigma and that thing is super handy. And I know if I wanted to solve for say 1 through 10 I can just use i(i+1)/2. But what if the index number is greater than one? The equation doesn't work anymore. Is there a modification or different equasion to use? Thanks

So say we have one atom of Helium, and one atom of anti-Helium, when they come into contact the total energy produced should be equal to this (If I didn't fudge on the calculations which is why I'm asking this): where mH is moles Helium, mAH is moles Anti-Helium, mMH is the molar mass of Helium, and mMAH is the molar mass of Anti-Helium. I just was bored so I decided to try to come up with a formula for calculating the total energy of an atom, and I chose helium for whatever reason.

I am writing from turkey,. in assumption we hold PhD degree ,can we work at european countries or usa?

How much would time pass between watching the sun set from ground level and then watching it set again from the top of a sky scraper? I heard once that this could be done using one of the towers of the World Trade Center. So I assume one could also do this using the Sears / Willis Tower in Chicago. Someone also told me that the world's tallest tower in Dubai is so huge that the local weather broadcast tells of two times for sunset. One time is for the observed sunset at ground level and another time is for the observed sunset from the observation deck near to the top of the tower. unfortunately, I have recently gotten involved in a debate with someone who believ…

Paper: Author [Jordan Micah Bennett] (myself): advertising links removed by moderator ... I am new here. Please express your thoughts.

I have this hash function: hash = ((2860486313 * (3367900313 * x XOR 4093082899 * y)) RIGHTSHIFT 32) & 255 Anyone know if this will produce repeating sequences when the inputs are whole positive numbers starting at 0 and going up to 2^32? An example would be x and y starting at 0. X is incremented by 1 until x becomes 2^32, at this point x is reset to 0 and y is increased by 1. This is repeated until y is 2^32.

Circle is shared by infinite quantity of equal triangles. Sides a and b are radiuses of the circle. Side c is chord, At=1/4[(a+b+c)(-a+b+c)(a-b+c)(a+b-c)]1/2 At=1/4[(2r+c)(c)(c)(2r-c)]1/2 At=1/4[(4r2-c2)c2]1/2 At=1/4[4r2c2-c4]1/2 c=2Pi*r / infinity Ac= infinity*At Ac=(1/4)*infinity[4r24Pi2r2 / infinity2-16Pi4r4 / infinity4]1/2 Ac=1/4[16Pi2r4-16Pi4r4 / infinity2]1/2 Ac=Pi*r2 At is triangle area Acis circle area

Ladies and Gentlemen, good day, I have unraveled the pie mystery. We all know what pie is, the length of a circle. M=length of the circle K=2*Radius=Diameter M -- = pie K P = 3.145 + the rest Lets say R = 1 M = 3 + 0.145 If it were M = 3 It would make an even sided triangle. M = 3 + 0.1 + the rest "the rest" concides into a SINGLE dot. Of about 0.0456 So we have M = 3 + 0.1 + 0.456 If we fold out the circle and straighten it into a straight line we get --> ----- + ----- + ----- + - The total of which it comes means that the length of a circle is just a bit more than the total length o…