Mathematics

In the set theory we have inductive sets which are those sets like \( A \) which \( \emptyset \in A\) and \( \forall a \in A (a^{+} \in A. \) and \( a^{+}= a \cup \{a\} \). Then we have the infinity axiom which says there exists an inductive set: \[ (\exist A) [\emptyset \in A \and (\forall a \in A) a^{+} \in A]. \] Now my question is how do we can conclude than infinity sets, specially those sets that are uncountable such as \( \mathbb{R} \) exists?

Took me long enough, but here is the definitive proof to the collatz conjecture. Anyone able to endorse me to publish on arxiv? Collatz V2.1.pdf

What are your methods to find that great math problem to invest your time to work on? Or any other project. I have my own methods but I want to hear others before I share my own.

Solve for x. I don't have the math background to solve for x. But if you put in N and p, you will see this simplified equation. I plugged it into Wolfram Alpha, but solving for x is still a challenge. x^2 + (2 x^5)/N^2 alternate form (x^2 * (N^2 + 2 * x^3) / N^2 Plug in the known value N. Still impossible to solve. But if you plug in both x and N it proves true. Do you believe me now?

If PQR are point such that the bearing of Q from P is 300° and the bearing of R from P is 120°. Find the bearing of Q from R

Hello to everyone, Is it possible to write a mathematical formula that will give us the size of an object at various distances? For example, let's say we have a large cube that is 60 feet in size, and we wanted to know how many feet the cube would appear to be when we looked at it at these distances: .5 of a mile 1 mile 2 miles Is there a formula that can accurately calculate what the size of the cube would be when looking at it at these distances? Thank you, Chris

Irrationality and logical paradox 1: Rational thinking and the self of rational thinking If and only if we know the definition of self in human thinking, can we know the structure of human thinking. I will start by discussing the basis of rational thinking-formal logic and use logical paradox as testing. There are three basic laws of formal logic. 1: The law of identity 2: The law of non-contradiction 3: The law of excluded middle The law of identity states that something is what it is. Expressed as symbols: A = A. The law of non-contradiction says that a …

Wikipedia starts with this definition - but that looks to me like it would define an oval shape, ie one that is symmetrical. Elsewhere I have encountered the same kind of definition - taking two pegs with a length of string longer than the distance between and scribing a line with a third peg whilst pulling the string taut makes an ellipse shape. To me this looks like it describes only very specific sort of ellipse and is not a universal description of all ellipses. Rather than a cross section through a cone shape, this looks to me like it describes a cross section through a round cylinder. Am I missing something obvious here?

The camera is always oriented in a way that lower border of HFOV (horizontal field of view) is aligned with bottom side of the object. Dimension of the object for reference camera tilt angle are given as well as contour area of this object on image plane. Parameters of camera (fields of view, focal length) are also known. Is it possible to calculate new changed contour area on image plane when camera tilt angle is changed (due to changing object distance or/and camera height)? I would be grateful if someone could point me to methods of calculations applicable here. I have found such method as camera transform using pinhole camera model to represent object…

I have a grid through upon which a circle is drawn, as shown below. Now, for every square in the grid through which the circle runs, i want to calculate the proportion of the square covered by the circle. So one of the squares close up: I thought this would be relatively straightforward but i've ended up with a horribly convoluted way involving working at some angles where the circle crosses the squares, using that to find the area of the circle, then subtracting that from the area of a rectangle that contains that circle segment, and so on for other squares. Only need to do this for three squares as symmetry saves me a lot of work, but it's s…

Hi all! This is not a homework question, just a silly thing I've been working on. I have a set of 11 random variables and one constant (that I don't know the value of). Every time I run an experiment all 11 variables assume a value of either 0 or 1 (all together). The question is simple: how to calculate the total number of experiments that I need to do in order for the average value of those 11 variables (from all experiments) to approach the mean of 0.5 to an accuracy of, let's say, 99.9%. After that I should be able to find out the value of my constant. Thanks for the help!

Suppose have arbitrary ellipse with center (x,y) and its radius (a,b) . I want obtain rectangle that sides tangent of peripheral ellipse. the below image describe issue .

I found a book (http://hades.mech.northwestern.edu/images/7/7f/MR.pdf#page=531&zoom=100,0,222 (page 517)) and there are some equations that bugs me. On pictures you can see that with equations from pictures 1 and 2 we can get equation on picture 4. How does that happen? I tried to solve it by myself but I got different first row in equation on picture 4. It will be much better if you show me how to get the last equation step by step. All Beta i equal to 0. l and w are shown in the picture 3 (those are lengths). wbz is an input variable, we doesnt need to know what it equals to for now.

hello I am interested in topology anlysis what requirements or knowledge do I have to learn topology anlysis thanks you verf much

I thought you guys might find this interesting. Adding Time to a 2D Prime Factor Harmonic Matrix to demonstrate the “behavior” of standing vs moving prime factor “waves” Previously I had introduced the Prime Factor Harmonic Matrix which showed that prime factors behaved like waves or specifically 1 dimensional waves that either behave like moving waves or standing harmonic waves within a 2 dimensional matrix of natural numbers. A PFHM is simply any matrix of natural numbers that is dimensioned according to a primorial. Paul Ikeda's answer to What’s the significance of prime numbers in physics and nature? Finding large Primes …

I found an article with some equations and got some questions whether some of those equations are correct or not. On the picture you can see that matrix Tpi is on the left side, while matrix TR is on the right. Aren't they supposed to be vice versa? Link to the article: https://research.ijcaonline.org/volume113/number3/pxc3901586.pdf

Continuity and uncountability Discussion about continuity of line, how continuity is related to uncountability and the continuum hypothesis. The real line is made of real numbers which are points. Points are discrete objects, but lines are continuous objects. How does continuity arise out of discreteness when points make line? The idea of uncountability solves this problem. Rational numbers are countable, the line they make contains holes. Real numbers are uncountable, the line they make is continuous. So, continuity must be created by the uncountability of the points of a continuous line. One can imagine that uncountable points are so numerous on the real line that real …

Ok, you are going to laugh at this one. But I am seriously asking this question. I need to think outside the box if I want to break a one-way-function. In this case outside the triangle. My question is: Why can’t I combine the Law of Sines and the property of similar triangles to solve 2 different similar triangles of different sizes? And secondly why can’t I say the proportions in one triangle are not proportional to the same proportion in a similar triangle? I mean if all sides and angles are known in one and the other similar triangle all the angles are known, there has to be a method to solve the segments of the unknown, second similar triangle…

Hi, I discovered reverse Fibonacci sequence. Can you comment me what you think and what math value have this discovery? The article is in attachment. Thanks. Reverse Fibonacci sequence Short - Ondrej Janicko.pdf

I have been tearing my hair out over this lol. I am trying to work my holiday (vacation) entitlement out. Can somebody please tell me if I am right? I get 27 days holiday plus the bank holidays (public holidays). My work year is 1st of April to 31st of March. Due to Easter moving about that means this year I get 7 days as bank holidays. In total this year I get 34 days holiday entitlement If I worked full time I would do 7.5 hours per day and work 5 days per week = 37.5 hours per week. 34 holidays days x 7.5 hours a day = 255 hours holiday entitlement. If I was full time every time I take holiday day I would lose …

Hello, there are two circles in nature a real circle well defined in mathematics. And an imaginary circle in our head that can not be defined.

i have a question for any maths wizz here. something from my real life. i have a toolbox with a padlock that opens via a 4-digit sequence. so, for example 8734. and the padlock opens. so when i lock the toolbox sometimes im a bit lazy and i just move the 4 slot around a bit, without touching the 873. one of the other guys reckons its easier for someone to work out the code to open the lock if i have only moved 1, instead of all 4 of them. is he right? or does the law of averages mean there are still the same chances someone will guess it regardless of how many or few i move.

I am trying to find the maximum and minimum peaks of a function which goes as: y=x1 cos(f1+ teta) + x2 cos(2*f1); The peak values are straightforward for cases where the frequencies are equal or when they are non-multiples. I am having trouble to quantify the maximum and minimum values of 'y'. Note: teta, x1 and x2 all these vary from time to time. I am therefore looking for a generalised expression (accuracy <5%). Thanks in advance.

So I was recently thinking about solar angles. A fairly straightforward, everyday example of solar angles. Or so you'd think. However, recently one thing came to mind. Suppose it was 6 hours before or after noon during a fall or spring equinox (for our purposes it wouldn't matter) at the equator. Since it was "halfway" between sun-over-the-horizon and sun-overhead, I presume the solar angle would be 45 degrees, right? Now suppose at the same time someone else was, let's say, at 45 degrees latitude; (north or south for our purposes wouldn't matter) at the same time. How would one determine, then, what the solar angle there would be? Is t…

If the radius unit vector is giving us some direction in spherical coordinates, why do we need the angle vectors or vice versa?