Mathematics

After a recent update to our forum software, typesetting equations on SFN has changed a little bit. Although we are still using LaTeX, for a variety of reasons, we've elected to shift over from our custom-written LaTeX generator to the excellent MathJax library, which will take your equations from post text and render them in your browser. Much as before, the idea is that in your post, you surround equations with special characters, and MathJax will convert the contained text into an equation for you. There's two types of equation that you can typeset: Inline math is displayed in the flow of a sentence, such as \( y= x^2 \). This example was produced by using …

Every other section has one... this one should too (If it has I can't find it sorry). So I'll start off: 1) http://linuxfreak87.googlepages.com/ 1) Covers a lot of stuff, Maths and some physics. 2) http://mathworld.wolfram.com/ 2) Amazing maths resource, lot of advanced stuff. 3) http://www.purplemath.com/ 3) Basic and advanced maths here. Good tutorials. 4) http://www.dansmath.com/ 4) Again more good tutorias and weekly challanges. 5) http://mathforum.org/dr.math/ 5) LOTS of question solutions here, examples too. This one has helped me a lot in the past and still does 6) http://www.ics.uci.edu/~eppstein/junkyard/ 6) Lots of fun geometry…

Forum Rules Okay, so the "old" forum rules was becoming a little old, so I've re-written them. Please, please, please put your mathematics where it should go. For example, anything to do with Calculus or Analysis should go in that forum. Applied Mathematics includes statistics and simple mechanics. Refrain from posting non-mathematical material on these sub-fora; there's loads of other fora on here for various topics in science. Always try to use the correct and proper mathematical notation; we implement a LaTeX system here, and it would be great if people would use it to its full potential. We encourage people to post their problems here; however, if it …

Real numbers can be constructed directly from integers, without a construction of rationals.

Given natural numbers [math]\mathcal{N}=\left\{0, 1, 2, ... \right\}[/math], Why do they identify [math]x \in \mathcal{N}[/math] with [math]\left\langle 0,y \right\rangle[/math] rather than [math]\left\langle x, 0 \right\rangle[/math]? Does it matter? If yes, how / when?

Consider these definitions: I think, there is a mistake in this definition of well-ordering which makes the latter impossible. Am I right?

There is a theorem in logic that says that given a countable formal language, any consistent formal theory in this language has a countable model. What is paradoxical about this statement? For example, the language of the axioms of Zermelo-Fraenkel Set Theory ZFC only consists of the membership relation ∈. Hence, if ZFC is consistent, it has a countable model. However, it is easy to prove from the axiom system ZFC that there exist uncountable sets. How is it not a contradiction?

There are two beautiful proofs for the above, but I have also a semi-intuitive "explanation" for it: We learned that multiplying n by m is adding n to itself m times. The problem here is that the notion of m times implicitly refers to multiplication. IOW, such a definition is circular. OTOH, when we already have a multiplication defined in the system, defining power, or exponentiation, as multiplying n by itself m times, is not a problem.

Let A be a set with elements {a, b, c, ...}. With these elements we can make sets of pairs, e.g., {a, b}, {a, c}, {b, c}, ... These pairs are not ordered, i.e., {a, b} = {b, a}, because by definition sets which have all the same elements are equal. How can we make ordered pairs, say <a, b>, such that <a, b> ≠ <b, a>?

Hi all. What are the units; is 1 gram times 300,000 Km/s doing joules ? Is it tonnes and metres/second doing watts.hour ? Do not come up with ounces, inches and BTUs, please 🙄 The formula has been everywhere with no grasp of sensing the magnitudes. Light for one gram of mass please ?

I believe I have discovered a new way to graph an ellipse.

I was looking at the 6x-+1 thread and I agree with Studiot that he still needs a test for Primes to simplify the computation. I was unaware of the 6x+-1 and I don’t want to hijack his thread. But to test for Primility could you multiply the number in question by any known Prime number and see if the product is only divisible by those numbers? I mean you already know the Prime factor you used. If in doubt test with another known Prime. If 6x+1 describes all Prime numbers, it is not a sieve you need but a test for Prime numbers to complete the computation problem. I know it sounds too simplistic. But has anyone heard of it before? If I am wrong just ignore. I just didn’t w…

Stillwell's "Reverse Mathematics" says on p.41, Unfortunately, there is no example of such model. Does anybody know such? For the reference, here are the axioms 1-4:

A few days ago I solved a challenge I had made myself, and think the division is neat, with a lot of nice symmetries and such, but several searches on the web and I have not found its name, or a breakdown of it, to study the angles and descriptions and such. So I am presenting it here, in the hopes that someone will recognize it, and point me to a link with its description. Its made of clay and was done by eye with pen and steak knife, so its not exact, but it works. What is this division called? Regards, TAR

I find Pi very interesting and mysterious. It goes like 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679...................................................................... to infinity. Pi is an irrational number, meaning it has an infinite, non-repeating decimal expansion. Fun fact is that it contains our Contact number,Passwords,Date Of Birth etc somewhere in those numbers. It also comes in many equations of physics. Everything is mostly spherical in our universe due to gravity. So pi is everywhere as pi is used in calculations involving spheres. I also saw a theory in speculations which is now locked,it was bui…

The fundamental operating principle for all standard isolation transformers remains electromagnetic induction (Faraday's Law). There are no widely used "alternative operating principles" for isolation transformers. This setup is not used for transferring AC power. But, by changing principles of operation, the math changes based on the data. This is the normal setup for an Isolation transformer. But, when you make one change to the core setup, like this. All the mathematical data changes. I can’t find any math for these changes. So I’m looking for someone who may be willing to help, a Mathematician. To keep things simple for now, think of an ideal model, no resistance …

Inverse power expansion of any number ! I give below the expansion of any number x which can be Natural Real or Complex as : 1 - (1/(x+1)^n) = (x/(x+1)) + (x/(x+1)^2) + (x/(x+1)^3) + ,,,,,, + (x/(x+1)^n) Where n is any Positive integer Or 1 = (x/(x+1)) + (x/(x+1)^2) + (x/(x+1)^3) + ,,,,,, + (x/(x+1)^n) + (1/(x+1)^n)

ok, I sent my documents to many publishing's and many places to get it either verified by peers or published by someone that counts in regard to CMI's (Clay Mathematics Institute) standards. The only thing I have had success at is being dismissed or told we cannot at this time determine a good enough understanding of your submitted document to warrant its publishing in our journal. AM I CORRECT, or is gatekeeping really this bad people cannot do math or follow my given steps to see if it works? 1.pdf _1_by_Branden_Lee_Friend.pdf P.S. RH and GRH I have solutions for both- Here is my main problem = I cannot get it compiled properly. rather is a pain and makes my work lac…

There is this legendary https://en.wikipedia.org/wiki/Collatz_conjecture even getting Veritasium video "The Simplest Math Problem No One Can Solve": that using rule "divide x by 2 if even, take 3x+1 otherwise" at least experimentally from any natural number there is reached 1 - any thoughts? It seems natural to try to look at evolution of x in numeral systems: base-2 is natural for x->x/2 rule (left column), but base-3 does not look natural for x->3x+1 rule (central column). However, rANS ( https://en.wikipedia.org/wiki/Asymmetric_numeral_systems ) gluing 0 and 2 digits of base-3 (removing 1 bit of information) looks quite natural (right column) - maybe some rule co…

This is disorganized. But I thought it had potential. Can you take the slope of a point and the start of the graph and the slope at the end of the graph and combine it with an approach similar to Newton's Method, to determine where a given value occurs? I know it sounds stupid, but I am serious. I haven't had a calculus course in 20 years. But if you look at the picture (which is also messy), it just might give you some ideas. The problem starts out to find a limit. On a graph the limit of the relative minimum is the desired value. Limit notation finds a limit 0 (zero) when x equals a known value. But it would be more useful to find the value of x when the limit equals…

I have not been following developments in this area, so I’m wondering, what AI’s that are specifically designed for symbolic maths (other than Wolfram Alpha) are freely available (ie no payments) out there?

Does someone know this? While I was making a small study on circle packing recently, I came across this problem that left me scratching my brains. I found this problem interesting and wanted to share. It goes something like this: Q) We want to reduce the size of circles and as we do so, fill them up into a different and bigger circle as much as possible (maximum). As the radius of the small circles approaches to zero and fills up the mother circle, 1.Does the packing density approaches to 1 (filling up the entire mother circle)? OR 2.Does the packing density approaches to that of the hexagonal lattice arrangement (i.e. 0.906...) and therefore not filling up the entire mot…

I have developed a new way to understand the behavior of numbers under the Collatz Conjecture. My approach involves classifying numbers into three distinct groups based on their behavior during the Collatz sequence, and I propose that all natural numbers eventually reach the first group, leading to 1. Here is a breakdown of the three groups: Group A: This consists of even numbers that, when divided by 2, always result in 1. These numbers are powers of two (e.g., 2, 4, 8, 16, ...). When repeatedly divided by 2, they eventually reach 1. Group B: This group consists of even numbers that, when divided by 2, result in an odd number. These numbers are reduced to odd numbers and…

Hello. I study quite wide and have had a bunch of opinions on 'false mathematics' and it's prevalence in science and everyday people. I spent time after years thinking and studying wondering how to practically respond and handle approaching 'real' maths when I got to put ideas into chatgpt. I want to place this on this thread to get constructive feedback and I ask bare minimum read the first page and the last article, addendum, to understand why it can help. I believe it quite conclusive for practical application. It is meant to be by design practical and highly useful so. Forgive me for uploading a mentioned chatgpt prime 'original' so to call 'alpha'.

Hello, my name is Phil, and I'm currently working on a robotic arm for a school project. The goal is to draw a circle on paper. My arm is a 3-axis arm with control on a 3D scale. For coding, I need to find the exact distance from the ground to Point C (the tip of the pen) and the 2D coordinates X,Y of Point C. To draw a circle, I also need to find the angles a and B of the robot motor using only the CS, D, Sol and X, Y values. Please help! The image describes the rest. Note that there may be errors in the formulas shown in the image. Make sure to tell me if you find any. Thank you!