Analysis and Calculus

Given 0<a<π/2 , b>0 find a c>0 such that : for all ,x : if 0<x<π/2 and |x-a|<c ,then |((sqrt sinx) +1)^2-((sqrt sin a) +1)^2|<b

Hi, I read an article about infinities, and as always, I don't get it. The writer says : "℘(ℕ)" and "ℕ" are not in bijection.. but, it seems easy to me to create a bijection : You take the binary writing of a number, and you take the rank integer that correspond to each 1 0 <=> {} 1 <=> {0} 2 <=> {1 } 3 <=> {0 ; 1 } 4 <=> { 2 } ... 259 <=> { 0; 1 ; 8 } .. etc and so on you have an integer for each set of integer and vice-versa, isn't it a bijection ? So what did I got wrong ?

I ran into a coin flip problem where flipping 4 coins has a 6/16 or 3/8 probability of landing 2 heads and 2 tails. I expected this value to be 1/2, because you have a 50% chance of getting heads or tails. Then that is only 6 of the possible 16 outcomes, instead of 8. Then I realized that the number of possible outcomes where there is an even number of heads and tails actually decreases, compared to the total possible outcomes, the more times you flip the coin. I was wondering if someone could, please, troll me about the reason why this doesn't disprove the mathematics of probabilities, since the outcome of flipping more and more coins in a row approaches closer a…

My first of several proofs: Consider any total linear ordering, <*, of the reals. To make it simpler consider <* for S={x: 0<x}. At this point we don't know if <* is a well ordering or not. I will show by math induction that a well ordering of S must produce a countable number of minimums for a particular collection of subsets of S. Then I'll show all numbers, z, must be in this collection or set of minimums. Thus, the conclusion must be that if R can be well ordered it must be a countable set and we know this is not true. The above is a preliminary test before going further to make sure my topic does not get closed

do you think it is reasonable for a 12 year old to learn calculus...and if so how would he/she learn it in a way that does not confuse him/her ?

Please forgive me for any grammar mistake. I'm a civil engineer and completed my Msc (Maths) focusing on Numerical Study 10 years ago. After my semi retirement as a result of my financial freedom, i have been studying some practical Maths problem for fun. Recently I've been trying to model and solve a 2 digit lottery drawing game, and i failed. It's purely my imagination since i didn't see this in anywhere. But who knows it may exist? Suppose we have a lottery game of 2 digits, drawn from 2 separate but identical electrical drums as lottery company always have. Each drum consists of 10 balls, numbered from 0 to 9, to be drawn as a pair and the drawn balls …

I'm a freshman in university and I'm studying Computer science and engineering. This will be my second year of studying. We don't have Calculus as a mandatory class but I can take it from elective classes. Is calculus necessary for my future as a student and would it help me in data science or AI? That's what I'm really interested in and I want to work for either of them. Would Calculus make my education easier in the future and in my work? In my next semesters, I want to take just Artificial intelligence and Data Science classes (Data mining, Data Science, Mechanical Learning, etc). Is calculus used there? Thanks for your time reading and ans…

We can imagine the general science with perfect understanding. The complex analysis can't help you to imagine with theoretically or practically. All theorem stuffs can be combination with infinity space. But that is not reality. That theorems created for the best calculation of the calculate physical or intangible properties of the materials -with needed prices-. I guess that is acceptable for me.

In my work I have faced an optimization problem to resolve which I have to solve the following expression [math](x+5)^x=7[/math]. I know that to get I can use the Omega function Lambert W Function, however, I can't understand how it works. Thus, I ask for help of those of you who know how to solve this kind of equations (showing as much steps as you can) in order to give me reference point for further studying of this topic.

For 100 years we have been told that the reals form a larger infinity than the counting numbers, and that the reals are in fact "uncountable". Here is the pattern required to enumerate the reals (that is to "prove" that they are countable). continuum.pdf I don't for a moment suggest that Cantor's method is at all sensible or correct. In fact it is the most unmathematical hand-waving you could imagine. Commercial link removed by moderator

I say they are not.

Hi, Ok, I was looking for a way to apply the cantor argument to rational number (because I'm masochist) and I think I found one. I'm sure somebody will be happy to disprove my idea : I write rational numbers in a special way. Let's say you have a/b I decompose a and b into sums of 1s.. a= 1 + 1 + .... + 1+1+1 b= 1+ 1+ .. +1+1.. first I simplify, then I use it to create a pseudo number like this : when there's a 1 in the first line, and 1 in the second : it's 3. When 0 and 0 => 0, when 1 and 0 => 2 and when 0 and 1 => 1 So for instance 4 / 5 = > 33331000000.... 12/6 = 2/1 => 3200000... I then use it to fill a cantor-like arr…

So everyone knows that a^2+b^2=c^2, but is there a set of numbers where a^2+b^2=2c^2? How would one go about finding these different set of numbers?

If one takes the nine variables, a, b, c, d, e, f, g, h, and i and square them all, a^2, b^2, c^2, etc. Are there numbers where there is the same distance from the middle going out? So e^2-d^2=f^2-e^2, c^2-e^2=e^2-g^2, e^2-b^2=h^2-e^2, and a^2-e^2=e^2-i^2? How would one go about finding such numbers?

What is the most elegant (simple or natural) solution of the equation a+8b+27c+64d+125e=0

Good day to everyone reading this. Thanks for your time.I've got this question here (more like an research assignment) which requires me to predict further values in a given set of values.I've attached a picture for a better understanding.The data is the cases of influenza in a country over the years.There's values missing in from May onwards.We have to use the previous set of data, come up with a "Prediction model" and use that to predict the values until end of 2019.The thing is, our teacher is very incompetent, and only told us to use "polynomials from the graphs we make in excel" and use that...Anyone got any clues/hints on how i could come up with this prediction mod…

Hi, I hope someone can help me with this problem! I have a distribution of 2000 numbers but I only know the first 10. The first 10 numbers are: 2025, 1000, 335, 300, 187.5, 135, 99.5, 20, 17.5, and 13.5. I know that the total of all 2000 numbers is about 12,000. What I am looking for is a recognised long tail curve model which using the first 10 numbers only predicts a total for all 2000 numbers in the sequence. I need the total to ideally be between 11,000 and 13,000. I did look at Zipfs law but I'm not sure this works. I am not a mathematician but would appreciate any recognised models/distribution curves/laws you could suggest and what the model you sugg…

Hello everyone, I have been having a hard time with this equation... I would really like to know if anybody has an idea on how to solve it... All the suggestions are very much appreciated :)

Hello, lets say I have coordinates for 3 points, and I want to find a function that satisfies the following Function pass through all the points Function is strictly increasing Function type is either: exponential, logarithmic, or involves x powers; in other words, we will omit sinusoidal functions and rational functions. we can think of any number of points as an example. so, lets say: point p1 = (6.5 ,1) p2 = (7.0, 2) p3=(7.48, 3) how do I find a fitting function for these? I can easily spot that this cannot be a logarithmic function (because slope is decreasing), nor can it be in the form ax^b unliss the power is b>…

Hello everyone, I am trying to solve this triple integral problem , but I am having some issues. I tried with the 2 different approaches. 1.- I converted the variables to spherical coordinates, and I think it went well, until the moment to evaluate the integral using those limits (-1 , -2). I couldn't pass that. 2.- Conversion to cylindrical coordinates, but no luck at all there. So, could someone be so kind in giving me some light around this? Please. Not sure if I am follow a right approach.

How to evaluate the following double integral where A,B and C are constants?

I am looking for case where there is continuous function, but its derivative is not-continuous... Could you know any such example....?

It is my belief that RH is a genuinely arithmetic question that likely will not succumb to methods of analysis. Number theorists are on the right track to an eventual proof of RH, but we are still lacking many of the tools. J. Brian Conrey"...the Riemann Hypothesis will be settled without any fundamental changes in our mathematical thoughts, namely, all tools are ready to attack it but just a penetrating idea is missing." Y. Motohashi"...there have been very few attempts at proving the Riemann hypothesis, because, simply, no one has ever had any really good idea for how to go about it." A. Selberg"I still think that some major new idea is needed here" E. Bombieri …

I would like for my idea on taking a derivative using a new technique evaluated: Some theory (below) before the definitions. This is to convey how I conceptualized the beginning of what I believe is a "New Calculus". I thought about how an arc of a circle can be defined in a topological sense. This led me to the definition of a line, and eventually, a circle, square, rectangle, and equilateral triangle. Therefore, I want to convey the initial part, as it is paramount to the understanding of what follows in terms of definitions. A circle is formed by very short lines ( not horizontal or vertical, but "angulated") on the circumference, as the limit of those lines, “…

This is a Real World Factory. I have a production line that provides 12 different products in various sizes on demand. I know the products, their sizes and the total labor for each batch. The problem is to calculate the labor cost of each product. They are produced in mixed batches where different product types are produced at the same time. My assumption is that each product has an initial labor cost plus additional incremental labor costs for each additional size larger than standard, which may or may not be a straight line. Is it possible to determine cost based on analyzing the composition of these batches without using brute force programming?