Numbers Definition and 1000 Threads

Are the following correct (all numbers are approximations); d from the Earth to the Sun is 90 million miles = 9 x 10^ 7 miles = 144 million km = 1.44 x 10 ^ 8 km ? d from the Earth to the Moon is 240 thousand miles = 2.4 x 10^ 5 miles = 400 thousand km = 4 x 10 ^ 5 km? m of the Earth = 6 x...

I noticed that for any integer greater than 4 there exists at least one perfect square in the open interval (n, 2n). I think I have proved the statement, but as I am not a professional, I'd like someone to review my proof. By induction we see that it is true for n=5 because 5<9<10. Now suppose...

What are imaginary numbers? Does anyone know a good book for it?

If the solution of the quadratic equation \frac{-b \pm \sqrt{b^2-4ac}}{2a} produces a new kind of number, the complex numbers a \pm i b so, the solution the cubic equation should to produce a new kind of number too, and the solution of the quartic equation too, etc...

$A=\begin{Bmatrix} {1,2,3,4,5,------,2015} \end{Bmatrix}$ if we pick $n$ numbers from $A$, we call it the set $B$ ,and the sum of any three numbers from $B$ are multiple of 27 ,find $max(n)$ , and the largest number we can choose from $A$

I was wondering if scientists or mathematicians have any use for complex numbers involving negative roots of I as in i=(-1)^(1/2). but my question is more what would be (-1)^(-1/2)?

Find all the four-digit numbers $ABCD$ which when multiplied by $4$ give a product equal to the number with the digits reversed, $DCBA$. (The digits do not need to be different.)

I don't quite know where to start with this one: "A natural number p>1 is called irreducible if it has the property that, for any natural numbers a and b, p|ab always implies that either p|a or p|b (or both). Prove that if a natural number p>1 is irreducible, then it also has the property...

Hi, a friend of mine gave me a math problem which I've spent hours trying to find different methods to solve. But none of them work and I'm now out of ideas. The problem goes like this: So for example, ##17^2 = 1^2 + 2(12^2) ⇒ 17 = 3^2 + 2(2^2) ## or ## 3^2 = 1^2 + 2(2^2) ⇒ 3 = 1^2 + 2(1^2)##...

Homework Statement Complex Analysis Problem: The euler Numbers E_n, n=0, 1, 2,..., are defined by 1/cosh(z) = the sum from n=0 to n=infinity of E_n/n! z^n (|z|<pi/2). show that E_n=0 for n odd. Calculus E_0, E_2, E_4, E_6 Homework Equations Not entirely sure what to put here for this one...

Homework Statement Express (-1)1/10 in exponential form (My first time posting - I hope I got the syntax right!) Homework Equations The Attempt at a Solution [/B] I got the solution, it's ejπ/10, but I'm not sure why. Here's my work: (-1)1/10 = (cos(π) + jsin(π))1/10 = cos(pi/10) +...

Hello, Please, someone, explain what the // in the hint below stands for: "Show that the numbers of the form ±m√2/n for m, n ∈ N are dense." Hint: "To find a number in (x, y), find a rational in (x//√2, y//√2). Conclude from this that the set of all (irrational) numbers of the form ±m√2/n is...

Homework Statement Determine a positive rational number whose square differs from 7 by less than 0.000001 (10^(-6)) Homework Equations - The Attempt at a Solution Let p/q be the required rational number. So, 7> (p/q)^(2) > 7-(0.000001) ⇒ √(7) > p/q > √(7-.000001) ⇒√(7) q> p >...

$S=({10^1+1,10^2+1,---------,10^{1000}+1})$ please prove the non-prime numbers in $S \geq 990$

A car goes from repose (0 mph) to 50 mph in, say, 30 seconds. Math tells us that there is an infinite amount of numbers between 0 and 50 (or between any two other numbers). Therefore, isn't it "obvious" or "intuitive" that it would take a car an infinite amount of time to go from 0 mph to 50...

Hi,I'm facing a problem finding the values of complex numbers, I'll put two examples then I'll explain the issue. ex1: (-e)^{iπ} , my answer is (-e)^{π^2±2mπ^2} The book answer is (-e)^{π^2} ex2: e^{2 arctanh(i)} , my answer is e^{[iπ/2±mπ/2]} = ie^{±mπ/2} The book answer is i...

Is there a standard way of representing numbers of arbitrary size or precision for storage in a text file, JSON message, variable etc.? I am thinking of representing integers as decimal strings e.g. "-12345678901234567" and floats as an ordered pair (array) of strings representing decimal...

Hello, I'm having a little trouble figuring out the following problem: Consider the set of number a, 2a, 3a, ..., na where a and n are positive integers. (i) Show that the expression for the mean of this set is \frac{a(n+1)}{2}. So far the only work I've been able to muster up is: Mean =...

Find three different complex numbers that satisfy the equation in the form a + bi. I know that: Re(z) = a + bi = a Im(z) = a + bi = b Re(z) = 4Im(z) a = 4b I'm stuck after this point. How do you find what is a and what is b?

Homework Statement [/B] I'm supposed to find the quantum numbers (n, L, J) for the first 3 energy levels in Iridium (Z=77), given that the first 4 ionization energies are ##76.1, 13.4, 12.8, 11.2 keV##. Homework EquationsThe Attempt at a Solution I know that the electronic configuration is...

Alright here's my confusion, if i take say 3x^2 + 4x^2 ill end up with 7x^2 which i accepted was the correct way to think about it, but if i try the same problem without the x variable doing the same method, 3^2 + 4^2 = 7^2 this is obviously not the correct answer. Instead 3^2 = 9 and 4^2 = 16...

Homework Statement Prove that there are infinitely many prime numbers written ##ak+b##, with ##a,b,k## integers greater than 1 Homework EquationsThe Attempt at a Solution Please could you tell me if you agree with that proof ? By contradiction: Assume that there is an integer ##k## such that...

Let $a,\,b,\,c,\,d$ be different positive real numbers such that $a+\dfrac{1}{b}=b+\dfrac{1}{c}=c+\dfrac{1}{d}=d+\dfrac{1}{a}=x$. Find $x$.

Let $x,\,y,\,m,\,n$ be positive real numbers such that $m^2-m+1=x^2$, $n^2+n+1=y^2$ and $(2m-1)(2n+1)=2xy+3$. Prove that $m+n=xy$.

Homework Statement http://www.math.harvard.edu/archive/21b_spring_09/faq.html I'm having trouble understanding this explanation, particularly this part. "The Kyle numbers are 1, 2 because adding the first to 2 times the second column gives zero. " Sorry for this basic question but I was...

I'm not a logician or mathematician but a philosopher (with dyscalculia) so please forgive me for skipping the technicalities... My question is this: Is there in the theory of non-well-founded sets (hypersets) something analogous to the set-theoretic construction of the natural numbers in ZF...

Hello! (Wave) There are given three vectors $V_1, V_2, V_3$ of dimension $m$, the elements of which are real numbers. I want to write an algorithm that determines if there are three numbers, one of each of the matrices $V_1, V_2$ and $V_3$, that have sum equal to $0$. Can you write an...

This relates to a question I asked recently on Quantum Dots, but I'll rephrase it and hopefully any chemists out there can help. If we have (n,l) = (1,2) where n and l are quantum numbers can we determine the orbitals? and hence the number of electrons in a quantum dot? i.e. And also I've...

Hi. I am trying to create a program that I will give the maximum range (1,...,max) from which to generate random numbers, and make it generate N=maxgen random numbers (which later I can use for example in another program). Below you can see the code I wrote: #include <iostream> #include <ctime>...

Given the two standard definitions (1) A computable set is a set for which there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set. (2) A computable number is a number which can be approximated to any degree of...

I was able to prove a), but I am unsure how to prove b. Is there some sort of geometric interpretation I should be aware of?

Hi all, I'm preparing for a deferred exam this semester after falling ill last year. Just looking over my course notes and have a question. I understand how this works in the big picture scheme. What I don't understand however is how my instructor simplified the original equation. 1. Homework...

Homework Statement I'm going crazy. I've done this problem nearly 20 times and keep getting the same answer. I've read my textbook so many times too! What am I doing wrong? Homework Equations Zcapacitor = 1/(jwC) Zinductor = jwL Zresistor = R The Attempt at a Solution Z for the...

What does it mean to take positive rational numbers to whole-number powers?

Homework Statement So I'd rather not type out the whole equation I am differentiating with respect to t... Sorry admins. My written work is on the image. I just want to make sure my work is correct. Homework Equations The equation is a differential characteristic equation with cos and sin...

my turn to have something answered o0) 1. Homework Statement The problem is to show that Fermat numbers are relatively prime, which I could just look up somewhere but I want to use the mod operator that is used in Concrete Math, which says ##n \bmod m = n - m\lfloor{\frac{n}{m}}\rfloor## So if...

I want to create an array of numbers between 0 and 0.1 where the points are clustered around an arbitrary point x1 (0 < x1 < 0.1). I want the points to get exponentially closer together near x1 from either side and and get further apart towards the outer limits. I am using MatLab and was trying...

Homework Statement I have to make a program that would end when entered a 0 and print out negative numbers and even numbers separately but what I have so far is not working. The Attempt at a Solution numbers = [] negative_numbers = [] while True: number = input("Enter a number: ")...

I am really not sure and do not understand how you find out what are the magic numbers in case of nucleus. Here in leson lecturer said that magic number is ##114##, and in other resourses I find number ##126##? Do we have any real confirmation of this?

[Mentor's note: this was originally posted in the Quantum Physics forum, so that is what "this section" means below.] ---------------------------------------------------- I wasn't sure whether to post this question in this section or the general math section, so I just decided to do it here...

This problem has been on my mind for a while. ---------- **Problem:** Show that **if** \begin{equation} |z_1+z_2+\dots+z_n| = |z_1| + |z_2| + \dots + |z_n| \end{equation} **then** $z_k/z_{\ell} \ge 0$ for any integers $k$ and $\ell$, $1 \leq k, \ell \leq n,$ for which $z_{\ell} \ne 0.$...

Considering the interval [0,1], say for each number (binary) on the interval you form the sequence of numbers: number of zeros up to the nth place/number of ones up to the nth place. Then as n goes to infinity the sequence of numbers (for the given binary number) will go to somewhere in...

Homework Statement I need to write a Python program, which would: 1) Ask for a name (input function) 2) Keep asking for the name if it is not entered correctly(if it has a digit in it) 3) If the name is entered correctly it will print the name Homework Equations How should I continue the...

Hi, Can we treat prime numbers as an Ortho-normal basis of "Infinite" dimensions to represent every possible number. Treating numbers as vectors. Thanks.

So if you do a search for R-Simplexs you should find that. RSimplex(n,d)=Pochhammer(n,d)/d! Well so to does RSimplex(n,d)=If(n<d, Pochhammer(d+1,n-1)/n!, Pochhammer(n,d)/d!) Or something like that my maths package is down so I'm not sure quite how it works. Anyway the relationship between...

Hi everyone, I need a little bit of help with an optimization problem and finding the critical numbers. The question is a follows: Question: Between 0°C and 30°C, the volume V ( in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula: V = 999.87 −...

Hi, So I'm writing a programme in Fortran95 atm and I want to produce an array of 1s and 0s. I've used a random number and random seed generator to produce 10 numbers between 0 and 1 and I want to use a NINT statement to round these random numbers to 0 or 1. However when I try this the...

This really isn't a homework question but I wasn't sure where to post it. I was watching a video by numberphile about complex numbers and the professer being interviewed said the most important thing about complex numbers is that they help bring algebra and geometry together. What did he mean by...

Homework Statement Given an integer n and an angle θ let Sn(θ) = ∑(eikθ) from k=-n to k=n And show that this sum = sinα / sinβ Homework Equations Sum from 0 to n of xk is (xk+1-1)/(x-1) The Attempt at a Solution The series can be rewritten by taking out a factor of e-iθ as e-iθ∑(eiθ)k from...

Homework Statement I'm a little confused by the wiki article, and I can't seem to get the correct answer. Suppose ##A = 01100101 = +101## is an 8-bit two's complement number. I'm trying to multiply ##A \times 101 = 01100101 \times 101 = (+101) \times (-3) = -303##. Homework EquationsThe...