Numbers Definition and 1000 Threads

Homework Statement Homework EquationsThe Attempt at a Solution hey hello every one I want to ask a question that is add 1+2+3+4.....10000000. I think its very easy. for example let us add first 5 numbers 1+2+3+4+5 now we can find a pattern that adding first and last digit will be always same...

I am a physics student trying to self-learn Chern numbers and Chern class. The book I am learning (Nakahara) introduces the total Chern class as an invariant polynomial of local curvature form ##F## ## P(F) = \det (I + t\frac{{iF}}{{2\pi }}) = \sum\limits_{r = 0}^k {{t^r}{P_r}(F)} ## and each...

I've just had my first batch of lectures on complex numbers (a very new idea to me). Algebraic operations and the idea behind conjugates are straightforward enough, as these seem to boil down to vectors. My problem is sketching. I have trouble defining the real and imaginary parts, and I don't...

Ask the user for a number between 1 and 11; stop asking when the user enters 0 OR when the total goes over 21. Display the total on the screen. For example: #include<iostream> #include<cmath> using namespace std; int main(){ int num, total; cout << "Enter a number between 1 and 11...

$A=$$\square$[FONT=Times New Roman]1 [FONT=Verdana]$\square$[FONT=Times New Roman]2 $\square$[FONT=Times New Roman]3[FONT=Verdana]$\square$[FONT=Times New Roman]4 [FONT=Verdana]$\square$[FONT=Times New Roman]5[FONT=Verdana]$\square$[FONT=Times New Roman]6 [FONT=Verdana]$\square$[FONT=Times New...

Homework Statement Homework Equations character equation The Attempt at a Solution Should I set a = ax2 b= bx c =c in the character equation?

Homework Statement Use Eisenstein's criterion to show that there exists irreducible polynomials over Q or arbitrarily large degree, and from this deduce that the field of algebraic numbers is an infinite extension of Q Homework Equations none The Attempt at a Solution Note that x^n+4x+2 is...

Hey guys! I have heard of this concept in various places and sort of understands what it attempts to do. Can anybody please explain it to me in more detail like how it works, how to notate it, and how to expand it to infinities and infinitesimals. Thanks in advance! Aakash Lakshmanan xphysx.com...

Homework Statement Please see questions (c) and (e) on the attachement 2.Relevant Equations The Attempt at a Solution So long story short, these two questions were given out as a challenge in one of our Swedish lessons to see if we could remember our high school calculus, which I shamefully...

Why is it that the distance between two real numbers ##a## and ##b## in an ordered interval of numbers, for example ##a<x_{1}<\ldots <x_{n-1}<b##, is given by $$\lvert a-b\rvert$$ when there are in actual fact $$\lvert a-b\rvert +1$$ numbers within this range?! Is it simply that, when measuring...

I have just begun reading about Einstein's summation convention and it got me thinking.. Is it possible to represent ∑aibici with index notation? Since we are only restricted to use an index twice at most I don't think it's possible to construct it using the standard tensors (Levi Cevita and...

I am currently an undergraduate students at university and i am keen on learning some mathematics that is not taught in school and i have chosen number theory as my main topic . Recently I have picked number theory by Hardy but I found it is quite hard to understand sometimes as I have quite a...

Hello everyone. I wanted to prove the following theorem, using the axioms of Peano. Let ##a,b,c \in \mathbb{N}##. If ##ac = bc##, then ##a = b##. I thought, this was a pretty straightforward proof, but I think I might be doing something wrong. Proof: Let ##G := \{c \in \mathbb{N}|## if ##a,b...

let equation 1: x % n1 = 0, equation 2: x % n2 =1, where n1 and n2 are known positive integers, any multiple of n1 will solve eqn1 and any multiple of n2 (and adding 1 to the multiple) will solve eqn2, but is there a short way to simultaneously solve the two equations to find x instead of...

Homework Statement Consider 3 nonzero complex numbers $$z_1,z_2,z_3$$ each satisfying $$z^2=i \bar{z}$$. We are supposed to find $$z_1+z_2+z_3, z_1z_2z_3, z_1z_2+z_2z_3+z_3z_1$$. The answers- 0, purely imaginary , purely real respectively. Homework EquationsThe Attempt at a Solution I have...

Homework Statement ask to find all the values in z to the equation to be true[/B]Homework Equations [/B]The Attempt at a Solution this is my atemp of solution i don't know what else do, because the problem ask for z values well i must add that i am thinking about x=0 and y= pi/2 will solve...

Hi, New member here and have been dabbling with some aspects of George Cantor's work. I think I have found a way to put the irrationals in one to one correspondence with natural numbers but thousands of mathematicians over the years might disagree. Is there a subtle error ( or even a blatant...

Homework Statement Write this complex number in the form "a+bi" a) cos(-pi/3) + i*sin(-pi/3) b) 2√2(cos(-5pi/6)+i*sin(-5pi/6)) Homework Equations my only problem is that I am getting + instead of - on the cosinus side.(real number) The Attempt at a Solution a) pi/3 in the unit circle is 1/2...

Homework Statement Homework Equations Theta = arctan (y/x) The Attempt at a Solution Hopefully this is the right section to post in, but I am a bit confused with complex numbers. I am working on the problems above and I just wanted to make sure I am doing each part correctly. I think A...

Hello I'm hard at work trying to find a pattern for the prime numbers and this keeps cropping up. To be honest though, to me it comes across like pseudo science. I mean I never really hear people talk about it. This seems an obvious thing to look into but I don't know anyone who does. Prime...

I know that there are several models of the real numbers, some where the Continuum Hypothesis holds, others where it does not. I would like to understand why the usual definition of the reals, limits of Cauchy sequences of rational numbers under the usual absolute value norm, isn't one of these...

If the axiom of induction was extended to include imaginary numbers, what effect would this have? The axiom of induction currently only applies to integers. If this axiom and/or the well ordering principle was extended to include imaginary numbers, would this cause any currently true statements...

Hi all, I have spent a couple of hours on this perplexing question. Solve the simultaneous equations: z = w + 3i + 2 and z2 - iw + 5 - 2i = 0 giving z and w in the form (x + yi) where x and y are real. I tried various methods, all to no avail. I have substituted z into z2 , I got the wrong...

Mod note: moved from a homework section What properties do prime numbers exhibit which can be used in proofs to define them? Like rational numbers have a unique property that they can be expressed as a quotient of a/b. Even numbers have a unique property of divisibility by 2 and thus they can be...

Hello! (Wave) According to some notes of computability theory: Addition of binary numbers $$10011\\ +11111 \\ ------ \\ 110010$$ I haven't understood how they do the addition, since it holds that $1+1=0$... (Sweating) Could you explain it to me?

The problem The following equation ##z^4-2z^3+12z^2-14z+35=0## has a root with the real component = 1. What are the other solutions? The attempt This means that solutions are ##z = 1 \pm bi##and the factors are ##(z-(1-bi))(z-(1+bi)) ## and thus ## (z-(1-bi))(z-(1+bi)) =...

Is there any prime number pn, such that it has a relationship with the next prime number pn+1 p_{n+1} > p_{n}^2 If not, is there any proof saying a prime like this does not exist? I have the exact same question about this relation: p_{n+1} > 2p_{n}

If I have 2 complex numbers, A and B, what is the correct way to evaluate this expression: ## E = AB - B^*A^*## I was under the impression that when taking the product of complex numbers, you always conjugate one factor, but in this instance, it is quite important which one is conjugated, no...

Show that in 10 consecutive numbers there is at least one number which is co-prime to other 9 numbers.

We should note that we can write any complex number as $\displaystyle \begin{align*} z = r\,\mathrm{e}^{\mathrm{i}\,\theta} \end{align*}$ where $\displaystyle \begin{align*} r = \left| z \right| \end{align*}$ and $\displaystyle \begin{align*} \theta = \textrm{arg}\,\left( z \right) + 2\,\pi\,n ...

Hi, When I using Matlab 2008, the symbols and numbers were big enough to see but now I use Matlab 2013 but symbols and numbers or what I write is too little. How can I make them bigger? Thank you.

I am using complex numbers and was wondering if there's any way that I can get output to match my exact input when performing basic arithmetic on them. For example, if I use type = complex_ or complex256, with A = 1. and B = 6.626 x 10^(-34), then C = A*B yields C = 6.626 x 10^(-34) as wanted...

First let's write this number in its polar form. $\displaystyle \begin{align*} \left| z \right| &= \sqrt{\left( -2 \right) ^2 + 2^2} \\ &= \sqrt{4 + 4} \\ &= \sqrt{8} \\ &= 2\,\sqrt{2} \end{align*}$ and as the number is in Quadrant 2 $\displaystyle \begin{align*} \textrm{arg}\,\left( z...

is the function x²+3 surjective for real numbers. how do you test for surjectivity in general?

Compare the numbers $2^{2016}$ and $3^{201}7^{604}$.

My statement: The first transfinite ordinal, omega is the first number that cannot be expressed by any natural number, therefore it is not included in the set of natural numbers. The set of natural numbers is a subset of real numbers, every natural number can be taken out of it, but still true...

If the odds of randomly picking a 3 digit number correctly are 1000-1, then what are the odds of that same number being picked 4 times in 364 picks?

Homework Statement 6 degenerate energy states at E=7/2 h-bar w in isotropic 3D harmonic oscillator. pick one possible state( for example, (nx,ny,nz)=(1,0,1)), and find possible l, m quantum numbers you may use orthonormality of spherical harmonics[/B] Homework Equations pick one possible...

Homework Statement Showing all necessary working solve the equation ##iz^2+2z-3i=0## giving your answer in the form ##x+iy## where x and y are real and exact,Homework EquationsThe Attempt at a Solution ##iz^2+2z-3i=0, z^2+(2/i)z-3=0##,using quadratic formula →##(-2/i± √8)/2 , z= √2+1/i## and...

Homework Statement How would I go about solving 1/z=(-4+4i) The answer that I keep on getting is wrong The Attempt at a Solution [/B] What I did z=1/(-4+4i)x(-4-4i)/(-4-4i) z=(-4-4i)/(16+16i-16i-16i^2) z=(-4-4i)/32 z=-1/8-i/8 This is the answer that I got however it says that it is...

The unit right now is electrostatics, but this question is really just vectors, nothing to do with charges or anything... anyways here is the info: 1. Homework Statement Three identical point charges, A, B, and C are located as shown here: The force A-on-C is the same as the force B-on-C...

I work a lot in binary. I am organizing some of my work and need a way to write expressions. I can always create my own notation, but i would rather not invent something that already exists. 1011 is binary for 11 base 10. I use this {3,1,0} to represent the binary with just exponents. When I...

1. Give a formula for the values on m such that z^m=z z=cos(7pi/6)+i*sin(7pi/6) 2. If i use de movires i get 3. m*7pi/6=7pi/6 + k*2pi But then i get the value that k=12/7, Which is the wrong formula. The correct answer is 1+12k for k=0,1,2...

Homework Statement Let ##z_1,z_2,z_3## be three complex numbers that lie on the unit circle in the complex plane, and ##z_1+z_2+z_3=0##. Show that the numbers are located at the vertices of an equilateral triangle. Homework EquationsThe Attempt at a Solution As far as I understand, I need to...

Prove that $8^{91}\gt 7^{92}$.

so(4) is the symmetry algebra of Keplerian motion. Its structure is well known. The principal quantum number n must be a positive integer. The associated Casimir operator has eingenvalues n^2 - 1 . The secondary quantum number j is integer and can take any value from zero to n-1. The...

Dear Physics Forum friends, what are some good books for learning the p-adic numbers? What are the necessary pre-requisites? Do I need to know introductory number theory or basics of algebraic/analytic number theory?

Homework Statement Reflection of the line ##\bar{a}z + a\bar{z} = 0## in the real axis is Homework EquationsThe Attempt at a Solution I know that a line in the complex plane is represented as ##\bar{a}z + a\bar{z} + b= 0## and that its slope ##μ = \dfrac{-a}{\bar{a}}##. I'm not sure how to do...

Find all positive integers whose square end with 444.

Or basically anything that isn't a positive integer. So I can prove quite easily by induction that for any integer n>0, De Moivre's Theorem (below) holds. If ##\DeclareMathOperator\cis{cis} z = r\cis\theta, z^n= r^n\cis(n\theta)## My proof below: However I struggle to do this with...