Numbers Definition and 1000 Threads

Everybody says that it is used in engineering or somewhere but how can you use it. in real world it is impossible to take square of any number and get negative answer. how can it have any use when it does not even exist. and people talk about imaginary plane, what is it? Thanks for helping...

Homework Statement Solve z^5 + 16 conjugate(z) = 0 for z element of C. z^5 + 16z' = 0 http://puu.sh/2EBqC.png Homework Equations The Attempt at a Solution My first thought was to use z = a+bi and z' = a-bi So: (a+bi)5 + 16*(a-bi) = 0 + 0i And then expand and simplify to the real and non real...

Where do numbers come from? What is the logical basis for the existence of numbers? Are numbers defined in mathematical logic as the cardinality of set? For example, it would seem to me that 3 is defined as the cardinality of any set that has 3 elements. IIRC it was Whitehead and Russel...

Find all real numbers $$a$$ such that the equation $$ |x-|x-|x-4||| =a $$ has exactly three real solutions.

In a bag there are 30 identical balls numbered from 1 to 30. Choose one after the other three balls (without Off Reset). What is the average value of the sum of the numbers of three balls chosen? I am not sure on how i am going to solve this so i think that we will have a variable X where X1...

Homework Statement Prove the following statements about the inner product of two complex vectors with the same arbitrary numbers of components. (a)<u|w>=<w|u>* (b)|<u|w>|^2=|<w|u>|^2Homework Equations 1. <u|w>=(u*)w 2. (c_1+c_2)*=c_1*+c_2* 3. c**=c 4. ((c_1)(c_2))*=(c_1*)c_2*The Attempt at a...

1. Find the intervals of increase and decrease 2. C(x)=x^{1/3}(x+4) 3. C(x)=x^{4/3}+4x^{1/3}; C'(x)=\frac{4}{3}x^{1/3}+\frac{4}{3}x^{-2/3}=\frac{4x^{1/3}}{3}+\frac{4}{3x^{2/3}}=\frac{x^{2/3}}{x^{2/3}}*\frac{4x^{1/3}}{3}+\frac{4}{3x^{2/3}}=\frac{4x+4}{3x^{2/3}} I am wondering...

Homework Statement In a circle we can place k numbers. The numbers can range from 1 to n. One position in the circle is fixed, say by 1. We have to place the other k-1 places with numbers in the range 1 to n such that no adjacent numbers are equal. Homework Equations The Attempt at...

Hello I understand how to approach finite potential well. However i am disturbed by equation which describes number of states ##N## for a finite potential well (##d## is a width of a well and ##W_p## is potential): $$ N \approx \dfrac{\sqrt{2m W_p}d}{\hbar \pi} $$ I am sure it has something to...

Planck team published several sets of of basic cosmic parameters in their report http://arxiv.org/pdf/1303.5076v1.pdf see for example Table 5 on page 22. The rightmost column of Table 5 is labeled "Planck+WP+highL+BAO". That seems to be the set of numbers that Ned Wright chooses to report, for...

Homework Statement Question: Homework Equations Any relevant to complex numbers. The Attempt at a Solution Given, Arg(\frac{z}{w})= Arg(z)-Arg(w) z=x+yi z1 = -1-2i z2 = 2+3i Arg(z-z1)=Arg(z2-z1) LHS: Arg(x+yi+1+2i) Arg((x+1) + i(y+2)) tan(\theta)=\frac{y+2}{x+1}...

1. Find the critical numbers of F(x) = x^{\frac{4}{5}}(x-4)^{2} 2. Power rule then chain rule 3. F'(x) = \frac{4}{5}x^{\frac{-1}{5}} (x-4)^{2}*2(x-4) I know two critical numbers are 0 and 4 and I am having problems finding the third one.

I've been tasked with showing that a Lagrangian under a set of transformations changes by a time derivative. All has gone well, except I'm left with two remaining terms, that I am completely confident, aren't there by mistake (as the 16 terms that should be expected have all popped out with the...

EDIT: Found the answer, seems I overlooked part of the solution in the learning materials ( answer extended into another page) the Solution does indeed equal what i thought it did. Homework Statement So this is the problem i have: (2(-1)^n -((n*pi)^2(-1)^n)-2)*(8/(n*pi)^3) where n...

Ok, I don't know if this method is already known or not, but I found this all by myself after some observations... so here it is... Suppose we want to square a number, say 67. What i have found is this: 1. First get 652 which is [6*7][5*5] = 4225 2. Forget the digit in the unit's place, ie...

I'm trying to write down an axiomatic development of most of mathematics, and I'm wondering whether it's logically permissible to use natural numbers as subscripts before they have been defined in terms of the Peano Axioms. For instance... the idea of function is used in the Peano axioms...

Here's a sample history from fairly far back in the past, going up to the present (S = 1) in 20 expansion ratio steps, and then in another 20 expansion steps, going out a good stretch into the future, when distances will be 25 times what they are today. I could have asked for a wider expanse of...

If σ(N) is the sum of all the divisors of N and τ(N) is the number of divisors of N then what is the sum of sum of all the divisors of first N natural numbers and the sum of the number of divisors of first N natural numbers? Is there any relation between σ(N) and τ(N) functions? Can I do that...

Prove that $$a^3+b^3 \ne to \ c^3 \ if \ a,b \ and \ c \in \ {N}$$ This is not a challenge,I am asking for help... Any help is appreciated... Thanks...

Hi, At the end of our lecture today, the lecturer gave us this simple yet impossible puzzle. My friend and I have tried to find the answer but in vain... Using only the numbers 3, 3, 3 and 3 once and using only the four arithmetic + - * / once can you make the number 7. The closest I...

Prove the following : $\displaystyle \psi(n)= -\gamma \,+\,\sum^{n-1}_{k=1}\frac{1}{k}$

Here is the question: Here is a link to the question: Would you help with these math problem? - Yahoo! Answers I have posted a link there so the OP can find my response.

Homework Statement A Carmichael number is a composite integer n greater than or equal to 2 such that b^{n-1} \equiv 1 (mod n) for all integers b that re relatively prime to n. Let n be a Product of at least 3 distinct odd primes. Prove that if (p-1)\mid (n-1) for every prime divisor p of n...

I am a bit confused over something that should be relatively easy to research , however, I am having a hard time finding a direct answer to my question. When finding the extrema of a function , we find at what points the first derivative is 0 or undefined .. with the stipulation , if I am...

let z,w be complex numbers. Prove: 2|z||w| <_ |z|^2 + |w|^2

Homework Statement Is there a general formula for the sum of such a series (or can it be self derived) ? 2^2 + 4^2 + 6^2 + 8^2 ... N^2 (all the way till some even number N) Homework Equations \sum r^2 (from r=1 to r=N) = 1/6 * n(n+1)(2n+1) The Attempt at a...

i am studying real analysis from terence tao lecture notes for analysis I. http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/ from what i understand , property is just like any other statement. for example P(0.5) is P(0) with the 0s replaced with 0.5 . so the notes says (assumes ?)...

Hey guys, just looking for an explanation for the following algorithm. It is in my textbook, and there isn't really an explanation. I don't really see how the algorithm works, but I will add what I do know, and hopefully one of you can help. Thanks. //this initial declarations produces an...

Can you help me to construct a 1-1 mapping from real numbers onto non-integers? thanks

Hi there, eI have two numbers: z1 = 2 + i z2 = exp(iδ) * z1 i are complex numbers and δ is a real number. I need to answer a question - what does the graphical representation of z2 have in relation to the graphical representation of z1. Thanks for any help!

I have to prove that the cardinality of the set of infinite sequences of real numbers is equal to the cardinality of the set of real numbers. So: A := |\mathbb{R}^\mathbb{N}|=|\mathbb{R}| =: B My plan was to define 2 injective maps, 1 from A to B, and 1 from B to A. B <= A is trivial, just...

Homework Statement Find tan A, tan B I have a right angle triangle. Length a = t, length b = k, hypotenuse = p. The Attempt at a Solution Usually I would just use the normal rule of \tan a =\frac{opp}{adj} but how can I get an answer here? I can't just say \tan a =\frac{t}{k}...

Everything for computers has to be numbers?? Why every data, every information has to be represented in numbers for the computers. For us humans, we can take in data in various forms(or is it?). But for computers be it anything it is represented in numbers. Isn't there any other way? Hope...

Homework Statement For all non zero natural numbers n prove that: 1- 24\mid n(n+1)(n+2)(n+3)(n+4) and that : 2- 120\mid n(n+1)(n+2)(n+3)(n+4)(n+5) The Attempt at a Solution 1- For n=1 we get that 24 divides 120 so we assume that 24 divides n(n+1)(n+2)(n+3)(n+4) and we...

Homework Statement Prove that there are infinitely many n such that 6n+1 and 6n-1 are both composite. Homework Equations The Attempt at a Solution I have no idea where to start. I was thinking that this must be some form of Euclid's theorem but I don't know how to work that into...

Hi, The formula of caffeine is C8H10N4O2. The oxidation numbers of O & H are -2 & +1 according to the book. How do I determine the oxidation numbers of C or N. Note: The substance is a molecular substance so we cannot apply the following rule: "the oxidation number of an atom in a monatomic...

(1) The number of divisers of the form $2^2.3^3.5^3.7^5$ which are is in the form of $4n+1$ where $n\in\mathbb{N}$ (2) Calculate Total no. of positive Divisers of $7!$ which are is in the form of $3t+1\;,$ where $t\in \mathbb{N}$

Hi there, I recently discovered a formula for the nth term that works for any finite sequence of numbers. I was just wondering whether a formula has already been discovered, and if not, how and where I should publish it. To give you an example of what i mean: one formula for the nth...

Homework Statement Question 1: You find an old map revealing a treasure hidden on a small island. The treasure was buried in the following way: the island has one tree and two rocks, one small one and one large one. Walk from the tree to the small rock, turn 90 to the left and walk the same...

arg(\dfrac{z}{z-2}) = \dfrac{\pi}{3} sketch the locus of z and find the centre of the circle I've sketched the locus of z but I can't seem to find the centre of the circle. Is there a way to do it algebraically? I've attempted to use z = x + iy, but to no avail.

Homework Statement A non-transcendental number is one that's a root of a (non-constant) polynomial with rational coefficients. Does allowing radicals as coefficients, eg: 5√3, 2^(1/3) get us any new different numbers? Homework Equations The Attempt at a Solution 1. In some cases we get no new...

One thing I've been hearing for years is that *just around the corner* is this huge wave of retirements of baby boomer engineers, scientists, professors, etc., leaving all these open positions to be filled by younger people, and so it makes perfect sense to get a degree in engineering or get a...

Homework Statement A lift starts from rest and travels with constant acceleration 4 m/s^2.It then travels with uniform speed and comes to rest with constant retardation of 4 m/s^" The total distance traveled is d and the total time taken is t. Show that the time spent traveling at a constant...

Homework Statement Evaluate: Homework Equations sin\frac{\pi }{7}.sin\frac{2\pi }{7}.sin\frac{3\pi }{7} The Attempt at a Solution Using z^{7}-1 got: cos\frac{\pi }{7}.cos\frac{2\pi }{7}.cos\frac{3\pi }{7}=\frac{1}{8}

Hi. I was thinking about getting Numbers by apple to do data analysis for an intro to modern physics course and an optics lab. I was wondering if anybody thinks it is a good product and easy to use like most things apple?

Author: Titu Andreescu, Dorin Andrica Title: Complex Numbers from A to ...Z Amazon Link: https://www.amazon.com/dp/0817643265/?tag=pfamazon01-20

Homework Statement Sketch the line described by the equation: |z − u| = |z| z = x+jy u = −1 + j√3 The Attempt at a Solution (x+1)^2 + j(y-√3)^2 = (x+jy)^2 I just don't quite get where to go with this please give me a headstart

x=1825+91/1217 y=7+2/3 z=1827+2/3 Is there any way to turn x into z only using the first two terms, andor a constant, and the operators ' + ', ' - ', ' * ', ' / '. I know I can take ((x)-(x mod 10)) + y = z, but this uses a modulus. ... Basically the core of the question is can I change any...

Homework Statement Let z be a complex number such that z^n=(z+1)^n=1. Show that n|6 (n divides 6) and that z^3=1. Homework Equations n|6 → n=1,2,3,6 The Attempt at a Solution The z+1, I think, is what throws me off. Considering z^n=1 by itself, for even n, z=±1 and for odd n...

Homework Statement Here is the whole problem. Homework Equations Not sure The Attempt at a Solution As you can see I got the first part. I solved the equation at part a.) for A(c) and plugged it into the D.E. and then solved for B(c). I need help on how to do the next part. How...