Numbers Definition and 1000 Threads

First I'll write what I know: Algebraic number: one of the roots to a polynomial over rational numbers. Polynomial: A function for x. Example: ##f(x) = x^2-2## although I won't write the ##f(x)## part when writing a polynomial. Root of a polynomial: All values for x where the polynomial is...

is there any way to prove or disprove the statement: y=3x^2+3x+1 is prime for all x belongs to natural numbers...

draw on a argand diagram |arg(z + 1)| = \dfrac{\pi}{2} I got the correct drawing... but I'm not sure why it's correct. What I thought was arg(z + 1) = \dfrac{\pi}{2} and that's a half line from the point (-1,0) going upwards, and arg(z + 1) = -\dfrac{\pi}{2} and that's a half life...

Homework Statement Prove that their are an infinite amount of primes by observing that in the series 2^2+1, 2^{2^2}+1,2^{2^3}+1,2^{2^4}+1,... every 2 numbers are relatively prime. The Attempt at a Solution I was going to take 2 of the numbers in the series and look at their difference...

a + b + c = a * b * c where a, b, c are positive integers. I can think of only one solution to this. {1, 2, 3}. Is there any other solution to it? Can you prove or disprove?

I'm working on an assignment that is due in roughly two weeks and I'm stuck on a problem. I have what I believe may be a solution but am unsure whether or not it is 'complete'. Here is the problem: "Let C be a circle or a straight line. Show that the same is true of the locus of points...

Arrange the numbers: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 such that the summation of each two successive numbers is a complete square easy interesting question

I took the prime numbers from this link: http://nl.wikibooks.org/wiki/Wiskunde/Getallen/Lijst_priemgetallen I did take the first three lines I did the following with the numbers The prime 11 = 1+1 = 2 The prime 13 = 1+3 = 4 The prime 17 = 1+7 = 8 and so on This is the result for the...

Let E(x) denote the number of numbers relatively prime to x. Please help me prove that the function E(x) is multiplicative,i.e., E(xy)=E(x).E(y)

http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989

My linear algebra uses "Kyle Numbers" to compute some kernels. But it does not elaborate on what they are and how they are used to compute the kernel? Please help.

I have a question about the HUP. As I understand the HUP, it only applies to conjugate attributes that do not commute, such as position and momentum. However, many good quantum numbers do commute, so does this mean that the HUP does not apply to simultaneous measurement of such good quantum...

Given n numbers x1,x2...xn belong to N. x1+x2+x3...xn=m How many different combinations of x1,x2,x3...xn are there?Is there any formula useful here? Note:x1,x2,x3... need not be distinct and also can be 0. Thanks

Let's start with: $$ \int \frac{dx}{1+x^2} = \arctan x + C $$ This is achieved with a basic trig substitution. However, what if one were to perform the following partial fraction decomposition: $$ \int \frac{dx}{1+x^2} = \int \frac{dx}{(x+i)(x-i)} = \int \left[ \frac{i/2}{x+i} -...

Let p[n] be the following property of Fibonacci numbers: p[n]: f_{n+1} * f_{n-1} - (f_{n})^{2} = (-1)^{n}. Prove p[n] by induction. This is the proof I wrote. i used regular induction. Is weak induction sufficient to prove it or do I need to prove this by strong induction? proof: BASE STEP...

matrix inversion with complex numbers?? or faster way? Homework Statement The Attempt at a Solution i managed to get the answer, but it took me like 30min. to work this by hand. i probably worked it differently than my instructor's method above, but wat i did was get the coefficients of V...

Problem Statement: Do the sieve of Eratosthenes from 2 to 100 and find all the primesSo I'm trying to do the sieve of Eratosthenes in fortran 90 (I'm using Plato IDE)My efforts to solve this/ method to use: Obviously, I want the program to do a LOOP starting with every whole number from 2...

Hi guys, I've been trying to help a friend with something that I learned in class but I'm now finding it hard to solve myself. The problem goes as follows: Use geometry to show that |z3-z-3| = 2sin3θ For z=cisθ, 0<θ<∏/6 Now, I chose ∏/12 as my angle and plotted all this on an Argand diagram...

Homework Statement The question : http://gyazo.com/7eb4b86c61150e4af092b9f8afeaf169 Homework Equations Sup/Inf axioms Methods of constructing sequences ##ε-N## ##lim(a_n) ≤ sup_n a_n## from question 5 right before it. I'll split the question into two parts. The Attempt at a...

Are Transfinite numbers accepted as genuine numbers?

Homework Statement I'm trying to convert something like 1.25^-03 into it's standard number composed of standard decimals using a calculator (0.0125) - if you know what I mean. Thanks.

Let me start by writing about the natural or counting numbers. The story of how, where and when we invented them is lost in the misty dawn of history. But perhaps our African ancestors, like our living simian cousins (and some other animals) evolved the ability to distinguish between few and...

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...