Numbers Definition and 1000 Threads

Homework Statement Assuming 10 people pick a number between 1-120 and no two numbers can be the same, how many combinations of numbers can their be?Homework Equations C=N^s The Attempt at a Solution So I know the total possible for 120 would be just 120^10, but if I want to solve for the...

How many real numbers $x$ satisfy $\sin x=\dfrac{x}{100}$?

Submitted by @PeroK Consider all 7-digit numbers which are a permutation of the digits 1-7. How many of these are divisible by 7? Can you prove the answer algebraically, rather than simply counting them? Please make use of the spoiler tag

Let $\left\{ p_{1},p_{2},\dots,p_{h}\right\}$ a set of consecutive prime numbers. I want to show that, if $h$ is large enough, then doesn't exists a natural number $n$ such that $$n\equiv1\textrm{ mod }p_{i},\,\forall i=1,\dots,h.$$ I think is true but I have no idea how to prove it. Am I wrong?

Homework Statement The minimum number of comparisons required to find the minimum and the maximum of 100 numbers is ... Homework Equations ##T(n)=T(\lceil \frac{n}{2} \rceil) + T(\lfloor \frac{n}{2} \rfloor) + 2## The Attempt at a Solution Recurrence for the above problem is ##T(n)=T(\lceil...

show that for x,y positive integers satisfying $3x^2+x= 4y^2+y$ each of x-y , 3x+3y+ 1 and 4x + 4y + 1 are squares. ( above equation has atleast one solution x= 30 and y = 26)

Mod note: This thread was moved from a technical math section, so doesn't include the homework template. I know this has been asked before, but none of the other posts have helped me. I cannot for the life of me figure out how to solve a system of equations with complex numbers. Here is a very...

I am new to the world of Science & Mathematics but am eager to learn all I can. I go to my local library and open up books on the topic such as Physics, Engineering and Electronics and there are swathes of formulas all of which I don't understand. I stare at them wondering what keys they must...

I have a question which comes from Rudin's Principles of Mathematical Analysis; specifically, from the introduction. In example 1.1, the author clearly shows that no rational numbers satisfy the equation ##p^2 = 2##. So, I am trying to imagine myself in a scenario in which I am in a time before...

I need a proof that the set of natural numbers with the the relationship of divisibility form a distributive lattice with gcd as AND and lcm as OR. I know it can be shown that a AND (b OR c) >= (a AND b) OR (a AND c) for a general lattice, and that if we can show the opposite, that a AND (b OR...

Homework Statement A program finds the area under the Gaussian Distribution Curve between ±σ using Simpsons Rule. Modify the program to investigate the effect of the number of strips. Do this by using a DO loop in the main program for the following sequence of number of strips (n); n-2, n-4...

Prove the following \sum_{k=1}^n \frac{H_k}{k} = \frac{H_n^2+H^{(2)}_n}{2} where we define H^{(k)}_n = \sum_{j=1}^n \frac{1}{j^k} \,\,\, ; \,\,\, H^2_n = \left( \sum_{j=1}^n \frac{1}{j}\right)^2

Hello! This is not really a homework question, more of a question of what I should do for "homework", but I hope it is acceptable. My question is regarding a method of finding at which point (if at all) two different numbers, when multiplied, reach the same number. For example, how could I...

Homework Statement Find the Geometric image of; 1. ## | z - 2 | - | z + 2| < 2; ## 2. ## 0 < Re(iz) < 1 ## Homework EquationsThe Attempt at a Solution In both cases i really am struggling to begin these questions, complex numbers are not my best field. There are problems before this one...

Homework Statement let z' = (a,b), find z in C such that z^2 = z' Homework EquationsThe Attempt at a Solution let z = (x,y) then z^2 = (x^2-y^2, 2xy) since z^2 = z', we have, (x^2-y^2, 2xy) = (a,b) comparing real and imaginary components we have; x^2-y^2 = a, 2xy = b. Now, this...

Hello, I'm debating between taking either abstract algebra, theory of numbers, or intermediate symbolic logic as a math elective. Does anyone have any idea which would make my life easier?

Hi, Let $n >6$ be a perfect number (A number $n$ is called perfect if $s(n)=2n$ where $s(n)$ is the sum of the divisors of $n$) with prime factorization $n=p_{1}^{e_{1}}p_{2}^{e_{2}}\cdots p_{k}^{e_{k}}$ where $1<p_{1}<p_{2}<\ldots <p_{k}$. Prove that $e_{1}$ is even

Homework Statement suppose in a box there are 20 red, 30 black,40 blue,and 50 white balls.what is the minimum numbers of balls to be drawn, without replacement,so that you are certain about getting 4 red, 5 black, 6 blue and 7 white balls? Homework EquationsThe Attempt at a Solution so there...

Homework Statement 1) 2w+iz = 3; 2) (3-i)w - z = 1 +3i 2wi - z = 3i; 3w - iw - z = 1 + 3i Substract (2) from (1): 2wi - z - (3w-iw-z) = 3i - (1+3i) 2wi -3w +iw = -1 3iw - 3w = -1 3w(i-1) = -1 3w = -1/(i-1) = -0.5i - 0.5 w = -i/6 - 1/6 But the answer is i/6 +...

Hey! :o I am looking at the divide-and-conquer technique for the multiplication of two $n-$bit numbers.First of all, why does the traditional method of the multiplication of two $n-$bit numbers require $O(n^2)$ bit operations?? (Wondering) The divide-and-conquer approach is the following: Let...

This number is rational and normal, right? http://www.wolframalpha.com/input/?i=0.01234567890123456789... edit - You'll have to edit in the ".." because the forum doesn't recognize it as part of the link.

Homework Statement goal: solve for t; all else are constants $$cos(\omega t)=1-e^{-(\frac{t}{RC})}$$Homework Equations noneThe Attempt at a Solution i turned the cos to complex notation & rearranged $$e^{i\omega t}+e^{-(\frac{t}{RC})}=1$$ $$ln(e^{i\omega t}+e^{-(\frac{t}{RC})})=0$$ and i...

It is known that the Goodstein theorem http://en.wikipedia.org/wiki/Goodstein's_theorem which is a theorem about natural numbers, cannot be proved from the standard axioms of natural numbers, that is Peano axioms http://en.wikipedia.org/wiki/Peano_axioms . It is also known that Goodstein...

Homework Statement [/B] Please redraw this figure by assuming that an electron can have spin quantum number ms = +1/2 (arrow up), ms = 0 (marked as "I"), or ms = -1/2 (arrow down). It is important to clearly state your arguments/reasoning. http://s30.postimg.org/jz7tfeha9/wow.png Homework...

In this assignment, you are going to write a function called sortMe that sorts the elements of an array in numerical order from highest to lowest values (descending order) or vice versa (ascending order). The interesting point of the function is that sortMe does NOT re-arrange elements in the...

Can anyone tell me why for example the speed of light is squared in "E=mc^2" ? Also what does square root mean and why is it in certain equations like for example time dilation? What happens if you exclude the square root and the y^x in a equation? I am still studying high school physics, but...

Hey! :o Give a RAM program to read $n$ positive integers followed by an endmarker ($0$) and then print the $n$ numbers in sorted order. I have done the following: Read 1 LOAD 1 STORE 1 LOAD =2 STORE 2 while: JZERO endwhile READ *2 LOAD *2 STORE *2 LOAD 2...

Homework Statement Write down number 1+i and 1+i\sqrt{3} in trigonometry form.[/B]Homework Equations For complex number z=x+iy \rho=|z|=\sqrt{x^2+y^2} \varphi=arctg\frac{y}{x} And [/B]The Attempt at a Solution Ok. For z=1+i \rho=\sqrt{1+1}=\sqrt{2}...

Homework Statement Solve the following complex equation for z: zi = sqrt(3) - i Homework EquationsThe Attempt at a Solution Do I have to equate the real and imaginary parts ?, this is what I tried zi = (x+iy)i = exp(i*log(x+iy))

Let L be the level number of a bipartite graph G, and so L1 be the first level of n1 vertices, L2 be the second level of n2 vertices, ... Lk be the kth level of nk vertices. Then a bipartite graph G12 is created by a combination of L1 and L2, G23 is of L2 and L3,...,Gij is of Li and Lj. The...

Just want to know if there are applications in the derivation of prime numbers. My instructor and the textbook that we are using seems to be obsessed with it, there is at least one problem about deriving prime numbers in each chapter. And also different versions like palindromic prime, emirp...

Q4) Let a and b be real numbers with a < b. 1) Show that there are infinitely many rational numbers x with a < x < b, and 2) infinitely many irrational numbers y with a < y < b. Deduce that there is no smallest positive irrational number, and no smallest positive rational number. 1) a < x <...

Homework Statement [/B] Ally starts at rest with a height H above the ground and slides down a frictionless slide. The bottom of the slide is a height h above the ground. Ally then leaves the slide horizontally, striking the ground a distance d from the end of the slide (where she left the...

Hey! :o I have to find an open and dense subset of the real numbers with arbitrarily small measure. Since the set of the rational numbers is dense, could we use a subset of the rationals?? (Wondering) How could I find such a subset, that the measure is arbitrarily small?? (Wondering)

Homework Statement This problem is very easy, but I'm not sure how best to "prove" it. This part of the question just states: Prove that (1/z)* = 1/(z*) where z* is the complex conjugate of z. Homework Equations The Attempt at a Solution So the complex conjugate of z = x + iy is defined is...

Hey! (Wave) Let the ring of the integer $p$-adic numbers $\mathbb{Z}_p$. Could you explain me the following sentences? (Worried) It is a principal ideal domain. $$$$ The function $\epsilon_p: \mathbb{Z} \to \mathbb{Z}_p$ is an embedding. (So, $\mathbb{Z}$ is considered $\subseteq...

Question: Show that the set of all functions of the form f(x) = ax+b, with a and b real numbers forms a vector space, but that the same set of functions with a > 2 does not. Equations: the axioms for vector spaces Attempt: I think that the axiom about the zero vector is the one I need to use...

Dear all, I have done question 1 of exercise 2.1 from the book Alan F beardon, Abstract Algebra and Geometry. Please answer some of my doubts. Q1. a) Show that √(2/3) is irrational. b) Use the prime factorization of integers to show that if √p/q is rational, where p and q are...

I am confused, since some claims about the first Godel incompleteness theorem and real numbers seem mutually contradictory. In essence, from one point of view it seems that the Godel theorem applies to real numbers, while from another point of view it seems that the Godel theorem does not apply...

I ran into an interesting problem while working on a problem set. Given a $10$-digit number $n$ (for our purpose, we will allow $n$ to have leading $0$'s, so you can treat this as a string of $10$-digits). Define a function $f$ that maps $n$ to another $10$-digit number $m$ written in its...

Hi guys, I sure this is an astonishingly dumb question, but I am new to embedded systems, so don't be too harsh. I am taking embedded systems in final year at uni and working through some introductory tutorial sheets. One question asks; -If two n-bit numbers are added together, what memory...

I think its fairly obvious to most people why a number being rational (or not) is extremely important. But I honestly do not see why being transcendental is as interesting of a property (though its clearly somewhat interesting). What interesting applications are there of knowing a number is...

Hey there, I'm now a Computer Science student (3rd year, 2 more to go) and so far I'm a bit unhappy with my course. Why? Well, I like programming and stuff, but all I'm seeing right now are classes with tons of concepts (Operational Systems concepts, Software Engineering Concepts, AI concepts...

This is just a follow on from this thread, https://www.physicsforums.com/threads/complex-numbers-and-vector-multiplication.509944/ Basically I've noted that, in 2d at least that the complex multiplication of A and B is equal to (A dot conj(B)) + (A cross B)i Would that then mean his initial...

Hi all, f(x) = 3x^2+2x+10 I recognized that this a quadratic and used the quadratic formula. I came up with -1/3+-\sqrt{29}/3. But the answer has a i for imaginary. When I was under the \sqrt{116}, I broke that down, but didn't realize there would be an i Can someone explain that one to me...

(Wave) i have to subtract binary numbers using the method where you take the 1's complement and then the 2's complement. but I am doing something wrong. say for example 11-1. take 1's complement of 1 which is 0 and then take the 2's complement by adding 1 so 0+1=1 and now you go back and add...

I have a comprehensive list of MK5(SAO) and BD-HD numbers with RA2000, DEC2000, Proper Motions and etc. I want to equate the MK5(SAO) and BD-HD numbers with Constellation Designations(delta Ori, gamma Tau), NGC and IC Numbers. I have tried: http://simbad.u-strasbg.fr/simbad/sim-fid...

Homework Statement I want to demonstrate that the numbers that are multiple of a and b at the same time, are the multiples of ab. Let a be 2 and b be 3. In the middle of the proof i get to a point that i have to prove that if 3*k2 is multiple of 2 then k2 is multiple of 2.Homework Equations...

Homework Statement I'd like to separate this function to U(x) + i*V(y) form. It's a homework problem that is asking if it is an analytic function. Searching thru trig substitutions, but looking ahead I don't see much luck... Any suggestions or help is greatly appreciated. Homework...

If $a,b\in \mathbb{R}^{+}.$ Show that $a>b\implies a^{-1}<b^{-1}.$