Numbers Definition and 1000 Threads

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...

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...

(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 $a>b\implies a^{-1}<b^{-1}.$

Homework Statement "Put each of the following into the form Acos(ωt+θ)..." (a.) 4ejt+4e-jt Homework Equations Euler's Identity: ejθ = cos(θ)+jsin(θ) Phasor Analysis(?): Mcos(ωt+θ) ←→ Mejθ j = ej π/2 Trignometric Identities The Attempt at a Solution I attempted to use phasor analysis to...

Without any rough work

Find the sum of all real numbers $a$ such that $5a^4-10a^3+10a^2-5a-11=0$.

Hi, I'm trying to figure out how to compute probability related to a problem I am tackling for work, and I think I have a handle on how to do it with smaller numbers, but no idea how to approach it for larger numbers. (And I need to explain the answers to a judge in simple terms). So here is...

Homework Statement Suppose one extracts a ball from a box containing ##n## numbered balls from ##1## to ##n##. For each ##1 \leq k \leq n##, we define ##A_k=\{\text{the number of the chosen ball is divisible by k}\}.## Find ##P(A_k)## for each natural number which divides ##n##. The Attempt...

Find all irrational numbers $k$ such that $k^3-17k$ and $k^2+4k$ are both rational numbers.

I know this post is in the topology thread of this forum, for group theory, this seemed like the reasonable choice to post it in. I realize group theory is of great importance in physics and I'm trying to eventually understand Emmy Noether's theorem. I'm learning group theory on my own, and...

This is, perhaps, more a question of philosophy of math rather than math itself. While it may be trivial to most people fluent in math, it was a bit surprising for me to learn recently that the set of algebraic numbers is countable. However, I quickly realized why that is: Each algebraic number...

Is it purely coincidental that the internal symmetry related flavor quantum numbers(like isospin and weak isospin) and the spacetime symmetry related spin quantum number have SU(2) as underlying group? They refer to seemingly unrelated things but it is remarkable how ubiquitous SU(2) is.

Do we use imaginary numbers just in the intermediary steps of a predictive theory? For example, in QM, in order to make predictions in the real world, you square the wave function. The wave function might have have all the information, but in order to predict something you must operate on it to...

Hello! I am very unsure of how to solve this question. The question states z^2=a+bi, where a and b belong to real numbers. Find all possible solutions for z. I think that the solution includes the De Moivre's formula, however I am very confused by how to do this or what the formula means...

Hi! Can you tell me how the theta changes into theta minus pi/2? Can you show me, please?

Homework Statement A) how many numbers have distinct digits from 1000 to 9999? B) how many odd numbers have distinct digits from 1000 to 9999? The Attempt at a Solution a) the first place value has choices from 1-9, the second has choices from 0-9 but one number was used in...

after it was found out that the first 9 pi digits 141592653 result in the end sum of 9, i searched for its iteration in the large digit chain of pi. after scanning stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt it was found that .141592653 occurs at the 427238911 place and ends on the...

[SIZE="4"]Definition/Summary A perfect number is a number which is the sum of its proper divisors (half the sum of its total divisors). Even perfect numbers are a Mersenne prime times a power of two; odd perfect numbers are not known to exist. [SIZE="4"]Equations Sum-of-divisors...

[SIZE="4"]Definition/Summary Let \mathbb{R} be the set of all real numbers. We can extend \mathbb{R} by adjoining two elements +\infty and -\infty. This forms the extended real number system. In notation: \overline{\mathbb{R}}:=\mathbb{R}\cup \{+\infty,-\infty\} The extended real...