Numbers Definition and 1000 Threads

How do we distinguish the decimal expansions of irrational numbers, and products thereof, from random sequences? Is an arbitrarily specified (not claimed to be perfectly randomly selected) numeric string, e.g. the 10^10th to 10^19th digits of the decimal extraction of the square root of 2.2...

Hi. If you have seen the above image which shows a parabola then you can also see that there is a colored portion of the parabola that have solution in "another dimension" - the "another dimension" can give me new numbers to form a solution of a function like f(x) = x2 + 1. 1. Is this "another...

Homework Statement Let ##x\in\Bbb{R}## such that ##x\neq 0##. Then ##x=LIM_{n\rightarrow\infty}a_n## for some Cauchy sequence ##(a_n)_{n=1}^{\infty}## which is bounded away from zero. 2. Relevant definitions and propositions: 3. The attempt at a proof: Proof:(by construction) Let...

I need to explain to a student the meaning of number systems. I try to explain him that it is like a family of numbers that have some proprity. If one have an idea to expalin him the term, it will be helpful. I remind note about the term: A number system can be complex system number, rational...

I stumbled upon these numbers on my test recently. It is raelly basic stuff, but i want to know, what would actually happen if such thing happened in the real world. We basically have a ball made of 20Kg of "person". And it it accelerates at 1.8*10^5 m/s² for 1/30 of a second reaching 6000 m/s...

DSP Guide .com has the highly rated textbook for digital signal processing. Chapter 30 pg 561 on Complex Numbers http://www.dspguide.com/ch30.htm (chapters are free to download) Hes talking about representing sinusoids with a complex number. Author states "Multiplying complex numbers A and...

A set of numbers 1,2,...,4N gets randomly divided into two groups with equal amount of numbers. Calculate the probability:7 a) Each group has an equal amount of odd and even numbers, b) All numbers that are divisible by N, to fall in only one of the groups, c) All numbers that are divisible by...

I understand how we associate high energies with small wavelengths and thus small distance scales, but we also tend to associate small distance scales with ordinary quantum mechanics, and hence low quantum numbers (low energy). Also, many high-energy processes are active across large distance...

00110100 00110011 00100000 00110100 00111001 00100000 00110100 00110011 00100000 00110100 00110001 00100000 00110100 00110100 00100000 00110100 00110001 00100000 00110010 00110000 00100000 00110011 00110011 00100000 00110011 00110011 00100000 00110011 00110000 00100000 00110011 00110001

Homework Statement I want to know how to insert a 2's complement number into a larger register and keep the same value. I would like to know of some pitfalls that I might run into using a generalized method, if any. Homework EquationsThe Attempt at a Solution If I have say 1 in a 3 bit...

Problem statement: In a lottery, players win a large prize when they pick four digits that match, in the correct order,four digits selected by a random mechanical process. A smaller prize is won if only three digits are matched. What is the probability that a player wins the small prize...

I have a problem to put the complex number in mode (1000/3, ∠36.87), apparently the division simbol gives some syntax error

√2 is irrational but √22 is rational Is there any way to know if given some irrational number α, if αn is rational for some n? Or can it be proven that ∏n or en are irrational for all n?

I just need to know. Why exactly what's the complex number i=√–1 put in the wave function for matter. Couldn't it have just been exp(kx–wt)?

Hello, I want to write on the bars inside the subplots of a seaborn.FacetGrid a number that represents their height on the y-scale. How can I do that? Suppose the code for the FacetGrid is g = sns.FacetGrid(df, row = 'feat1', size = 5, aspect = 2) g = (g.map(sns.countplot, 'feat2', hue =...

Homework Statement [/B] The proposition that I intend to prove is the following. (From Terence Tao "Analysis I" 3rd ed., Proposition 6.1.7, p. 128). ##Proposition##. Let ##(a_n)^\infty_{n=m}## be a real sequence starting at some integer index m, and let ##l\neq l'## be two distinct real...

Homework Statement if ## x + iy## = ## \frac a {b+ cos ∅ + i sin ∅} ## then show that ##(b^2-1)(x^2+y^2)+a^2 = 2abx##Homework EquationsThe Attempt at a Solution i let ## ... ##x + iy = ## \ a(b+cos ∅ - i sin ∅)##/ ##(b + cos ∅)^2 + sin^2∅ ##...got stuck here... alternatively i let ## b +...

Quick question. While going over complex numbers in my book, I think I came across a typo and I wanted to be sure I had the right information. In the paragraph going over dividing complex numbers, my book has: ##|\frac{z_1}{z_2}|=|\frac{z_1}{z_2}|## That's obviously true. Should that be...

Anybody can help me?? The problem is when the value of (r1o = r, and r2o=r), the result will be infinite,,,what the the probably test for this case?? I can't test floating point numbers for equality ( if r == 0.5 and r == -0.5). But, when running this program without test floating point, it...

Regarding the recent discovery by Ken Ono and colleagues of the fractal structure of partition numbers for primes: a great lever of intuition would be to see a diagram, or any presentation of the numbers that reveals this fractal structure. Perhaps the fractal structure is somehow hidden in a...

Say you have an un-damped harmonic oscillator (keep it simple) with a sine or cosine for the forcing function. We can exploit Euler's equation and solve for both possibilities (sine or cosine) at the same time. Then, once done, if the forcing function was cosine, we choose the real part as the...

Hi I was playing around with various sets of numbers while thinking about optimizing neural networks and was wondering if numbers derived as below have a specific name given a set: [7, 5, 3, 8, 1, 5] the difference set is [-2, -2, 5, -7, 4] the difference set for that is [0, 7, -12...

I was wondering and this might be a stupid question... I have approx. 200+ armatures with a GAS number stamped on them Like "GAS 3237". There are probably 20 different numbers or so. Where can I find a list of what these numbers are or mean?

Suppose there are numbers 1, 2, 3, 4, 5, 6, 7, 8. Question is: How many ways can we pick 4 non adjacent numbers (order does not matter)? Now, as per formula it is C(n-r+1,r) = C(8-4+1,4) = C(5,4)=5. Crosschecking, I could find only four: 1,3,5,7 : 1,3,5,8 : 1,4,6,8 : 2,4,6,8 Not...

Homework Statement A single electron atom has the outer electron in a 4f1 excited state. Write down the orbital and spin angular momentum quantum numbers and the associated magnetic quantum numbers for this state. Homework Equations I don't think there is any relevant equations. I think it...

Homework Statement Use NVA to solve for ##i##. Enter your answer in polar form with the angle in degrees. Homework EquationsThe Attempt at a Solution My nodes are as follows: ##V_1## on the left middle junction, ##V_2## is the junction in the very center, and ##V_3## is the junction on the...

Homework Statement Identify the element oxidized and the element reduced, in this chemical equation: H3AsO4+H2S ---> H3AsO3+S+H2OHomework Equations none The Attempt at a Solution [/B] So I have learned the rules for oxidation numbers: 1. The oxidation number of an element is always 0...

This might not be the usual kind of question posted here, but I am trying to solve a geocaching puzzle. The puzzle is called "An Irrational Location", and the only information provided is more or less the following: ~~~~~ No rational person should attempt to visit the posted coordinates Cache...

I am searching for a shortcut in the calculation of a proof. The question is as follows: 2.12 Prove that: $$|z_1|+|z_2| = |\frac{z_1+z_2}{2}-u|+|\frac{z_1+z_2}{2}+u|$$ where $z_1,z_2$ are two complex numbers and $u=\sqrt{z_1z_2}$. I thought of showing that the squares of both sides of the...

Homework Statement A state of a system of many noninteracting particles can be specified by listing which particle is in which of the accessible single particle states. In each microscopic state we can identify the number of particles in a given single particle state ##k##. This number is...

My residue is wrong. What is the solutions and the steps to achieve it ?

I came across the following argument that attempts to show that the notion of infinite decimal numbers is incoherent. Try adding these two numbers:05.4123482100439884... 16.3482518100560115... ___________________ 21.760600020?999999...By the Axiom of Choice, "There exist arbitrary infinite...

Multiplying big numbers is a very common application of the FFT, and as such, there are many papers on the subject available online. However, these papers all use sophisticated algorithms where a simple one seems to work. My question is, what's wrong with the simple algorithm: Multiplication...

In the Debye-Huckle Equation there are a few z terms referring to atomic number. But what if the ion is polyatomic? Is it just the sum of the atomic numbers or is there something else that needs to be used? Never mind, it's the charge number not the atomic number.

"Quantity in a group" If you have 6 apples and you subtract 4, then you have 2 apples left "in the group". "Quantity in an Indexed group" I'm a computer programmer - I manipulate arrays of data (a.k.a. matrix) In a math formula format: x1, x2, x3... xn (as a side note - in a computer format...

Example: Say I want to calculate the evaporation rate of water and so I record the mass of some amount of water every 30 seconds for 5 minutes. The uncertainty in the scale is inherently .0001g and so that would be the uncertainty in the mass of any individual measurement, but how would I...

Homework Statement I don't understand the lemma. Homework EquationsThe Attempt at a Solution Isn't all prime number not a product of primes? The lemma doesn't make sense to me... Moreover, if m=2, m-1 is smaller than 2, the inequality also doesn't make sense. Please help me

Homework Statement My teacher gave our class this problem to do Two players take turns placing an unused number from {1; 2; 3; 4; 5; 6; 7; 8} into one of the empty squares in a 2 by 4 array. The game ends once all the squares are tiled. The 1st player wins if the product of the numbers in the...

I was just playing with some numbers and I noticed this weird pattern. Because of the complexity of the problem I am finding it hard to describe it in words. But you can easily understand it by looking at the picture. Whenever I form a series by adding numbers in Arithmetic progression to the...

Homework Statement Fix ##n,m \in \mathbb{N}##. The set of polynomials of the form ##a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0## satisfying ##|a_n| + |a_{n-1}| + \cdots + |a_0| \le m## is finite because there are only a finite number of choices for each of the coefficients (given that they...

I've read that it is unsatisfactory to consider infinitely many basis vectors to span an infinite dimensional space. For example, for the infinite dimensional Hilbert space, {e1,e2,e3...} we could use this to make an arbitrary infinite tuple (a,b,c,...). If this is looked down upon, then why are...

The total number of numbers less than 1000 and divisible by 5 formed with 0,1,2,...9 such that each digit does not occur more than once in each number is what? Solution:Divisible by 5 ==> number ending in 0 or 5. Number of ways with no repeated digit: [0, 9]---> ends in 5 = 1 way (only 5...

Determine all prime numbers $p$ such that the total number of positive divisors of $A = p^2 + 1007$ (including $1$ and $A$) is less than $7$.

Hello I have used a random number generator to create a list of uniformly random numbers, between 0 and 1. The usual check that I do is sorting the list, and histograming the difference between the following and the previous one. The shape of the histogram should follow an negative...

Why should a person prefer irrational coordinate system over rational? My friend stated that its because most lines such as ##y=e## cannot be plotted on a rational grid system. But that cannot be true since ##e## does have a rational number summation ##2+1/10+7/100...## which can be utilised to...

Hi, I just have a few questions I'm struggling to find straightforward answers to online. The 4 quantum numbers of an electron in an atom describe the energy level, shape and suborbital of the orbital, and the fourth assigns a value to the electron's spin. Question 1) why is it in lone atoms...

Homework Statement Prove that algebraic numbers are denumerable Homework EquationsThe Attempt at a Solution This is a very standard exercise, but I haven't looked at its proof and want to see if I can prove it myself. With each element ##(a_n, a_{n-1},...,a_1,a_0 ) \in \mathbb{N}^n## we can...

Homework Statement ##\mathbb{R} \setminus C \sim \mathbb{R} \sim \mathbb{R} \cup C##. Homework EquationsThe Attempt at a Solution I have to show that all of these have the same cardinality. For ##\mathbb{R} \cup C \sim \mathbb{R}##, if ##C = \{c_1, c_2, ... c_n \}## is finite we can define ##...

Homework Statement (1) Prove that there exists no smallest positive real number. (2) Does there exist a smallest positive rational number? (3) Given a real number x, does there exist a smallest real number y > x? Homework EquationsThe Attempt at a Solution (1) Suppose that ##a## is the...

Hello everyone. Iam reading about complex numbers at the moment ad Iam quite confused. I know how to use them but Iam not getting a real understanding of what they actually are :-( What exactly is the imaginary part of a complex number? I read that it could in example be phase... Thanks in...