Numbers Definition and 1000 Threads

This challenge was suggested by jgens. The ##n##th harmonic number is defined by H_n = \sum_{k=1}^n \frac{1}{k} Show that ##H_n## is never an integer if ##n\geq 2##.

Homework Statement Hi there, you can see from my nickname that I am a noob in maths :D. So, here should is one problem that I cannot solve, even though I know some basics of complex numbers. Its the 2nd problem from the revision exercises, so please be gentle :) Homework Equations Find...

1.show that there is no axiom for set union that correspond to "Existence of additive inverses" for real numbers, by demonstrating that in general it is impossible to find a set X such that $A\cup X=\emptyset$. what is the only set $\emptyset$ which possesses an inverse in this sense? 2. show...

Homework Statement Taking step size h = 0.2, use Euler’s Method to determine y(1.6), given that dy/dx = ln(2y+x) ; y(1)=1.2 Record your results to 5 decimal places at each step. Homework Equations N/A The Attempt at a Solution My question is to do with the method, not the...

Does any known rational number look irrational at first glance but when calculated to 100s or 1000s of digits actually resolve into a repeating sequence? Have they deceived mathematicians?

consistently thought of as actually emergent functions that take the desired accuracy as input? As them being numbers would imply the apparently paradoxical concept that infinite complexity can exist in a finite volume of space.

in the following exercises, assume that x stands for an unknown real number, and assume that $x^2=x\times x$. which of the properties of real numbers justifies each of the following statement? a. $(2x)x=2x^2$ b. $(x+3)x=x^2+3x$ c. $4(x+3)=4x+4\times 3$ my answers a. distributive property b...

Find the real numbers $c$ for which there is a straight line that intersects the curve $y=x^4+9x^3+cx^2+9x+4$ at four distinct points?

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 11) Find the vertex of f(x) = -2x^2 - 8x + 3 algebraically. My Answer: (-2,0) 12) Multiply and simplify: (6 - 5i) (4 + 3i) My Answer: 39 - 2i

Author: G. H. Hardy, Edward M. Wright Title: An Introduction to the Theory of Numbers Amazon Link: https://www.amazon.com/dp/0199219869/?tag=pfamazon01-20

http://www.dkriesel.com/en/blog/2013/0802_xerox-workcentres_are_switching_written_numbers_when_scanning? http://realbusinessatxerox.blogs.xerox.com/2013/08/06/always-listening-to-our-customers-clarification-on-scanning-issue/?CMP=SMO-EXT#.UgFXIiblAW2 It's looks like compression hash collision...

HI folks , working on Stirling nums , how to prove ? s(n,3)=\frac{1}{2}(-1)^{n-1}(n-1)!\left(H_{n-1}^2-H_{n-1}^{(2)}\right) where we define H_k^{(n)}= \sum_{m=1}^k \frac{1}{m^n} I don't how to start (Bandit)

Hello. I have some problems with proving this. It is difficult for me. Please help me.:confused: "For arbitrary irrational number a>0, let A={n+ma｜n,m are integer.} Show that set A is dense in R(real number)

Is it possible to have an infinite string of the same number in the middle of an irrational number? For example could I have 1.2232355555555.....3434343232211 Where their was an infinite block of 5's. Then I was trying to think of ways to prove or disprove this. It does seem like it might...

Can anyone point me to some references? Greetings All. I am searching for a couple of numbers, but my books are packed away and stored somewhere due to moving. I was hoping someone could provide the best accepted observational values and the reference sources for those numbers. First I am...

According to Mahan, phonons or photons doesn't have occupation number. Is this true?http://i.tinyuploads.com/MBwW0j.jpg

The question asks me as follows: "What is the maximum number of comparisons required for a list of 6 numbers? Is the correct answer as follows: The maximum number of comparisons required for a list of 6 numbers is 5 comparisons. If this is not right, then can somebody please help and explain...

Can somebody tell me which example is right when a question that is given to me says to bubble sort a list of numbers 7, 12, 5, 22, 13, 32? I found two examples and one was with a graph that included Original List, Pass 1, Pass 2, Pass 3, Pass 4, Pass, 5, and Pass 6, the numbers with 7 on one...

in this problem we drop the use of parentheses when this step is justified by associative axioms. thus we write $\displaystyle x^2+2x+3\,\,instead\,\,of\,\,\left(x^2+2x\right)+3\,or\,x^2+\left(2x+3\right)$. tell what axioms justify the statement: 1. $\displaystyle...

justify each of the steps in the following equalities. i don't know where to start. what i know is i have to use properties of real numbers. please help! 1. $\displaystyle \left ( x+3 \right )\left(x+2\right)\,=\,\left ( x+3 \right )x+\left ( x+3 \right )2\,=\,\left ( x^2+3x \right )+\left (...

Explain why the sum, the difference, and the product of the rational numbers are rational numbers. Is the product of the irrational numbers necessarily irrational? What about the sum? Combining Rational Numbers with Irrational Numbers In general, what can you say about the sum of a rational...

Homework Statement Taken from Spivak's Calculus, Prologue Chapter, P.28 b) Notice that all numbers in Pascal's Triangle are natural numbers, use part (a) to prove by induction that ##\binom{n}{k}## is always a natural number. (Your proof by induction will be be summed up by Pascal's...

The real numbers x and y satisfy x^3-3x^2+5x-17=0 and y^3-3y^2+5y+11=0. Determine the value of x+y.

Prove that all polynomials with real coefficients, having complex roots can occur in complex conjugates only. It's easy to prove in a quadratic equation... ## ax^{2} + bx + c = 0 ## ## \displaystyle x = \frac{-b \pm \sqrt(b^2 - 4ac)}{2a} ## But how to prove the same in general? Please...

Hi, I have some theories about physical facts derived from the size of powers in physics, compared to the first fraction of an irrational number. I do not know if this is redundant with present day science, but I am curious about it. Regards, Justin

I have a list of chaos numbers Average each 10 results as display below Sum each 10 results as display below Average the 30 results as displayed below here’s my question: I believe that I can see as the average goes up we have larger sums So I think I can predict something from the last...

Hi everyone, I've been bumping on this problem for a while and wondered if any of you had any clue on how to approach it. My question is whether the following equality is possible for 4 distinct prime numbers : PxPy + Pw = PwPz + Px where Px, Py, Pw, Pz are odd prime numbers, and each...

Determine all 3 digit numbers P which are divisible by 11 and where \frac{P}{11} is equal to the sum of the squares of the digits of P.

Homework Statement An eight digit number is a multiple of 73 and 137. If the second digit from the left of the number is seven, find the 6th digit from the left of the number. Homework Equations N.A. The Attempt at a Solution I don't know any clear method for solving this problem...

"Simple" Line Integral in Complex Numbers If anyone could please double-check my final result for this question it would be greatly appreciated. Rather than write out each step explicitly, I'll explain my approach and write out only the most important parts. "[E]valuate the given...

Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression: Z = Z1 X Z2 / Z1 + Z2 If Z1 = 4 + j10 and Z2 = 12 - j3, calculate the impedance Z in both rectangular and polar form. Homework Equations Multiplication and division of complex...

you can list and match up all rational numbers with irrational numbers this way.. lets say i have an irrational number 'c'. Rational->Irrational r1->cr1 r2->cr2 . . . rn->crn There exists an irrational number that is not on this matching, (not equal to any of the crx's) this...

I'll write down what i know and point it out if I'm wrong.So we normalize the wave function because -∫|ψ(x,t)|^2dx should always be equal to 1 right? Has this anything to do with transition from ψ to ψ^2?

I can find for example Tan(2x) by using Euler's formula for example Let the complex number Z be equal to 1 + itan(x) Then if I calculate Z2 which is equal to 1 + itan(2x) I can find the identity for tan(2x) by the following... Z2 =(Z)2 = (1 + itan(x))2 = 1 + (2i)tan(x) -tan(x)2 = 1...

we all know Fibonacci numbers,just for information they are the numbers of sequence whose t_n=t_{n-1}+t_{n-2} and t_0=t_1=1 \text{PROVE THAT:} $$1+S_n=t_{n+2}$$ where, $$S_n=\text{sum up-to n terms}$$ $$t_n=\text{nth term}$$

Please I have read texts about changing the bases of numbers but still I have difficulties in doing, may s'body instruct me for example.. Change 3145 to base 8 Thanx..

This is a solved problem and I am having a hard time working through the answer. Question . Choose two numbers uniformly but without replacement in {0,1,...,10}. What is the probability that the sum is less than or equal to 10 given that the smallest is less than or equal to 5? Answer...

I guess the best way to start this is by admitting that my conceptual understanding of the Cauchy-Schwarz Inequality and the Lagrange Identity, as the title suggests, is not as deep as it could be. I'm working through Marsden's 3e "Basic Complex Analysis" and it contains a proof of the Cauchy...

I have found some trouble in trying to prove this question.please help mw with that. Q1) If (a+b)/2 is a rational number can we say that a and b are also rational numbers.? Justify your answer. I have tried the sum in the following way. Assume (a+b)/2=p/q (As it is rational) Lets...

I keep hearing even by very brilliant Engineering co-students that they require a lot of text-based theory before going into numbers. However, there is also a good deal of good Mathematicians that state they can think in numbers, requiring theory, but not strictly in a text form, or at least an...

I was recently given the challenge to take a string of numbers (ages) and + x - / to equal another number (age). As part of the challenge each number can only be used once and you must only use numbers here to do multiply, add to, subtract from or divide by. NUMBERS 7 9 11 37 45 45 47 75...

Sorry about the intriguing title; this is just a continuation of the discussion in https://driven2services.com/staging/mh/index.php?threads/5216/ from the Discrete Math forum. The original question there was how to introduce mathematical induction in a clear and convincing way. Since the current...

There are lots of examples of numbers where "is it a rational number" has been an open question for a while before being proved as not being rational. Pi and e being famous examples. Some of them are still open, like pi+e, or the Euler-Mascharoni constant, but I think the general consensus is...

Can the arithmetic mean of a data set of complex numbers be calculated? if so, can the method be demonstrated?

Hi All, I'm trying to figure out the probability of winning the lotto. 8 numbers are drawn between 1 and 45. The first six are 'winning' numbers, the last two are the 'supplementary' numbers. To win division 1, you need to get all six winning numbers right: \binom {45}6 = 8145060 Hence...

Find all 10-digit numbers ##a_1a_2a_3a_4a_5a_6a_7a_8a_9a_{10}## (for example, if ##a_1= 0##, ##a_2## = 1, ##a_3 = 2## and so on, we get the number 0123456789), such that all the following hold: - The numbers ##a_1,~a_2,~a_3,~a_4,~a_5,~a_6,~a_7,~a_8,~a_9,~a_{10}## are all distinct - 1 divides...

I'm trying to understand the notation (3, 1, 2/3) for the up quark and (3, 2, 1/6) for the left-handed up and down quarks... Is the first number related to SU(3), the second SU(2) and the third I believe is the hyper charge... Not sure what the significance is of the first two numbers... I...

Homework Statement Graph the following numbers on a complex plane. A) 3-2i B)-4 C)-2+i D)-3i D)-1-4i Can smomeone help me how to get started on this question? I'm not sure what it wants me to do

How do you prove/disprove the following: For any integer n higher then 1, there exists at least one prime number in interval [n+1, n^2]?

Homework Statement If ##f## is continuous on ##[a,b]## and ##f(a) < f(b)##. Prove that there are numbers ##c, d## with ##a \le c < d \le b## such that ##f(c) = f(a)## and ##f(d) = f(b)## and if ##x \in (c,d)## then ##f(a) < f(x) < f(b)##. Homework Equations The Attempt at a...