Numbers Definition and 1000 Threads

Homework Statement Hey everyone I couldn't really fit a good description into the title. Basically here's what it is. Consider an atom in which all the states with principal quantum number n = 3 and angular momentum quantum number l = 2 are occupied by electrons (this is called a closed...

Homework Statement . Prove that ##\{x_n\}_{n \in \mathbb N} \subset \mathbb R## doesn't have any convergent subsequence iff ##lim_{n \to \infty} |x_n|=+\infty##. The attempt at a solution. I think I could correctly prove the implication ##lim_{n \to \infty} |x_n|=+\infty \implies## it...

Homework Statement Given two positive numbers calculate their weighted average(Note: This is not actually a homework question, but silly me have doubts, so I put it in this category) Homework Equations Two given positive numbers a,b. No separate weights are available to weigh each...

Homework Statement use Eular's formula to find the greatest prime number under : If I wasn't forced to use this method I would set up a program to loop through checking for primes Homework Equations F(n) = n^2 + n + 41(0 to 39) or depending on your PoV f(n) = n^2 - n + 41(1 to...

Hello. I contribute a small study: For : a, b, c, d, e, n \in{N} / a^3=b^3+c^3+d^3+e^3 Family 1ª) a=3n^6+3n^3+1 b=3n^6+3n^3 c=3n^4+2n d=n e=1^3 Example: For \ n=1 \ then: 7^3=6^3+5^3+1^3+1^3 For \ n=2 \ then: 217^3=216^3+52^3+2^3+1^3 For \ n=3 \ then: 2269^3=2268^3+249^3+3^3+1^3 For...

I'm using the Modern Physics by Tipler (6th edition) book. In sec 7.1 it talks about the first excited state being either E_(112 ) E_(121 ) E_(112). My question is what is the process of finding the n_(1),n_(2),n_(3) quantum numbers ? How i understand you pick random values and from their find...

Homework Statement Consider a spinless particle in a central field in a state described by: \psi_a(r) = (x^2 - y^2) e^{-\alpha r^2} \psi_b(r) = xyz e^{-\alpha r^2} Find quantum numbers l and l_z (or their appropriate superposition) for these two cases. Homework Equations...

How is it possible that the more numbers in an equation, the worse I become at it, where the more variables there are, the easier it is and the faster I can do it? Is there possibly a universal law regarding this, or am I alone in suffering this condition? I love math, but as it turns out, I...

Question 1) Write ⊆ or ⊄: {x/(x+1) : x∈N} ________ QNOTE: ⊆ means SUBSET ⊄ means NOT A SUBSET ∈ means ELEMENT N means Natural Numbers Q means Rational Numbers Question 2) Which of the following sets are infinite and uncountable? R - Q {n∈N: gcd(n,15) = 3} (-2,2) N*N {1,2,9,16,...} i.e...

Homework Statement The statement that is purported to be true is \frac{a/b}{c/d} = \frac{ad}{bc}Homework Equations The Attempt at a Solution So, I am going along with my proof, and I believe it to be going nicely. However, there is one step that I am unsure of: \frac{\frac{a}{b} d}{c} =...

Hello All, I am having 1000 consecutive numbers always starting with 1, and there could be upto 24 missing numbers from the list. My question is, what pieces of information should I have in order to find out those missing numbers. So far I came up with, 1. Sum of missing numbers. 2...

I am confused if complex numbers really are vectors. They seem to behave as vectors in addition, but not in multiplication. So why are the complex numbers defined to be vectors although they don't follow the same principles always. Another confusing thing for me is the "complex vector"...

Hello, I have an array of length M. Some of the indices are non-negative. I need to derive a function/analytic expression (preferably linear or convex) that finds the span of indices for which the indices are non-negative. Example: Let p denote the desired vector. Let, p = [0 0 0.3 2.6...

After all, numbers are part of the universe. :biggrin:

Hello everyone. Thanks for this amazing forum. I hope I can be forgiven for asking for a software problem rather than a topic specific puzzle. I am looking and happy to pay for a downloadable program I can run from my desk top which will return all possible combinations of numbers for...

At approx. step 46000 the following code puts "Inf" out, but I can't understand why since it multiplies by itself a value smaller than 1. The sin is ok, but the loop for the power fails : #include<stdio.h> #include<math.h> double power(double x, int n) { double result=1.0; for(int...

I'm modelling the Diesel cycle using excel and I'd like to have the 4 different states numbered on my P-v diagram. I can mark these four points using shapes, but I'm not sure how to do it using numbers instead of these markers. Can this be done?

I have been reading about dimensionless numbers. My question is: are there any natural dimensionless numbers? All seem to be either equations, like the fine structure constant, or ratios, like β - mass/mass. 22 of the 26 standard model inputs are mass related and only become dimensionless...

Which is the best book on complex numbers? I'm new to this topic so I would like to begin my study with the basics. I prefer books that deal with concepts in a great detail for a better understanding. The book must also contain good problem sets(high order thinking) for practise. I'm aiming to...

Homework Statement If f'(x) = x^2(x-1)^2(x-3)^2, how many local extrema does f(x) have? Homework Equations Extrema occur at critical points. Critical points are values of x such that f'(x) = 0 or = ±∞ The Attempt at a Solution Not all values that zero the derivative are critical points...

Homework Statement I'm trying to determine the number of critical numbers for the function (3x-x^3)^(1/3). Homework Equations Critical numbers are where the derivative of the function is = 0 or does not exist. Critical numbers must also exist within the domain of the function. The...

C++-- while-loop Homework Statement calculate the 3 largest number of a sequence Homework Equations you ask the user to input a sequence of numbers, and enter the value 0 to stop entering numbers. c++ The Attempt at a Solution i managed to calculate the the maximum of the series of...

For instance, math 101 is beginning algebra, math 102 is intermediate, 103 is a reasoning course, 109 and 110 are both college algebra, but 109 comes with "modeling" and either are fine but one is preferred over the other. I just want math out of the way, and 109 is the only thing that fits my...

Homework Statement Given: sin(x) = \frac{e^{ix}-e^{-ix}}{2} Show that sin(x) can be written as: sin(x) = \sum_{n=0}^n \frac{x^{(2n+1)}}{(2n+1)!} Homework Equations e^x = \sum_{n=0}^n \frac{x^{n}}{(n)!} The Attempt at a Solution I'm unsure how to treat the imaginary number in...

Other than the fact that prime numbers are infinite?

Thank you for viewing my thread. The following is a problem from my homework that is submitted online. I have already exhausted my attempts, but I'm curious as to where I went wrong. I would appreciate if someone could lead me towards the solution. Homework Statement Find the critical...

Homework Statement Give a possible set of values of the four quantum numbers for all the electrons in boron atom and a nitrogen atom if each is in the ground state. I know the principles behind this. It comes from Zumdahl's Chemistry textbook (ninth edition, p. 345, number 95). The...

I was thinking that if you could use quaternions to rotate an object using quaternion algebra that there might be a way to rotate an object using complex numbers in some fashion. I was looking at quaternion rotation of a vector and the amount of operations seemed to be a lot. Of course it levels...

I need to prove that $$H_n = \ln n + \gamma + \epsilon_n $$ Using that $$\lim_{n \to \infty} H_n - \ln n = \gamma $$ we conclude that $$\forall \, \epsilon > 0 \,\,\,\, \exists k \,\,\,\, $$ such that $$\,\,\, \forall k \geq n \,\,\, $$ the following holds $$|H_n - \ln n -\gamma | <...

Why do we represent waves as complex numbers? Why won't real suffice? Thanks for any help.

Homework Statement 1) Apparently it's a true statement that the quantum numbers 2, 0, 0, 1/2 can apply to any of Cl's electrons. But chlorine's electron configuration is [Ne]3s^2 3p^5. What happened to the n = 3 electrons? 2) How many valence electrons can a ground state oxygen atom have...

A) I understand that complex numbers come in the form z= a+ib where a and b are real numbers. In the special case that b = 0 you get pure real numbers which are a subset of complex numbers. I read that both real and imaginary numbers are complex numbers so I am a little confused with notations...

Homework Statement I am to consider the Zeeman Effect. I need to calculate the energy level shifts for a given magnetic field corresponding to different quantum numbers. I'm having a hard time knowing when a quantum number Q should be interpreted as just Q or as (Q, Q-1, ..., 0, ..., -Q)...

Convert the following numbers to their floating point binary equivalent. Can someone check my work? a) 18.25 so I got 10010.01 I couldn't find an online conversion calculator anywhere. can you also check my answer for this one? b) 1027.375 I got 10000000011.010

1111010 x 1001 is a negative * a negative so I should get a positive right? which I got 0001001010. BUT, if it's -122 x -9 = 1098. How come I get a positive number that doesn't equal 1098. Aren't you supposed to disregard the most left bit if it's more numbers than your original like wouldn't...

[Mentor's note: This post does not use the template because it was originally posted in a non-homework forum. I moved it here instead of deleting it and asking the poster to re-post, because he has already shown a reasonable amount of effort.] I am having a bit of trouble with this homework...

Perform the following operations involving eight-bit 2's complement numbers and indicate whether arithmetic overflow occurs. 1) 01110101 + 11011110. So I have a +Positive + a -Negative number. So I just added normally, and got the result of 01010011. I realized before I started the problem I...

Homework Statement A Solid rod with .375 in. D sits glued in the hole with .38 in. D. There is glue only on the annulus of the rod. A force is applied to the back side of the rod until the glue bond is fully sheared and the rod falls out. Find the shear stress Homework Equations...

From numbers 1 to 10 find the probability the number chosen is even number or a multiply of 3 Here in this question what mean by (multiply of 3)

I don't understand something. Perform the following operations involving eight-bit 2's complement numbers and indicate whether arithmetic overflow occurs. If I have $$ 01110101 +11011110 $$ I know that the second term is negative because there is a 1 in front. Now, because it is negative...

Perform the following operations involving eight bit 2's complement numbers and indicate whether arithmetic overflow occurs. 1. 00110110 + 01000101 = 01111011 Overflow: there is none because we are adding to positive numbers. Did I do this correctly?

Homework Statement Show that (1+i) is a root of the equation z4=-4 and find the other roots in the form a+bi where (a) and (b) are real.Homework Equations Using De Moivre's Theorem zn=[rn,nθ] Modulus(absolute value of z) = 4 Argument = ? The Attempt at a Solution r4=4 → r = (4)^(1/5)...

Hi MHB, [FONT=HelveticaNeue] This problem has given me a very hard time because I have exhausted all the methods that I know to figure out a way to find for the values for both a and b but no, there must be a trick to this problem and I admit that it is a question that is out of my reach...

Hi there, As my Maths skills suck, I'm not entirely sure if I've worked out the following correctly: Using the combinations calculator - http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html - the total amount of possible numbers drawn in a game (80), and how...

Convert the decimal numbers 73, 1906, -95, and -1630 into signed 12 bit numbers in the following representations: a) Sign and magnitude b) 1's complement c) 2's complement So 73 is easy. It's positive so I know it starts with 0. so I know that 73: sign and mag = 000001001001, 1s complement =...

Determine the decimal values of the following 1's complement numbers: So i understand that if the left most bit number is a 1 it is a negative, and if it is a 0 it is poisitive. But my question is why do they start out with -511 when $$2^9$$ is obviously -512. Why are they adding 1 to it...

Determine the decimal value of the following unsigned number. So here was the first one I did. Which is easy. I completely understand this one. (3751)8 = 2025 I know this because: $$1 + 5 * 8^1 + 7 * 8^2 + 3 * 8^3 = 2025.$$ But then they gave me this one. b) (A25F)16. <-- They want me to...

Homework Statement Let a and b be real numbers with a < b. a. Derive a formula for the distance from a to b. Hint: Use 3 cases and a visual argument on the number line. b. Use your work in part (a) to derive a formula for the distance between (a,c) and (b,c) in a plane. c. Use the...

Greetings , Im taking an online course on mathematical thinking, and this question has me stumped. r is irrational: Show that r+3 is irrational Show that 5r is irrational Show that the square root of r is irrational. Im sorry if i posted this in the wrong forum, but I am not sure...

Homework Statement (a) Find the remainder when 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divided by 5. (b) Generalize this resultHomework Equations Congruence Modulo a\equivb mod n also a=n*q+b where q is some integer.The Attempt at a Solution The remainder for 1^99 would be 1. The remainder for...