Numbers Definition and 1000 Threads

Hello, I am embarking to read Spivak's book on Calculus, and have come across some difficulty with something that is perhaps rather trivial. In the third edition, there is a section entitled Basic Properties of Numbers. Near the end of page 7, the author begins discussing how he will use...

Hello I have 5.8 moles of KOH. 1Mole of KOH= 56.11g So: 5.8moles of KOH x 56.11g/1mole= 325.438g of KOH If, I want to follow the significant figures rules, what is the answer? Is it 330g? If yes, it seems inaccurate.

It is known that prime numbers become sparser and sparser, with the average distance between one prime number and the next increasing as n approaches infinity. Dividing an even number by 2 results in a bottom half from 1 to n / 2 and a top half from n / 2 to n. For a particular sufficiently...

I am asked to come up with two 4-bit binary numbers, that when subtracted, provide the wrong result for both the unsigned and signed cases, inspecting only the first 4 bits of the output. I have come up with numerous combination where the unsigned is correct, the signed is wrong, and vice...

Resident number theorist and global moderator at MMF (Charles R Greathouse IV) has graciously given me permission to reproduce an image he created to demonstrate the different classes of numbers: Rings are depicted in a ring, fields in an octagon, and algebraically closed fields in a...

Homework Statement Prove for complex number z1, z2, ..., zn that: \mathbb{R}e\left \{ \sum_{k=1}^{N} z_{k}\right \} = \sum_{k=1}^{N}\mathbb{R}e\left \{ z_{k} \right \} Homework EquationsThe Attempt at a Solution Not sure how to setup this problem. I was thinking: \mathbb{R}e\left \{...

Let $a, b, c, d$ be real numbers such that $$a=\sqrt{4-\sqrt{5-a}}$$, $$b=\sqrt{4+\sqrt{5-b}}$$, $$c=\sqrt{4-\sqrt{5+c}}$$ and $$d=\sqrt{4+\sqrt{5+d}}$$. Calculate $abcd$.

So, I'm not 100% sure if this is actually in the correct forum or whether it should be under Mathematics. Anyway, our lecturer told us that we'd soon cover "Floating Point Numbers". Could someone give me a basic, somewhat simple explanation of what these are? Possibly with a few examples. Just...

Hi, A bit is a fundamental unit of information, classically represented as a 0 or 1 in your digital computer. I now number 100 is written in classical bits 0 and 1 as 1100100.Then How to represent 100 in qbits. cheers!

what is the defination of complex no?

Lets say z!=0, and zeC(is complex). So for example is z=2+3i. z^0=1 => (2+3i)^0=1. I am correct? I know that all numbers in zero make us one,but it works with complex numbers too?

I know that in logarithms we can not set as base a negative number,but look at this(in the brackets I will put the base.): log(-2)-8=3 Mathematics say that is wrong,but why? If we tell -2^3=-8 we have a correct result. So? Thank you!

Complex numbers? Since the system is not an ordered pair, how then is it defined using the complex system as an ordered system to plot the z axis (Plane) to use a function? At the point we input each point of the Real and imaginary plane into a function to get out an answer in the Z plane...

I first thought magnetic, but that only makes sense for ml, they're both projections though, does anyone know what they stand for? Thanks!

Hi. I read some basic cosmology where it is always said that density fluctuations, pertubations can be described in modes of waves. In particular if you use linearised theory where δ(x,t) is Fourier transformed δ(k,t). What exactly is the reason for this? What do the wave modes describe...

Homework Statement Compute how many n-digit numbers can be made from the digits of at least one of {0,1,2,3,4,5,6,7,8,9 } Assume, repetition or order do not matter. Homework Equations ## a_{1}, a_{2}, ..., a_{n} ## The Attempt at a Solution 10 choices for the 1st sub-index, 10 choices for...

Why are prime numbers important in real life? What practical use are prime numbers?

Why are prime numbers important in real life? What practical use are prime numbers?

(9x)^-1/2 So, I'm not entirely sure how to go about this question. It's got a negative exponent, so I assume its 1 / something. My guess for the answer would be: 1 / 3x [(25xy)^3/2] / x2y For this question, would I compute 253/2 and then x3/2 y3/2 and then divide by x2y

Determine the positive numbers $a$ such that $$\sqrt[3]{3+\sqrt{a}}+\sqrt[3]{3-\sqrt{a}}$$ is an integer.

Okay, this might be a weird question and I am not sure which sub-forum it belongs to - Math, biology or here. We have this concept of more or less. Given two quantities, we can see whether they are equal, more or less. So we assign each quantity some number, symbol to address it. Similarly...

$a,b,c,d,e,f,g \in N$ $a<b<c<d<e<f<g$ $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{d}+\dfrac{1}{e}+\dfrac{1}{f}+\dfrac{1}{g}=1$ please find one possible solution of a,b,c,d,e,f,g (you should find it using mathematical analysis,and show your logic,don't use any program)

Homework Statement Consider a vector z defined by the equation z=z1z2, where z1=a+ib, z2=c+id. (a) show that the length of z is the product of the lengths of z1 and z2. (b) show that the angle between z and the x-axis is the sum of the angles made by z1 and z2 separately. The Attempt at a...

I have seen a lot of examples of sets with same cardinality as the natural numbers. For instance the even numbers or the cartesian product. In any case the proof amounted to finding a way of labeling the elements uniquely. But I am curious - can anyone give me an example of a set, where this...

I have a view of complex numbers and the way they are taught. I think the whole concept of i as the sqrt(-1) is a terrible place to start. And calling it "imaginary" is worse yet. They should be called blue numbers, or vertical numbers, or something. They are anything but imaginary. It is...

Hi, I'm doing a mini-project in java that involves some nasty calculations with complex numbers- particularly with complex numbers in exponents. Thus far, I've had success using this class: Complex.java . The problem that I'm encountering involves taking the natural logarithm of a complex number...

I imagine most everyone here's familiar with the proof that there's an infinite number of primes: If there were a largest prime you could take the product of all prime factors add (or take away) 1 and get another large prime (a contradiction) So what if you search for larger primes this...

The commutator of two operators A and B, which measures the degree of incompatibility between A and B, is AB - BA (at least according to one textbook I have). But multiplying/substracting matrices just yields matrices! (http://en.wikipedia.org/wiki/Matrix_multiplication). So firstly, how can a...

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...