What is even: Definition and 664 Discussions

The break-even point (BEP) in economics, business—and specifically cost accounting—is the point at which total cost and total revenue are equal, i.e. "even". There is no net loss or gain, and one has "broken even", though opportunity costs have been paid and capital has received the risk-adjusted, expected return. In short, all costs that must be paid are paid, and there is neither profit nor loss. The break-even analysis was developed by Karl Bücher and Johann Friedrich Schär.

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  1. ?

    Can a Function be Both Even and Odd at the Same Time?

    I have been looking at my old calculus textbook because to my dismay I seem to have forgotten most of the calculus I learned. I am given 3 cases of ##(f+g)(x) ##. Case 1 both f and g are even: I know ##f(x) = f(-x) ## and ##g(x)=g(-x) ## for the domain of the function. I can reason by...
  2. Ganesh Ujwal

    Why isn't length contraction permanent even though time dilation is?

    Why isn't length contraction permanent even though time dilation is? It's my understanding that when something is going near the speed of light in reference to an observer, time dilation occurs and time goes slower for that fast-moving object. However, when that object goes back to "rest", it...
  3. J

    MHB Formally describe a Turing machine which decides if an input is odd or even.

    Hi, I need to use a transition function to describe a Turing machine that decides if $ a^n ∈ {a}^∗$ is odd or even. I've got an example in my notes that erases any input and halts. But I am struggling to do one for the odd and even question. Thanks for any help!
  4. M

    Even and Odd functions - Fourier Series

    Hello everyone, I know that the integral of an odd function over a symmetric interval is 0, but there's something that's bothering my mind about it. Consider, for example, the following isosceles trapezoidal wave in the interval [0,L]: When expressed in Fourier series, the coefficient...
  5. Fallen Angel

    MHB Perfect Numbers: Proving Even Exponents

    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
  6. B

    Why is the current voting system in the UK flawed and how can it be improved?

    Whenever I start discussing about this topic, I always get negative response and people say that I'm stupid for asking such a silly question. However, if you think logically, your vote has absolutely no impact on the results. Even if you manage to convince your family, friends and a hundred...
  7. M

    On partitioning an even number into a pair of (relative) primes

    An example:For m= 176 (132<176<172 one finds r=(3-2)x(5-2)x(7-2)x(11-1)x(13-2)=1650 relative primes (0<v<2x3x5x7x11x13), forming 825 asymmetric pairs, among them four partitions into prime numbers:19+157, 37+139, 67+109, 73+103, 79+97.
  8. ohwilleke

    Does LQG Do Nothing Cool Even If It Is Right?

    In "Loop quantum gravity and observations" by A. Barrau and J. Grain at http://arxiv.org/abs/1410.1714 the bottom line seems to be that the phenomenological implications of LQG relative to existing predictions from GR are so extremely subtle that they have virtually no practical effects that can...
  9. M

    MHB A group of even order contains an odd number of elements of order 2

    Hey! :o "Show that a group of even order contains an odd number of elements of order $2$." We know that the order of an element of a finite group divides the order of the group. Since, the order of the group is even, there are elements of order $2$. But how can I show that the number of...
  10. R

    Not even close to being an engineer, but got an engineering question

    Thanks in advance for indulging me. I was on another forum (a woodworkers forum) discussing bed design (I'm not really a carpenter either, sort of a intermediate woodworking hobbyist). My question there, and now here, has to do with figuring out the optimal placement for two posts holding up a...
  11. T

    In proof of SQRT(2) is irrational, why can't a,b both be even

    In the classic proof of irrationality of SQRT(2) we assume that it can be represented by a rational number,a/b where a, b are integers. This assumption after a few mathematical steps leads to a contradiction, namely that both a, b are even numbers. Why is that a contradiction? Well you can...
  12. 1

    Subgroup proof - is this even true?

    Homework Statement Prove that G cannot have a subgroup H with |H| = n - 1, where n = |G| > 2. Homework Equations The Attempt at a Solution Counter-example, the multiplicative group R and its subgroup, multiplicative group R+. Or, the additive group Z, and its subgroup of integer...
  13. Gliese123

    Why is cos(t)(cos(wt) - jsin(wt)) considered negligible in integration?

    Homework Statement Hi, I'm having a problem comprehending the odd-even trigonometry properties when doing an integration and I hope someone here feel like explaining since I can't seem to find anything of this in my course literature. I suppose it's more or less of a integration problem. f(t)...
  14. grandpa2390

    Decomposing Heavy Side Step Function into even and odd components

    Homework Statement Decompose H(x) into even and odd components Homework Equations e(x) = (f(x)+f(-x))/2 o(x) = (f(x)-f(-x))/2 The Attempt at a Solution i said f(x)=1 and f(-x)=0 and I got e(x)=1/2 and o(x)=1/2. but this isn't true. e(x)=1/2 but o(x) = 1/2 when x>0 and -1/2 when x<0. what...
  15. 1

    Finite group of even order has elements of order 2

    [The homework format does not appear on mobile] Problem: Show that a finite group of even order has elements of order 2 Attempt: The book gives a suggested approach that lead me to write the most round about, ugly proof I've ever written. Can't I just say: 1.) If G has even order, G/{1} has...
  16. G

    Natural Selection, why not even better?

    I'l start by saying that I'm not a creationist or something like that, I fully support evolutionism and the scientific approach. However, while natural selection can powerfully explain the traits of all current species, it can be hard to understand why if this is the mechanism driving...
  17. hellsteiger

    Expectation Value of Position for Even Wavefunction

    Homework Statement Hello, I need to calculate the expectation value for position and momentum for a wavefunction that fulfills the following relation: ψ0(-x)=ψ0(x)=ψ*0(x) The wave function is normalised. Homework Equations There is also a second wave equation that is orthogonal...
  18. S

    Having trouble understanding Odd or even functions of Fourier

    Homework Statement Is the function even, odd, or neither y(t) = \frac{2At}{w} for 0<t<\frac{w}{2} y(t) = \frac{-2At}{w}+2A for \frac{w}{2}<t<w Homework Equations even function f(-t) = f(t) off function f(-t) = -f(t) The Attempt at a Solution I just don't understand the concept, any help...
  19. M

    Orthogonal complement of even functions

    Homework Statement . Let the ##\mathbb R##- vector space ##C([-1,1])=\{f:[-1,1] \to \mathbb R\ : f \space \text{is continuous}\ \}## with the inner product ##<f,g>=\int_{-1}^1 f(t)g(t)dt##. Determine the orthogonal complement of the subspace of even functions (call that subspace ##S##). The...
  20. alexsylvanus

    Does the log property a*log(x)=log(x^a) still hold if a is even and x

    Does the log property a*log(x)=log(x^a) still hold if a is even and x I imagine that ln(-1)+ln(-1) can't equal zero, even by some mysterious magic involving complex numbers.
  21. evinda

    MHB Arrangements of numbers-odd and even positions

    Hello! :) I am given the following exercise: How many arrangements of the numbers $1,2,3, \dots, 2n-1,2n$ exist such that at the even positions there are only even numbers? How many arrangements are there,such that at least at one position there is an even number? :confused: Since, at the set...
  22. P

    Atomic Probability Densities Always Even?

    I know that for hydrogenic wavefunctions, the parity of a given state is (-1)^l . But does this mean that the probability densities for any such wavefunction is ALWAYS even? I'm trying to understand the Stark effect, and specifically why there is no first-order correction for he ground state...
  23. S

    MHB Proving Even # of Transpositions for Identical Permutations

    is there any easier way of proving that no matter how an identical permutation say (e) is written the number of transpositins is even. my work i tried let t_1...t_n be m transpositions then try to prove that e can be rewritten as a product of m-2transpositions. i had x be any numeral appearing...
  24. G

    Medical Feeling like a car is moving even when it is still?

    Currently I'm researching consciousness in relation to the physical universe. This thread is to ask if any physicists here know about this phenomena and can possibly describe why it happens and how it works. I'm not sure it is a phenomenon, but I do recall it happening to me more than once as a...
  25. T

    Is this even solvable? Kinematics.

    Homework Statement A ball is thrown vertically upward from ground level with an initial velocity V0. The ball rises to a height, h, then lands on the roof of a building of height 1/2h. The entire motion requires 10s. Find the height, h, and the initial velocity, V0. Homework Equations...
  26. F

    [Thermodynamics] Is this even possible?

    I'm not asking about the specific questions contained in the attached document - I know all the answers. I'm wondering if this is even possible. A to B: free expansion (which I take always means "adiabatic free expansion"). B to C: adiabatic compression. Adiabatic means no heat is...
  27. alyafey22

    MHB Subgroups of Z_n when n is even

    Contemporary Abstract Algebra by Gallian This is Exercise 24 Chapter 3 Page 70 Question Suppose $n$ is an even positve integer and $H$ is a subgroup of $\mathbb{Z}_n$. Prove that either every member of $H$ is even or exactly half of the members of $H$ are even . Attempt We consider some...
  28. J

    Understanding Roots of Unity: Proving Even Distribution with Math

    I don't understand why roots of unity are evenly distributed? Every time when we calculate roots of unity, we get one result and then plus the difference in degree, but I think this follows the rule of even distribution and I don't understand that, it is easy to be trapped in a reasoning cycle...
  29. PsychonautQQ

    Is This Function Even or Odd? Help Me Figure It Out!

    Hey PF. I was wondering if anyone can help me figure out i can tell if certain functions are even or odd. For example, the function i*cos(ax)*sin(bx) when integrated with respect to x between -1/2 and 1/2 is equal to zero. I believe this means that it is even because it is symmetric around the y...
  30. mesa

    Looking for comprehensive list (or link) of even power summations

    I have a function that results in 'exact' values for even powered summation series but it gives odd results for powers of '2' and '12+', how exciting! Unfortunately this also means the function is a far cry from a 'general solution'... Does anyone have a comprehensive list of power summations...
  31. Conservation

    Tension - how is mechanical tension even defined?

    Tension -- how is mechanical tension even defined? Hello, I'm currently a student in AP Physics having a little trouble with the concept of tension, especially that of a pulley system or an Atwood machine. First, how is tension even defined? Is it the reaction force to the applied force on...
  32. B

    Does that classical world even exist?

    I mean many people try to abstract the classical world but isn't it just the accumulation of QM properties that build and break down what appears to be an obvious and intuitive classical world. Does QM outright contradict the classical world or does it explain the base fundamentals of our...
  33. M

    How is NaOH considered a strong base does it even accept protons?

    Hello, Ive been seeing it everywhere" NAOH is a strong base". But in order for it to be strong, it has to meet the requirements which are: -The Kb of the reaction 6qvtA.pngmust be high. This means that base strenght is not determined by the dissociation % of a substance. Now I ve seen a...
  34. K

    The title for this content could be What are Spherical Even Even Nuclei?

    Hello, I came across the name spherical even even nuclei in an exercise about the hyperfine structure. What does it refer to? That the number of protons and the number of neutrons are both even? So that there is no nuclear magnetic moment?
  35. C

    MHB Even Functions, Symmetry, Inverse Functions

    Can someone explain why the answer is D a < 0 because it finishes downwards e < O because the y-intercept is in the negatives. b, & d = zero (but i don't get this) c is supposedly > 0 (nor do i get this) According to the solutions the graph is an even function, and symmetrical about the...
  36. feyn

    Is our current math even suited for general relativity ?

    i have a question, that nobody seems to be able to answer : is math actually suited for reality ? Basically the idea is that reality seems to be granular, for example we have planks time. Usually the difference is so small, that is doesn't matter, but if you bring things like infinity into the...
  37. L

    Why are certain transformations in the case of D4 group considered even or odd?

    Why ##\rho,\rho^2,\rho^3,\rho^4## are even transformation and ##\rho\sigma,\rho^2\sigma,\rho^3\sigma## are odd transformation. I'm talking about case of ##D_4## group, where ##\rho## is rotation and ##\sigma## is reflection.
  38. I

    What are the criteria for identifying singularities in complex analysis?

    I am getting two different answers with two different methods so can someone point out the error? \int\limits_{-\infty}^{\infty} \frac{1}{x^2}dx = 2 \int\limits_{0}^{\infty} \frac{1}{x^2}dx = - \frac{2}{x} |_{0}^{\infty} = \infty \int\limits_{-\infty}^{\infty} \frac{1}{x^2}dx = -...
  39. A

    How do I determine if a plane is even with respect to an axis?

    I know that the plane ##z=4-y## is even with respect to the x-axis and is not even with respect to the y-axis and z-axis from graphing the plane. How would I algebraically determine this?
  40. H

    We can't have elastic scattering even theoretically

    Consider a photon which is scattered by a crystal elastically. In an elastic scattering we have |k_i|=|k_f| and k_f - k_i = G where G is a reciprocal vector. But according to momentum conservation, the crystal must obtain a momentum \hbar G and hence the kinetic energy, so according...
  41. T

    Odd, Even, or Neither: Combining Functions in Algebra

    Homework Statement Consider two functions, either of which is even or odd. But neither is neither even nor odd. Determine which algebraic combinations(sum, difference, quotient, product) of the given functions will result in an odd function, an even function, and in a function that is...
  42. G

    Why is Goldbach conjecture that every even = a prime + a prime becomes

    more and more likely to be true the bigger the even? Primes become more rare, so it seems to me this notion is counter intuitive. :confused: A few recent papers all point to that Goldbach becomes more and more likely the higher up you go. A very large even can be the sum of two large odds or...
  43. A

    Determining if a function is odd or even

    Homework Statement Homework Equations The Attempt at a Solution $$f(-x)=\begin{cases} -x+5,\quad -2<x<0 \\ x+5,\quad 0≤x<2 \end{cases}\\ =f(x)$$ The issue is that I can't get to the second step. I know the function is even.
  44. A

    Prove: the biggest that N choose k gets is at k = N/2 for N even

    Is there a simple way to prove this? I tried to use induction, but you get down to some horrible fraction (letting N = 2m for some m) in the inductive step: \begin{pmatrix} 2(m+1) \\ k \end{pmatrix} = \frac{(2m)!}{k!(2m - k)!} \cdot \frac{(2m+2)(2m+1)}{(2m+2-k)(2m+1-k)} The inductive...
  45. T

    How long does it take to make homework that comes out even, when there

    I'm starting to get to a point where the numbers are getting sometimes well beyond 3 digits in length and, I'm constantly amazed at the fact that there are usually no decimals anyplace in the actual problem, and I was wondering how long does it take to find questions that don't have decimals in...
  46. r-soy

    MHB Probability of Even # or Mult. of 3 from 1-10

    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)
  47. P

    Is there current even with huge resistances?

    If I had a AA battery hooked up to both my hands, positive to my right hand and negative to my left hand, I would expect the resistance to be huge, maybe in the millions of ohms? According to Ohm's Law, if you have a voltage, and the resistance is not infinite, then there is a current, no...
  48. Y

    Older Photoshop won't even load in Win 7

    I am trying to load a very old version of Photoshop 6.0 into my Win 7 computer. It won't even install, it just stopped. Is there any compatibility mode I can make it work? Thanks Alan
  49. P

    Admissions Cornell physics PhD admissions? Is it pointless for me to even apply?

    I graduated 4 years ago from a small university and received a dual BS in EE and physics. I went into a decently ranked EE PhD program but dropped out after a year. I attempted to go back a couple times but just didn't care too much for the courses and dropped my classes both times. I have...
  50. Y

    Proving That Even Potential Leads to Even or Odd Wavefunction

    Homework Statement This problem comes from the Griffiths QM book and is stated as "show that if V(x) is an even function then the solution to the time-independent Schroedinger equation can be taken to be either even or odd." Now, I have seen the solution to this, but am not thoroughly...
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