What is Identity: Definition and 1000 Discussions

Identity theft occurs when someone uses another person's personal identifying information, like their name, identifying number, or credit card number, without their permission, to commit fraud or other crimes. The term identity theft was coined in 1964. Since that time, the definition of identity theft has been statutorily defined throughout both the U.K. and the United States as the theft of personally identifiable information. Identity theft deliberately uses someone else's identity as a method to gain financial advantages or obtain credit and other benefits, and perhaps to cause other person's disadvantages or loss. The person whose identity has been stolen may suffer adverse consequences, especially if they are falsely held responsible for the perpetrator's actions. Personally identifiable information generally includes a person's name, date of birth, social security number, driver's license number, bank account or credit card numbers, PINs, electronic signatures, fingerprints, passwords, or any other information that can be used to access a person's financial resources.Determining the link between data breaches and identity theft is challenging, primarily because identity theft victims often do not know how their personal information was obtained. According to a report done for the FTC, identity theft is not always detectable by the individual victims. Identity fraud is often but not necessarily the consequence of identity theft. Someone can steal or misappropriate personal information without then committing identity theft using the information about every person, such as when a major data breach occurs. A US Government Accountability Office study determined that "most breaches have not resulted in detected incidents of identity theft". The report also warned that "the full extent is unknown". A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the probability of becoming a victim to identity theft as a result of a data breach is ... around only 2%". For example, in one of the largest data breaches which affected over four million records, it resulted in only about 1,800 instances of identity theft, according to the company whose systems were breached.An October 2010 article entitled "Cyber Crime Made Easy" explained the level to which hackers are using malicious software. As Gunter Ollmann,
Chief Technology Officer of security at Microsoft, said, "Interested in credit card theft? There's an app for that." This statement summed up the ease with which these hackers are accessing all kinds of information online. The new program for infecting users' computers was called Zeus; and the program is so hacker-friendly that even an inexperienced hacker can operate it. Although the hacking program is easy to use, that fact does not diminish the devastating effects that Zeus (or other software like Zeus) can do to a computer and the user. For example, programs like Zeus can steal credit card information, important documents, and even documents necessary for homeland security. If a hacker were to gain this information, it would mean identity theft or even a possible terrorist attack. The ITAC says that about 15 million Americans had their identity stolen in 2012.

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  1. T

    General Relativity - Riemann Tensor and Killing Vector Identity

    Homework Statement I am trying to show that for a vector field Va which satisfies V_{a;b}+V_{b;a} that V_{a;b;c}=V_eR^e_{cba} using just the below identities. Homework Equations V_{a;b;c}-V_{a;c;b}=V_eR^e_{abc}(0) R^e_{abc}+R^e_{bca}+R^e_{cab}=0 (*) V_{a;b}+V_{b;a}=0 (**) The Attempt at a...
  2. A

    Proving vector identity using levi-civita tensor help

    Using the fact that we can write the vector cross-product in the form: (A× B)i =ε ijk Aj Bk , where εijk is the Levi-Civita tensor show that: ∇×( fA) = f ∇× A− A×∇f , where A is a vector function and f a scalar function. Could you please be as descriptive as possible; as I'm not sure...
  3. L

    Proving Algebraic Identity: $\frac{k^2}{k^2-m^2}$

    Any help please why the following algebraic identity is true \frac{k^2}{k^2-m^2} = 1 + \frac{m^2}{k^2-m^2} thanks
  4. C

    Trig Identity Problem: Solve sin \theta = -5/13 & cos \theta = -(√194)/13

    Sin \theta = -5/13, (3\pi / 2) < \theta < 2 \pi So I got cos \theta = - (sqrt 194) / 13 Is this the right answer?
  5. Z

    An identity about Gamma and Riemann function

    we know that \Gamma (s)= \int_{0}^{\infty}dxe^{-x}x^{s-1} however every factor of the Riemann Zeta can be obtained also from a Mellin transform \int_{0}^{\infty}dxf(x)x^{s-1} =(1-p^{-s})^{-1} where f(x) is the distribution \sum_{n=0}^{\infty}x \delta (x-p^{-n}) is there any...
  6. kreil

    Help with Reducing an Equation into Jacobi Identity Form

    Homework Statement Reduce the equation \partial_\mu {*} F^{\mu \nu} = 0 into the following form of the Jacobi Identity: \partial_\lambda F_{\mu \nu} + \partial_\mu F_{\lambda \nu} + \partial_\nu F_{\lambda \mu} = 0 The Attempt at a Solution I can't figure out what the '*' is supposed to...
  7. S

    Quick question about identity elements

    I saw this question in an abstract algebra text that I was reading. "Is it true that (w − x) − (y − z) = (w − y) − (x − z) is an identity for real numbers? Can you say why or why not?" I know that an identity element does not change the value of a real number. So 0 is the identity element...
  8. N

    Which symmetry follows Ward-Takahashi identity?

    Please teach me this: It seem to me the Ward-Takahashi is validated by the renormalization, if the theory can not be renormalized the proof of Ward identity is failed.In QED the Ward identity is validated by electrical charge renormalization. The Ward-Takahashi implies a current...
  9. icystrike

    Simple Identity Proof for Homework | Equations & Solution Attempt

    Homework Statement Homework Equations The Attempt at a Solution
  10. C

    Understanding When to Use + / - in Pythagorean Identity

    Homework Statement How would I know if let's say Sec^2 = 5 / 4 Sec = +/- \sqrt{5/4} Sec = + / - \sqrt{5} / 2 Now how would I know if whether to put a negative sign or a positive sign before the answer? Because the textbook says Sec Theta < 0 therefor they added the negative sign...
  11. D

    Verifying identity involving covariant derivative

    i am trying to verify the following identity: 0 = ∂g_mn / ∂y^p + Γ ^s _pm g_sn + Γ ^r _pn g_mr where Γ is the christoffel symbol with ^ telling what is the upper index and _ telling what are the two lower indices. g_mn is the metric tensor with 2 lower indices and y^p is the component of y...
  12. H

    Conclusions from Symmetric Equations Identity

    Homework Statement What conclusion can be drawn from the lines (x-x0)/a = (y-y0)/b = (z-z0)/c (x-x0)/A = (y-y0)/B = (z-z0)/C if aA + bB +cC = 0 Homework Equations The Attempt at a Solution I put everything in parametric form but that didn't do much for me. Is...
  13. M

    Why does Sin (right angle plus theta) equal cos(theta)?

    Homework Statement I am reading an explanation on a trig identity but I am not fully understanding it... Angle MOP = Theta Angle POP' = Right angle Angle AOP' = (Theta + Right angle) Take OP' = OP ( WHY must it be equal?) Angle MOP + P'OM' = 90 ( I understand this) Angle MOP = Angle...
  14. L

    Proving Feynman Identity with Induction

    I'm supposed to use the relationship A^{-1}=\int_0^\infty d \alpha e^{-\alpha A} to show that \frac{1}{A_1 A_2 \dots A_n}=(n-1)! \int_0^1 dx_1 \dots \int_0^1 dx_n \frac{\delta(1-x_1- \dots - x_n)}{(x_1A_1 + \dots + x_nA_n)^n} I decided that I should try and do this inductively. So far I...
  15. Z

    Proof of an identity in determinants

    How to prove that ||An||=|A|n2? This property is used in my book but they did not give any explanation/proof of it. Can someone help? Edit: n2=n2
  16. Q

    A fairly easy vector calculus identity question?

    I'm working on simplifying a big physical expression (I don't like the Navier-Stokes equations at all anymore), and I'm curious how to simplify the following term: \vec{v}\cdot (\vec{v}\cdot\nabla )\vec{v} where v is a fluid velocity - i.e. definitely spatially varying. I'm just not sure...
  17. J

    Vector field identity derivation using Einstein summation and kronecker delta.

    Homework Statement Let \vec{A}(\vec{r})and \vec{B}(\vec{r}) be vector fields. Show that Homework Equations \vec{\nabla}\bullet(\vec{A}\vec{B})=(\vec{A}\bullet\vec{\nabla})\vec{B}+\vec{B}(\vec{\nabla}\bullet\vec{A}) This is EXACTLY how it is written in Ch 3 Problem 2 of Schwinger...
  18. S

    Algebraic Proof of Combinatorial Identity

    Homework Statement Verify C(n,k) = C(n-1,k) + C(n-1,k-1) algebraically. Homework Equations N/A The Attempt at a Solution I've set the identity up factorially like so: (n-1)!/k!(n-1-k)! + (n-1)!/[(k-1)!(n-2-k)! I'm having a really hard time getting started here. That is the...
  19. S

    Cross Product Identity: Solving for (A X B)^2

    I've been trying to find what the square of two cross products is and can't find it. Can anyone tell me the identity for (A X B)^2 ?
  20. N

    Double Angle Identity Mystery: Solving 2/(tanx+cotx)=sinx

    Homework Statement 2/(tanx+cotx)=sinx Homework Equations Double Angle Identities, Pythagorean Identities The Attempt at a Solution 2/(tanx+cotx)= 2/[(sinx/cosx)+(cosx/sinx)]= 2/[((sinx)^2+(cosx)^2)/(sinxcosx)]= 2sinxcosx/[(sinx)^2+(cosx)^2]= 2sinxcosx = sin(2x) =/=...
  21. T

    Show this simple trigonometric identity add up to 0

    Homework Statement \cos (\frac{(-1)\pi x}{L})-\cos (\frac{3\pi x}{L}) Homework Equations The Attempt at a Solution the first cosine is the same as positive but is the second cosine simply equal to \cos (\frac{\pi x}{L})? thanks!
  22. N

    What is Manipulating Trig Identities to Solve for a Numerical Value?

    Homework Statement 3(sin(x)^4+cos(x)^4)-2(sin(x)^6+cos(x)^6)=1 (these are sinx raised to the 4 and 6 powers, not x^4or6) Homework Equations Pythagorean Identities The Attempt at a Solution I've tried using pythagorean identities to change everything to terms of sine or...
  23. Char. Limit

    Proving a Tangential Trig Identity

    Homework Statement I was reading on the Weierstrass substitution, and I came across the following trigonometric identity: tan^{-1}(\alpha) - tan^{-1}(\beta) = tan^{-1}\left(\frac{\alpha-\beta}{1+\alpha \beta}\right)Homework Equations I'm not really sure which equations are applicable here...
  24. maverick280857

    QM: Is this a Spherical Harmonic Identity?

    Hi, I came across the following expression in Landau and Lifgarbagez's Quantum Mechanics (Non-relativistic Theory) book: \left(\cos\theta\frac{\partial}{\partial r} - \frac{\sin\theta}{r}\frac{\partial}{\partial\theta}\right)R_{nl}(r)Y_{l0}(\theta,\phi) =...
  25. A

    Summation Identity for i^p power question, really simple

    Homework Statement \sum_{i=0}^{n} i^{p} = \frac {(n+1)^{p+1}}{p+1} + \sum_{k=1}^{p} \frac {B_{k}}{p-k+1} (^{p}_{k}) (n+1)^{p-k+1} where Bk is a Bernoulli number. There is no actual question here I would just like to know if this formula is for sums of i to any power, of course...
  26. G

    Identity Element of Binary Operations

    Homework Statement Determine whether the operation has an identity element. x*y = 3xy Homework Equations e*x = x*e = x, if this holds, e is an identity element The Attempt at a Solution My attempt: x*z = z*x = 3xz, then 3xz = x <=> z = 1/3 => e = 1/3. But the answer key in the...
  27. A

    Proving the Identity Function: Composed Functions

    Suppose that f composed with g equals g composed with f for all functions g. Show that f is the identity function. I really just don't know where to start.
  28. Saladsamurai

    Vector Identity Using Index Notation

    Homework Statement I am supposed to verify that \nabla\cdot(\mathbf{u}\times\mathbf{v}) = \mathbf{v}\cdot\nabla\times\mathbf{u} - \mathbf{u}\cdot\nabla\times\mathbf{v}\qquad(1)[/itex] I want to use index notation (and I think I am supposed to, though it does not say to explicitly) to...
  29. TheFerruccio

    Solve Parseval's Identity for 1+\frac{1}{9}+\frac{1}{25}+\cdot\cdot\cdot

    Homework Statement Obtain the result of the infinite sum 1+\frac{1}{9}+\frac{1}{25}+\cdot\cdot\cdot By applying Parseval's Identity to the Fourier series expansion of 0 if -\frac{\pi}{2} < x < \frac{\pi}{2} 1 if \frac{\pi}{2} < x < \frac{3\pi}{2} Homework Equations...
  30. M

    Binomial Coefficients Identity

    Homework Statement Prove that for an integer n greater than or equal to 2, nC1 - 2nC2 + 3nC3 - + ... = 0. (nCm means n choose m) Also, 2x1 nC2 + 3x2 nC3 + 4x3 nC4 +... = n(n-1)2^(n-2) Homework Equations (1+t)^a = 1 + aC1(t) + aC2(t^2) + ... The Attempt at a Solution I don't know...
  31. H

    Proving Exponential Identity: A Step-by-Step Guide

    Does anyone know how to prove this? exp(jAt)+exp(jBt)= 2exp(j(A+B)/2)cos((A-B)/2)
  32. R

    Proving Equations using Euler's Identity

    1. Use Euler's identity to prove that cos3(t)=3/4cos(t)+1/4cos(3t) 2. ei\theta=cos(theta)+i*sin(theta) 3. 3/4cos(t)+1/2cos(3t)=3/4((eit+e-it)/2)+1/4((ei3t+e-i3t)/2)
  33. icystrike

    Prove Identity: Alternatives to Derivation

    Homework Statement [PLAIN]http://img812.imageshack.us/img812/4068/deriveidentitybydesmond.jpg In fact i came up with this identity just wondering if there is alternative way to prove it.Homework Equations The Attempt at a Solution
  34. P

    What is the Origin of the Trigonometric Identity?

    I'm reading through a solution to a problem and at one point the following identity is used: \frac{1-\cos(\beta)}{\sin(\beta)}=\frac{\sin(\frac{\beta}{2})}{\cos(\frac{\beta}{2})} I've been trying to figure out where this comes from but with haven't got it yet. Any ideas?
  35. E

    Cross Product of Curl Identity

    Hi, I've been trying to derive the electromagnetic stress tensor on my own, and I've run into a bit of a problem. I have a cross product of a curl (\vec{E}\times(\nabla\times\vec{E})) that I need to expand, and the typical...
  36. I

    Verifying this Trigonometric Identity

    Hey guys. How are you all doing? I'm helping my younger brother out with his trigonometry homework. He is dealing with verifying trigonometric identities. However, he has the problem that I am getting nowhere with. Hope you all can help. Thanks in advance. :) Homework Statement Verify...
  37. T

    Trig Identity Problem: Finding Theta When Tan(theta) = Cos(theta)

    Homework Statement the problem is: tan(theta) = cos(theta) find theta: -pi < theta < pi Homework Equations tan(theta)=sin(theta)/cos(theta) sin^2(theta)+cos^2(theta)=1 The Attempt at a Solution
  38. S

    Partial Differentials Identity

    Homework Statement Prove that if z=z(x,y) is invertible that: (dz/dx)(dy/dz)(dx/dy)=-1 where the d's represent partial differentiation not total differentiation Homework Equations The Attempt at a Solution I guess you start with the 6 total derivatives and substitute them...
  39. F

    Help - Verify the Jacobi Identity (Arfken)

    Hello, I'm unfamiliar with the notation used in this problem with the commas. I understand matricies, identities, etc. but not sure about the commas.. Question 3.2.9: Verify the Jacobi Identity: [A,[B,C]] = [B,[A,C]] - [C,[A,B]] I see the BAC CAB rule here, but not sure how to show it...
  40. J

    Problem deriving Einstein tensor form Bianchi identity

    1. I can't understand one step in the derivation of the Einstein tensor from the Bianchi identity.I have looked in a lot of books and all over the internet and everyone glosses over the same point as if its obvious, but it isn't obvious to me. 2. Below is the entire derivation. It seems...
  41. G

    Proving a Double Integral Identity: Can Anyone Help with This Homework Problem?

    Homework Statement Can anybody prove the following double integral identity? How?: \int_{0}^{1} s(1-s) f(sx) ds = \int_{0}^{1} s^2 \int_{0}^{1} t f(tsx) dt ds Here f(x) is an arbitrary Riemann-integrable function. Thanks in advance. Homework Equations I've found the following but it...
  42. I

    An identity for functions of operators

    Is there an easy way to prove the identities: e^{\hat{A}}e^{\hat{B}}=e^{\hat{A}+\hat{B}}e^{[\hat{A},\hat{B}]/2} and e^{\hat{A}}\hat{B}e^{-\hat{A}}=\hat{B}+[\hat{A},\hat{B}]+\frac{1}{2!}[\hat{A},[\hat{A},\hat{B}]]+\frac{1}{3!}[\hat{A},[\hat{A},[\hat{A},\hat{B}]]]+...In Zettili they give that...
  43. M

    Is the Change of Basis Matrix in My Book Wrong?

    Homework Statement I have posted this problem on another website (mathhelpforum) but have received no replies. I don't know whether this is because no one knows what I am talking about or if it's just that no one can find a fault with my reasoning. Please please please could you post a reply...
  44. G

    Identity Element: a- = a Property Explained

    Is the following property exclusive to the identity elements: a- = a (inverse of a = a)?
  45. B

    Proving Trig Identity: Tanx = Csc2x - Cot2x | Homework Help

    Homework Statement tanx=csc2x-cot2x Homework Equations Quotient, Reciprocal, Pythagoreans The Attempt at a Solution 1/sinx + 1/sinx - cosx/sinx - cosx/sinx = 2/sinx - 2cosx/sinx = (2-2cosx)/sinx STUCK~
  46. L

    Proving Identity Using Constant Constraint r

    Homework Statement Let f(x,y,z)=0 and r=r(x,y,z) be another constraint. show that if r is held constant then (\partial x/\partial y)_r *(\partial y/\partial z)_r *(\partial z/\partial x)_r = 1 hint: consider dr and use the fact: (\partial x/\partial y)_z *(\partial y/\partial...
  47. N

    The Summation Identity (Combinatorics)

    Homework Statement Use the Summation Identity to count the cubes of all integers sizes formed by an n by n by n assembly of cubes. Homework Equations Summation Identity: Sum [from i = 0 to n] (i choose k) = (n+1 choose k+1). Sum [from i = 0 to n] (i^3) = (n^2)(n+1)^2 / 4 = (sum[from...
  48. L

    Trouble proving an identity

    Homework Statement required to prove: (\nabla^2+k^2)\frac{e^{ikr}}{r}=-4\pi\delta (r) Homework Equations im assuming we are working in spherical coordinates (not sure - could be cylindrical/2D polar) laplacian for spherical (considering its only a function of r) is...
  49. C

    Verify "Sin2(x)Cos2(x) - Cos2(x) = 0" Identity

    Homework Statement Verify that \frac{Csc(x)}{Cot(x)+Tan(x)}=Cos(x) is an identity. Homework Equations All of the trigonometric identities. Sin^{2}+Cos^{2}=1; tan^{2}+1=Sec^{2}; 1+Cot^{2}=Csc^{2}; etc. The Attempt at a Solution I've literally written about five pages worth trying...
  50. B

    Need Help with Trig Identity Problem - Any Assistance Appreciated!

    Hey all, hope you could help me, would be very gratefull if you could. Homework Statement Show that sin(x) + cos(x) = √2sin(x + π/4) Homework Equations sin(x+z) = sin(x)cos(z)+sin(z)cos(x) The Attempt at a Solution Ive been doing some of these trig identity problems without an...
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