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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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. Greg Bernhardt

    Anyone else been a victim of identity theft?

    I just found out someone in my city signed up for phone service using my SS#. I owed $120. I got it cleared up, but it's scary. What else can they do!? :frown: I thinking of signing up at http://www.lifelock.com Anyone have opinions of that service?
  2. V

    (Nevermind) Establish Trig Identity: Sums to Products

    Homework Statement Establish the identity: 1+cos(2θ)+cos(4θ)+cos(6θ)=4cosθcos(2θ)cos(3θ) Homework Equations cos(a)+cos(b)=2cos((a+b)/2)cos((a-b)/2) The Attempt at a Solution I understand how to do a simple cos(+/-)cos problem according to the Sums as Products equations, but I am...
  3. P

    Proof of integral identity (popped up in a Fourier transform)

    Homework Statement Prove; \int_{-\infty}^{\infty} \frac{sin(\gamma)}{cosh(\lambda)-cos(\gamma)} e^{i \omega \lambda}d \lambda= 2 \pi \frac{sinh(\omega(\pi-\gamma))}{sinh(\pi \omega)} Homework Equations Contour Integration/Residue Theorem? The Attempt at a Solution I have messed...
  4. T

    Prove a function is the identity

    Homework Statement Suppose f is one element of \mathbb{A}, and it has the property that f \circ g = g \circ f for every g \in \mathbb{A}. Prove that f = e (the identity function). Homework Equations \mathbb{A} = \{ g_{ab} : (a, b) \in \mathbb{R}^2, \, a \neq 0 \} g_{ab}(x) = ax + b The...
  5. J

    Identity Operator Proving without Bra-Ket Notation

    I am trying to follow a derivation in a book which is written without bra-ket notation, and presumably without the concept of state vectors. I can easily follow it if I may use the fact that \sum_{n}|\varphi_{n}\rangle\langle\varphi_{n}| is the identity operator. Analogously to the way I would...
  6. J

    Just a quick question on the identity matrix

    I'm just wondering, is an identity matrix, say I3 considered as an elementary matrix? It's obviously possible, since we can multiply any row of I with a constant 1. I'm just curious if there is a restriction for rescaling with a constant 1.
  7. R

    Proving the Vector Calculus Identity: (1/g^2)(g∇f - f∇g)

    I am trying to figure out a proof for this identity \nabla(f/g) = (1/g2) (g\nablaf - f\nablag) Any ideas?
  8. P

    Proof of Binomial Identity: Proving SUM(nCk)*2^k=(3^n+(-1)^n)/2

    Homework Statement Prove that for all positive integers n, the equality holds: SUM(nCk)*2^k=(3^n+(-1)^n)/2 Note: The sum goes from k=0 to n. AND k has to be even. Homework Equations Binomial Theorem The Attempt at a Solution I know that if we use the binomial theorem for x=2 and...
  9. Z

    Can you simplify \prod_{k=1}^{N-1} \sin{\frac{k\pi}{N}}?

    How would I go about showing \prod_{k=1}^{N-1} \sin{\frac{k\pi}{N}} = \frac{N}{2^{N-1}} I've tried using Euler's equation to substitute sin, but it just gets messy.
  10. Z

    Is the Complex Number Identity True for Imaginary Numbers and Integer Powers?

    let be n and integer and 'i' the imaginary unit is then true that n^{ \frac{2i\pi n}{log}} =1 i believe that is true
  11. E

    Can you prove this trig identity?

    Show that \displaystyle{\sum_{k=1}^{n-1}\sin\frac{km\pi}{n}\cot\frac{k\pi}{2n} = n-m}\quad\quad(m,n\in\mathbb{N}^+,\ m\le n)
  12. mnb96

    How to satisfy this identity (conformal model in geometric algebra)

    Hello, I have the following equation in x and y: xy - \sqrt{(x^2+a^2)(y^2+c^2)} = -\frac{1}{a^2}-\frac{1}{c^2} where the quantities a2 and c2 are given real constants, and I have to find real values for x, and y such that the equation above is always satisfied. Actually, I know that the...
  13. D

    Can anyone check this identity please?

    is this identity true? V is a vector, so VV is a second order tensor I have tried to prove this but the components of the tensor appear always as operands of the nabla. Thanks! Div(VV)=v.(Grad(V))
  14. D

    Can anyone check this identity please?

    Homework Statement I just want to check if this identity is true, since I have not found it anywhere, can anyone help me? v is a vector (and that nu is supposed to be a v too)
  15. C

    Understanding the Levi-Civita Identity: Simplifying the Notation

    Can somebody show me how \epsilon_{mni}a_{n}(\epsilon_{ijk}b_j c_{k}) Turns in to \epsilon_{imn}\epsilon_{ijk}a_{n}b_j c_{k} Something about the first \epsilon I'm not seeing here when the terms are moved around.
  16. D

    Common Trig Identity Derivations

    I'm looking for a source online that gives the step by step derivation of common trig identities, such as sin(2theta) = 2sin(theta)cos(theta), cos(2theta) = cos2(theta)-sin2(theta), sin2(theta) = (1 - cos(2theta))/2, ect. I did do 20 minuntes or so of searching online, nothing was exactly what I...
  17. A

    Verifying Identity: Easier Way to Solve?

    I need to verify this identity: (A\B)\DeltaC = (A\DeltaC)\Delta(A\bigcapB) (with delta standing for the symmetric difference, I don't know the proper latex code) I've tried it "brute force" several times, working out each side and simplifying it until the sides are equal (it's likely that I'm...
  18. I

    Pretty difficult trig proof (identity)

    Homework Statement \frac{sin\theta}{1-cos\theta} - \frac{cot\theta}{1+cos\theta} = \frac{1-cos^{3}\theta}{sin^{3}\theta} Homework Equations Trig identities.. The Attempt at a Solution Basically I got to: \frac{sin\theta+(cos^{2}\theta)(sin\theta)}{sin^{2}\theta} Homework...
  19. H

    Understanding Logarithmic Identities in Differential Equations

    This is related to differential equations, but I think my question has more to do with log identities than DE. I keep seeing equations like 1/8 lny = t + c simplified to get the solution y = ce^8t but I am unsure of the identity being used to get 1/8 into the exponent as 8. I...
  20. R

    How can I use trigonometric identities to simplify this equation?

    In the following question I figure that i need to prove that h holds true with the trigonometric identity subbed into the denominator. I'm not sure how to simplify the equation any further after that though. Can someone provide any insight...
  21. quasar987

    Determinant Identity for A-B and B A Matrices

    Hello matrices masters, If A and B are nxn square matrices, is there an identity for the determinant of the block matrix A -B B A ? Lots of thanks and praises.
  22. WannabeNewton

    Energy - Momentum tensor identity

    Homework Statement Show that \frac{1}{2}\frac{\mathrm{d} ^{2}}{\mathrm{d} t^{2}}\int_{V}\rho x^{j}x^{k}dV = \int_{V}T^{jk}dV .Homework Equations The Attempt at a Solution \partial _{t}T^{t\nu } = -\partial _{i}T^{i\nu } from conservation of energy - momentum...
  23. Y

    How to prove the Fierz identity using fierzing twice?

    Hello, how can i prove by "fierzing" twice that (\bar{\lambda} \gamma_5 \lambda) \lambda = - (\bar{\lambda} \lambda) (\gamma_5 \lambda)? Thanks
  24. S

    Ward-Takahashi identity and renormalization

    What I don't understand about WT identity is how it allows or helps you to renormalize a quantum field theory (es. QED). Not in details, just the basic ideas, if possible. Thanks in advice
  25. M

    LA - Identity Maps and Injectivity

    Homework Statement Suppose that W is finite dimensional and T:V\rightarrow W. Prove that T is injective if and only if there exists S:W\rightarrow V such that ST is the identity map on V. Homework Equations The Attempt at a Solution First, suppose that T is injective and let...
  26. I

    Solving for Identity of x*y = x + 2y - xy

    I'm having trouble finding the identity of an operation. Could someone check my work? I'm trying to find the identity of x*y = x + 2y - xy In order to find the identity, I need to solve x*e = x for e \begin{align*} x*e &= x\\ x + 2e - xe &= x\\ 2e - xe &= 0\\ e(2-x) &= 0\\...
  27. 5

    Find an expression for the nth partial sum using this identity

    Homework Statement The series, 1 / (1 x 2) + 1 / (2 x 3) + 1 / (3 x 4) + ... + 1 / [n(n + 1)] + ... is not a geometric series. (A) Use the identity 1 / [k(k + 1)] = 1 / k - 1 / (k + 1) to find an expression for the nth partial sum Sn and (B) use it to find the sum of the...
  28. ArcanaNoir

    Improper orthogonal matrix plus identity noninvertible?

    Homework Statement If P is an orthogonal matrix with detP = -1, show that I+P has no inverse. (Hint: show that (P^t)(I+P)=(I+P)^t) P^t is P transposed. I is the identity matrix given by PP^t=I a^-1 means inverse a a, b, P and such letters, capital or otherwise, are all matrices, limit to...
  29. M

    Counterexample to uniqueness of identity element?

    (Hopefully, this question falls under analysis. I was unable to match it well with any of the forums.) The proof that the identity element of a binary operation, f: X x X \rightarrow X, is unique is simple and quite convincing: for any e and e' belonging to X, e=f(e,e')=f(e',e)=e'. However...
  30. WannabeNewton

    Counterexample for set identity

    Homework Statement Consider the function f:X \to Y. Suppose that A and B are subsets of X. Decide whether the following statements are necessarily true (I am including just the one I had trouble with): (a) if A\cap B = \emptyset , then f[A]\cap f[B] = \emptyset Homework Equations The...
  31. B

    Help proving trigonometric identity

    Homework Statement cos\theta/1-tan\theta+sin\theta/1-cot\theta=sin\theta+cos\theta Homework Equations The Attempt at a Solution
  32. J

    How do I get from #2 to #3 in this trigonometry identity problem?

    I'm working on some trigonometry identity problems, and I'm stuck on this particular problem. This is how it is shown in the solution, but I cannot see how to get the highlighted part. Any help on how to get from #2 to #3 (the highlighted) is very much appreciated Jesper
  33. B

    Deducing Irrational Identity - a1=a2 & b1=b2?

    How do you deduce that a1 - \sqrt{N} b1 = a2 - \sqrt{N}b2 to be a1=a2 and b1=b2?
  34. L

    Complex Numbers identity help

    Homework Statement Let z1 = a (cos (pi/4) + i sin (pi/4) ) and z2 = b (cos (pi/3) + i sin (pi/3)) Express (z1/z2)^3 in the form z = x + yi. ]2. Homework Equations [/b] The Attempt at a Solution a(cos (pi/4) + i sin (pi/4)) b (cos (pi/3) + i sin (pi/3)) I then multiplied...
  35. M

    Identity Proofs of Inverse Trig Functions

    Homework Statement Prove the Identity (show how the derivatives are the same): arcsin ((x - 1)/(x + 1)) = 2arctan (sqr(x) - pi/2) Homework Equations d/dx (arcsin x) = 1/ sqr(1 - x2) d/dx (arctan x) = 1/ (1 + x2) All my attempts have been messy and it may be because I didn't...
  36. Phrak

    Is mass conserved by mathematical identity?

    In electromagnetism J denotes the oriented charge-current density, J=d*F. Conservation of charge immediately follows. J=d2*F=0(identically). All exact forms are closed. We can identify scalar mass as the norm of the one-form, μ=(E/c2,-p/c). *μ is then spatial mass density. Like...
  37. W

    Correct differentiation identity? (tensors, vectors)

    Hello, I'm working on some problems and I want to pose the following, though I am not completely sure it is correct. Can somebody point me to some sources on this? I have tried googling myself, but I only found differentiation identities with either just vectors and scalars on the on hand, or...
  38. P

    Proving Vector Calculus Identity Without Introducing Coordinates

    Can someone help me prove the identity \ u \times (\nabla \times u) = \nabla(u^2 /2) - (u.\nabla)u without having to write it out in components?
  39. S

    Can you solve the Kronecker identity?

    I'd like to see how many people can explain this identity: \frac{\partialx_{i}}{\partialx_{j}} = \delta_{ij}
  40. G

    Identity Function: How to Approach It?

    Let's say I have a function that preservers ordering i.e if x<y then f(x)<f(y) for all x. Obviously it must follow that it's the identity function but how can I approach this?
  41. K

    Why is the cube of a unitary operator = identity matrix?

    Hi there, If A is unitary I understand that it obeys AA+=1 because A-1=A+. Why does A3=1? The explanation simply says that "A just permutes the basis vectors".. It then goes on to say that since A3=1, then eigenvalue a3=1 also, which are 1, ei.2pi.theta/3, and ei.4pi.theta/3. This...
  42. G

    Plancherel's Identity proof - justifying order of integration?

    SOLVED With the assumption f(x)\in L^1(\mathbb{R})\cap L^2(\mathbb{R}) (in a Lebesque sense) I'm trying to include a short proof of Plancherel's identity into my dissertation but am having trouble justifying the change of integration at the end of the following line...
  43. F

    Prove this identity? Am I allow to do it like this?

    Homework Statement http://img560.imageshack.us/img560/5384/unledkb.jpg The Attempt at a Solution For 21. I simply did div(\mathbf{F} + \mathbf{G}) = \vec{\nabla} \cdot (\mathbf{F} + \mathbf{G}) = \vec{\nabla} \cdot \mathbf{F} + \vec{\nabla} \cdot \mathbf{G} = div(\mathbf{F}) +...
  44. N

    Trig Identity & Equations simplification

    So I've tried to wrap my head around this concept, and I just read the last two sections in this chapter in order to really get a proper mindset here. Despite reading, there are no examples in the book that pertain to these questions, nor is there anything saying what kind of problem it is and...
  45. L

    Solving Q1 of MathIII Paper60: Ricci Identity & Killing Vectors

    Hi I'm trying Q1 of this paper: http://www.maths.cam.ac.uk/postgrad/mathiii/pastpapers/2005/Paper60.pdf and have got to the bit where I need to show that \xi_{b;ca}=-R_{bca}{}^d \xi_d Now I know that R_{bca}{}^d \xi_d=R_{bcad} \xi^d = R_{adbc} \xi^d = \nabla_b \nabla_c \xi_a - \nabla_c...
  46. R

    Trigometric identity conversion within an integral

    Homework Statement The problem is finding the average value of momentum in an infinite potential well but the theory I understand, its the mathematical execution I'm having trouble with. Homework Equations The expectation value for the momentum is found using the conjugate formula...
  47. J

    How Is the Fourier Series Derived for Odd and Even Functions?

    I am so stuck on my revision and i really need someones help! I am using the definition of Fourier series as My lecturer has told us that if f is odd. Could someone please tell me how he has derived this because i can't understand how he's got to it, iv tried using trig identities and...
  48. Z

    How does this trig identity work?

    Homework Statement How does |sinx + cosx| = |sqrt(2)(x + (pi/4))| ? Homework Equations The Attempt at a Solution Some kind of co-function identity?
  49. L

    Is 1-(sin^6x+cos^6x)=(3sin^2x)(cos^2x) a Valid Trigonometric Identity?

    1-(sin^6x+cos^6x)=(3sin^2x)(cos^2x) I got this far: 1-(sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x)=(3sin^2x)(cos^2x) 1-(sin^4x-sin^2xcos^2x+cos^4x)=(3sin^2x)(cos^2x)
  50. M

    How do you prove the partial derivative identity with three variables?

    Homework Statement Suppose that the equation f(x,y,z)=0 can be solved for each of the three variables as a differentiable function of the other two. Prove that: (dx/dy)(dy/dz)(dz/dx)=-1 Homework Equations The Attempt at a Solution In the case of two variables where one is a...
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