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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    Proving the Unproven: A Finite Ring with Identity

    Let R be a ring with multiplicative identity 1R. Suppose that R is finite. The elemets xy1, xy2,...xyn are all different. So x y_i=1R for some i. A lemma that is not proven is given. If xyi=1R & yjx=1R, then yi=yj I need to show that yjx=1R. Right now I haven't got much. I took...
  2. rhody

    Good suggestions to protect your personal identity

    After reading an e-mail about a lawyer's identity being stolen and what he did to fight back I thought it was good enough to pass on. See what you think..
  3. I

    Prove Combinatorial Identity: Sum of x^3 up to n

    Hi, I would like some help in proving the following identity: \sum_{x=0}^{n}x^3 = 6\binom{n+1}{4} + 6\binom{n+1}{3} + \binom{n+1}{2} I tried doing it by induction but that did not go well (perhaps I missed something). Someone told me to use the fact that \binom{x}{0}...
  4. L

    Proving [b x c, c x a, a x b] = [a, b, c]^2 with Vector Identity Proof

    Homework Statement Hi. I need to prove that [b x c, c x a, a x b] = [a, b, c]2 for any three vectors a, b and c. Note that [a, b, c] = a(b x c)Homework Equations I tried using the identify (a x b) x c = (a.c)b - (a.b)c The Attempt at a Solution Using the above identity I got [b x c, c x a...
  5. O

    Basic integration identity- please jog my memory

    Hello all, I'm doing a question for the maths module in my physics degree (I'm a second year undergrad) and there's a question I'm doing on basis functions. Homework Statement Verify that functions of the type f_{n}(x) = A cos \frac{2\pi n x}{L} where n = 0,1,2... can be used as a basis...
  6. T

    Adding Identity Matrix to Matrix: Is 5 a Scalar?

    Say i have a matrix , \begin{bmatrix}{4}&{3}\\{-1}&{7}\end{bmatrix}+5 is it correct if i do it this way , \begin{bmatrix}{4}&{3}\\{-1}&{7}\end{bmatrix}+5\begin{bmatrix}{1}&{0}\\{0}&{1}\end{bmatrix} =\begin{bmatrix}{9}&{3}\\{-1}&{12}\end{bmatrix} is 5 a scalar = 5I where I is an...
  7. J

    Precalculus: proving trigonometric identity

    Homework Statement prove that: tan(1+cos(x))^2 = 1-cos(x) Homework Equations trig identities, like the pythagorean, sum/difference, double/half angle identities, power reducing identities, etc... The Attempt at a Solution i'm not sure where to start; i tried using the pythagorean...
  8. L

    Question on proving an identity

    So I'm given a problem in which I have to prove an identity. It goes: 2csc2x=csc^2xtanx I did the problem myself and could only get to 2csc2x=2\(sin2x)= 2\(2sinxcosx). I had no idea how to get further with the problem so I looked at the answer in the back of my pre-calculus book. It said...
  9. Q

    Deriving a vector identity using Pauli spin matrices

    Homework Statement I'm supposed to derive the following: \left({\bf A} \cdot {\bf \sigma} \right) \left({\bf B }\cdot {\bf \sigma} \right) = {\bf A} \cdot {\bf B} I + i \left( {\bf A } \times {\bf B} \right) \cdot {\bf \sigma} using just the two following facts: Any 2x2 matrix can...
  10. R

    Understanding the Relationship between Vector Dot and Cross Products

    Hi, I was looking at an EM problem today and realized I wasn't sure why (kxH)\dotk = 0 I tried writing it out explicitly and got (w 1,2,3 representing directions) A1(A2*B3-A3*B2) - A2(A1*B3-A3*B1) + A3(A1*B2-A2*B1) and I can't see why this should equal zero. This is troubling...
  11. L

    What is the principal part in this identity?

    Hi, I'm reading a book at the moment in which the author states the identity: \frac{1}{x-i\epsilon}=\frac{x}{x^2+\epsilon^2}+\frac{i\epsilon}{x^2+\epsilon^2} Which is fine, but then he goes on to state that this is equal to: P\frac{1}{x}+i\pi\delta(x) Where P is the principal...
  12. J

    Functions not satisfying parallelogram identity with supremum norm

    Homework Statement Find two functions f, g \in C[0,1] (i.e. continuous functions on [0,1]) which do not satisfy 2 ||f||^2_{sup} + 2 ||g||^2_{sup} = ||f+g||^2_{sup} + ||f-g||^2_{sup} (where || \cdot ||_{sup} is the supremum or infinity norm) Homework Equations Parallelogram identity...
  13. silvermane

    Combinatorial Proofs of a binomial identity

    Homework Statement Show that for all integers n,m where 0 ≤ m ≤ n The sum from k=m to n of {(nCk)*(kCm)} = (nCm)*2^(n-m) The Attempt at a Solution So for the proof, I have to use a real example, such as choosing committees, binary sequences, giving fruit to kids, etc. I have been...
  14. P

    What is the Cosine Double Angle Identity for Cos²(wt+a)?

    Cos^2 (wt+a) = 1+Cos(2wt+2a) ?
  15. K

    Help with proving a trigonometric identity

    Hi I've got this problem which has really been bothering me. How are you supposed to prove that: (Sin[A] Sin[2 A] + Sin[3 A] Sin[6 A])/(Sin[A] Cos[2 A] + Sin[3 A] Cos[6 A]) is identicle to tan[5A]. I am almost sure that I've got to use the factor formulae, but I've had no luck. Maybe...
  16. I

    Proving Identity for Non-Zero Symmetric Covariant Tensors

    Homework Statement For ease of writing, a covariant tensor \bf G.. will be written as \bf G and a,b,c,d are vectors. Let \bf S and \bf G be two non-zero symmetric covariant tensors in a four-dimensional vector space. Furthermore, let S and G satisfy the identity: [\bf G \otimes \bf...
  17. P

    Verify Identity: cos(x)-[cos(x)/1-tan(x)] = [(sin(x)cos(x)]/[sin(x)-cos(x)]

    Homework Statement Verify the Identity: cos(x)-[cos(x)/1-tan(x)] = [(sin(x)cos(x)]/[sin(x)-cos(x)] b]2. Homework Equations [/b] reciprocal Identities, quotient Identities, Pythagorean Identities [b]3. The Attempt at a Solution cos(x)-[cos(x)/1-tan(x)] =...
  18. M

    Identity Matrix: Is Inverse Always True for n>=2?

    Homework Statement let I_n be as an identity matrix where a_ij = 1 when i=j I just want to ask that is it true that all identity matrix has an inverse (determinant is not 0) for n>=2? The Attempt at a Solution
  19. P

    Determinant of a matrix with identity blocks

    Hi all, I'm studying my mathematics lesson, and there is an example I can't understand: Consider the matrix A=(0 In) (-In 0) with In the identity nxn We want to compute detA : We introduce the permutation p=(1 2 ... n n+1 ... 2n)...
  20. I

    Derivative Identity in Bloch's Theorem

    When you study physics, you never really delve into the reasons behind some of mathematical identities, i was curious about this one as it occurs in Bloch's Theorem (correct me if I go wrong)...
  21. kreil

    Trig Identity Homework: Solving |sin z|^2 = \frac{1}{2}[cosh(2y)-cos(2x)]

    Homework Statement Show |sin z|^2 = \frac{1}{2}[cosh(2y)-cos(2x)]Homework Equations cosh2y = cosh^2y+sinh^2y cos2x = cos^2x-sin^2xThe Attempt at a Solution Here is what I have so far |sinz|^2=|sin(x+iy)|^2=|sin(x)cosh(y)+icos(x)sinh(y)|^2 =sin^2(x)cosh^2(y)+cos^2(x)sinh^2(y)...
  22. Fredrik

    Geodesic implies the well-known identity 0=0

    I'm trying to do excercise 4.8 in "Riemannian manifolds" by John Lee. (It's about showing that the geodesics of \mathbb R^n are straight lines). The result I'm getting is that the definition of a geodesic implies the well-known identity 0=0, which isn't very useful. I must have made a mistake...
  23. M

    How to Prove the Small Gradient Identity?

    Hi, I was asked to prove this identity, I found the determinants for both the left and the right side, and now I basically have to prove that (d/dy)(f(dg/dz))=(df/dy)(dg/dz), the d's are actual partials though. Can anyone give me an idea on how to prove this? Thanks.
  24. P

    Identifying cos^2 (wt+θ) in Signals Example Problem

    While seeing a signals example problem, I encountered this: cos^2 (wt+θ) = [1+cos(2wt+2θ)] What identity is this?
  25. H

    Peskin Eq 11.72, mathematical identity

    In Eq 11.72 in the QFT text by Peskin, the following equality is stated: i\int\frac{d^{d}k_{E}}{(2\pi)^{d}}\log(k_{E}^{2}+m^{2})=-i\frac{\partial}{\partial\alpha}\int\frac{d^{d}k_{E}}{(2\pi)^{d}}\frac{1}{(k_{E}^{2}+m^{2})^{\alpha}}|_{\alpha=0} This suggests that...
  26. T

    Additive Identity in Linear Algebra: V + 0 = V

    Hi, I am new with linear algebra, and I'm having a hard time wrapping my mind around the 0 vector and the additive identity v + 0 = v, where 0 is the 0 vector. If I had a 2x2 matrix, and v + w = C + (C^T)*D ... (where (C^T) is the transpose, v & w are vectors, and C & D are matrices)...
  27. M

    The Bianchi identity as a new incarnation of the momentum-conservation law

    Could someone please explain to me in simple words (i.e., without referring to forms on the frame bundle, etc) why the Bianchi identity is the relativistic generalisation of the momentum-conservation law? Here comes my hypothesis, but I am not 100% convinced that it is correct. In Newtonian...
  28. R

    Proving the Exponential Identity for Complex Numbers

    Homework Statement Let z=x+iy prove that Exp[z1]*Exp[z2]=Exp[z1+z2] Homework Equations Binomial thm (x+y)^n=Sum[Bin[n,k]*x^n-k*y^k,{k,1,n}] The Attempt at a Solution I have no idea about this question... Please give me some help.
  29. K

    A matrix multiplied by it's inverse is the identity matrix, right?

    Matrix A= 2x2, R1= -1, -1, R2= -7, 3 Matrix b= 2x2, R1= 1,0, R2= 0, 1 A*?=b ____________ To solve, I put ? on the one side of the equation as ?=A^(-1)b. My answer is then just the inverse of A, because what is multiplied by the identity matrix is itself. It is shown to be incorrect...
  30. N

    Solving (-1)vcos θ Identity Problem - Hi Friends!

    Hi friends, I am not able to understand how the below shown identity becomes (-1) power v cosθ. cos(vπ − θ ) = cos vπ cos θ + sin vπ sin θ = (−1)power v cos θ ==> (-1)vcos θ Please help me understand this basic problem. Thanks, Nesta
  31. T

    Why Can't I Show the Simple Identity for the Spin-1 Operator in This Paper?

    I have a simple technical problem. I'm following a paper [Shore, G. Ann Phys. 137, 262-305 (1981)], and I am unable to show a very simple identity for the non-abelian fluctuation operator (eq 4.37): D_\mu\left[-D^2\delta_{\mu\nu}+D_\mu D_\nu-2F_{\mu\nu}\right]\,\phi=-(D_\mu F_{\mu\nu})\,\phi ...
  32. B

    Problems with identity in complex calc

    Hello, in a paper I have the identity \int_{-\infty}^{\infty} d x \sqrt{(x-i\epsilon)^2-1}= I_+ - I_- + i \int_{-1}^{1}(\ldots) where I_+ = \int_1^{\infty}(\ldots), I_=\int_{-\infty}^{-1}(\ldots) and \epsilon is a small positive number that will be taken to zero at the end. My...
  33. Z

    Prove that the additive identity in a vector space is unique

    Homework Statement Prove that the additive identity in a vector space is unique Homework Equations Additive identity There is an element 0 in V such that v + 0 = v for all v in V The Attempt at a Solution Assume that the additive identity is NOT unique, then there exists y...
  34. J

    Does Swapping the Limits of Integration Change the Integral's Sign?

    interval from a to b \int f(x) dx = interval from b to a (-)\int f(x) dx Is this correct? Swapping the interval endpoints changes the sign of the integral? It seems like they should be equal. Thanks for the help. By the way, I saw this property here...
  35. R

    Proof Sin^2(x)-Sin^2(2x)=Cos^2(2x)-Cos^2(x) - Get Help Now!

    sin^2(x)-sin^2(2x)=cos^2(2x)-cos^2(x) I need help with proving this trig identity. Every thing I've tried just makes the problem more confusing. How would you guys go about this?
  36. E

    :trigonometric identity question

    URGENT:trigonometric identity question Homework Statement tan2x+cos2x+sin2x=sec2x *the 2 stands for squared since I don't know how to make the squared symbol appear on a compter Homework Equations http://www.analyzemath.com/Trigonometry_2/Trigonometric_identities.html stuff from...
  37. A

    What is the Delta Function Identity?

    I know I haven't entered the formulae with the proper syntax, but I'm extremely exhausted at the time of posting, so please just read it and give advice, forgiving me this once for not using proper form (it's basically in latex code format). Homework Statement Show...
  38. H

    How Does the Index in This Vector Calculus Identity Work?

    Homework Statement I'm a bit confused as to the following vector calculus identity: [∇ (∇.A)]_i = (δ/δx_i )( δA_j/δx_j) Shouldn’t it be = (δ/δx_i )( δA_i/δx_i) why is it ‘j’ if we are taking it over ‘i’ ? Thanks.
  39. S

    Proving the Identity: cos(2x)-cos(4x)/sin(2x)+sin(4x)=tanx | Homework Help

    Homework Statement I'm supposed to verify this: \frac{cos(2x)-cos(4x)}{sin(2x)+sin(4x)}=tanx The attempt at a solution I reworked it every way I could think of, but it just won't work. I got desperate so I plugged it into some site and it said it was not a real identity, so I now I'm...
  40. P

    Using Identity to Handle Term: \dfrac{1}{(x-i0)(1-x+i0)}

    There is the identity \dfrac{1}{1-x+i0} = PV \dfrac{1}{x} - i \pi \delta(1-x) PV corresponds to Cauchy principal value. But how can I handle a term like \dfrac{1}{(x-i0)(1-x+i0)} and how can I use the identity above? I tried several things such as writing \dfrac{1}{(x-i0)(1-x+i0)} =...
  41. G

    Vector Identity: Validity Checked

    Homework Statement This is a problem from a textbook, Riley Hobson and Bence 'Mathematical Methods for Physics and Engineering'. It asks to check the validity of a vector identity. If a, b and c are general vectors satisfying a x c = b x c, does this imply c . a - c . b = c|a-b| 2. The...
  42. T

    How can you use the identity 1+tan^2x = sec^2x to simplify the equation?

    Homework Statement sec^2(x) tan^2(x) + sec^2(x) = sec^4(x) Homework Equations sin^2 + cos^2 = 1 1+tan^2 = sec^2 1+cot^2 = csc^2 The Attempt at a Solution First, I changed everything to sin and cos to try and make it clearer. 1/cos^2 * sin^2/cos^2 + 1/cos^2 = sec^4...
  43. T

    Curl of the transpose of a gradient of a vector: demonstration of an identity

    I would like to demonstrate an identity with the INDICIAL NOTATION. I have attached my attempt. Please let me know where I made mistakes. Any suggestion? I am trying to understand tensors all by myself because they are the keys in continuum mechanics Thanks
  44. Z

    How Does the Derivative of a Scaled Delta Function Affect Integration?

    Hello. Homework Statement I would like to solve the following: \[\int\limits_{ - \infty }^{ + \infty } {{\rm{d}}x\,f\left( x \right)\frac{{\rm{d}}}{{{\rm{d}}x}}\delta \left[ {a\left( {x - x_0 } \right)} \right]} \] The solution I found in a paper is: \[\int\limits_{ -...
  45. I

    Prove the Identity (cosecA+cotA)^2 similar to 1+cosA/1-cosA

    Homework Statement Hi all , again i am stuck onto this question :( , tried over 3 sheets alone on it lol.btw. thanks for your replies ;) . Prove the Identity (cosecA+cotA)^2 similar to 1+cosA/1-cosA Homework Equations hmm let's see.. sin2+cos2=1 , sec2= 1+tan2 cosec2= 1+cot2...
  46. S

    Verify Trig Identity: Find x so 1-sin(x) = 1

    Homework Statement Use a graphing calculator to test whether the following is an identity. If it is an identity, verify it. If it is not an identity, find a value of x for which both sides are defined but not equal. \frac{cos(-x)}{sin(x)cot(-x)}=1 Homework Equations None The...
  47. M

    Verifying Identity: Sec(x)Sin2(x) = 1 - cos(x)

    Homework Statement verify the following identity: Sec(x)Sin2(x) ______________________ = 1 - cos(x) 1 + sec(x) Homework Equations sec(x)=1/cos(x) sin2(x)=1-cos2(x) The Attempt at a Solution I never know how to start off these problems. I have to take the...
  48. L

    Can You Simplify csc(θ) - sin(θ) to cos(θ)cot(θ)?

    csc(theta) - sin(theta) = cos(theta)*cot(theta) I'm supposed to write a proof for this but to be honest I'm not really sure where I should even start. The prof taught to take one side of the equation and simply manipulate each part into its equivalent until the other side of the equation was...
  49. O

    Extension of Bezout's identity

    As a consequence of Bezout's identity, if a and b are coprime there exist integers x and y such that: ax + by = 1 The extension states that, if a and b are coprime the least natural number k for which all natural numbers greater than k can be expressed in the form: ax + by Is a+b-1...
  50. nicksauce

    Proving Feynman Slash Identity: 2a\cdot b

    Homework Statement I am trying to prove that \displaystyle{\not} a \displaystyle{\not} b + \displaystyle{\not} b \displaystyle{\not} a = 2a\cdot b using the relation \{\gamma^{\mu},\gamma^{\nu}\} = 2g^{\mu\nu} Homework Equations The Attempt at a Solution If I work backwards...
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