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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    B Identity Theorem for power series

    Consider this proof: Is it a valid proof? When we divide by ##z##, we assume that ##z \neq 0##. So, we cannot put ##z=0## on the next step. IOW, after dividing by ##z## we only know that $$c_1+c_2z+c_3z^2+...=d_1+d_2z+d_3z^2+...$$ in a neighborhood of ##0## excluding ##0##.
  2. T

    I Understanding the Dirac Delta Identity to Fetter and Walecka's Formula

    Hi all, I'm trying to verify the following formula (from Fetter and Walecka, just below equation (12.38)) but it doesn't quite make sense to me: where and The authors are using the fact that ##\delta(ax) = |a|^{-1}\delta(x)## but to me, it seems like the...
  3. P

    I Proof for subgroup -- How prove it is a subgroup of Z^m?

    Hi together! Say we have ## \Lambda_q{(A)} = \{\mathbf{x} \in \mathbb{Z}^m: \mathbf{x} = A^T\mathbf{s} \text{ mod }q \text{ for some } \mathbf{s} \in \mathbb{Z}^n_q\} ##. How can we proof that this is a subgroup of ##\mathbb{Z}^m## ? For a sufficient proof we need to check, closure...
  4. V

    Is it ok to assume matrices A and B as identity matrix?

    Since ##AB = B##, so matrix ##A## is an identity matrix. Similarly, since ##BA = A## so matrix ##B## is an identity matrix. Also, we can say that ##A^2 = AA=IA= A## and ##B^2 = BB=IB= B##. Therefore, ##A^2 + B^2 = A + B## which means (a) is a correct answer. Also we can say that ##A^2 + B^2 =...
  5. T

    I Identity involving exponential of operators

    Hey all, I saw a formula in this paper: (https://arxiv.org/pdf/physics/0011069.pdf), specifically equation (22): and wanted to know if anyone knew how to derive it. It doesn't seem like a simple application of BCH to me. Thanks.
  6. Vanilla Gorilla

    B Attempted proof of the Contracted Bianchi Identity

    My Attempted Proof ##R^{mn}_{;n} - \frac {1} {2} g^{mn} R_{;n} = 0## ##R^{mn}_{;n} = \frac {1} {2} g^{mn} R_{;n}## So, we want ##2 R^{mn}_{;n} = g^{mn} R_{;n} ## Start w/ 2nd Bianchi Identity ##R_{abmn;l} + R_{ablm;n} + R_{abnl;m} = 0## Sum w/ inverse metric tensor twice ##g^{bn} g^{am}...
  7. nomadreid

    I Prove Even # Transpositions in Identity Permutation w/ Induction & Contradiction

    There is a proof that shows by induction (and by contradiction) that the identity permutation decomposes into an even number of transpositions. The proof is presented in the first comment here...
  8. J

    A An identity with Bessel functions

    Hello. Does anybody know a proof of this formula? $$J_{2}(e)\equiv\frac{1}{e}\sum_{i=1}^{\infty}\frac{J_{i}(i\cdot e)}{i}\cdot\frac{J_{i+1}((i+1)\cdot e)}{i+1}$$with$$0<e<1$$ We ran into this formula in a project, and think that it is correct. It can be checked successfully with numeric...
  9. PhysicsRock

    What does the identity mean here?

    I don't understand why the identity is mentioned in the group's definition and how I am supposed to incorporate it into the table. I honestly have missed some lectures on Linear Algebra, and I can't find any examples or definitions for this in the prof's notes. I'd appreciate some help for sure...
  10. A

    Prove the identity matrix is unique

    I would appreciate help walking through this. I put solid effort into it, but there's these road blocks and questions that I can't seem to get past. This is homework I've assigned myself because these are nagging questions that are bothering me that I can't figure out. I'm studying purely on my...
  11. E

    B Trigonometric Identity involving sin()+cos()

    I'm trying to use the following trigonometric identity: $$ a \cos ( \omega t ) + b \sin ( \omega t ) = \sqrt{a^2+b^2} \cos ( \omega t - \phi )$$ Where ##\phi = \tan^{-1} \left( \frac{b}{a} \right)## for the following equation: $$ x(t) = -\frac{g}{ \omega^2} \cos ( \omega t) + \frac{v_o}{...
  12. chwala

    Prove the trigonometry identity and hence solve given problem

    Refreshing on trig. today...a good day it is...ok find the text problem here; With maths i realize one has to keep on refreshing at all times... my target is to solve 5 questions from a collection of 10 textbooks i.e 50 questions on a day-day basis...motivation from late Erdos...
  13. MevsEinstein

    B Is this identity containing the Gaussian Integral of any use?

    I found this identity: ##x\int e^{-x^2} dx - \int \int e^{-x^2} dx dx = e^{-x^2}/2## by solving the integral of ##x*e^{-x^2}## and then finding its integration-by-parts equivalent. Is this identity useful at all?
  14. S

    I Understand the Thermodynamic Identity: Is This Correct?

    I have a question about the Thermodynamic Identity. The Thermodynamic Identity is given by dU = TdS - PdV + \mu dN . We assume that the volume V and that the number of particles N is constant. Thus the Thermodynamic Identity becomes dU = TdS . Assume that we add heat to the system (we see that...
  15. S

    MHB Perfecting My Proof of Generalized Vandermonde's Identity

    My tests are submitted and marked anonymously. I got a 2/5 on the following, but the grader wrote no feedback besides that more detail was required. What details could I have added? How could I perfect my proof? Beneath is my proof graded 2/5.
  16. 1

    I Why did I lose 60% on my proof of Generalized Vandermonde's Identity?

    My tests are submitted and marked anonymously. I got a 2/5 on the following, but the grader wrote no feedback besides that more detail was required. What details could I have added? How could I perfect my proof? Beneath is my proof graded 2/5.
  17. L

    I Jacobi identity of Lie algebra intuition

    My intuition about the Lie algebra is that it tries to capture how infinitestimal group generators fails to commute. This means ##[a, a] = 0## makes sense naturally. However the Jacobi identity ##[a,[b,c]]+[b,[c,a]]+[c,[a,b]] = 0## makes less sense. After some search, I found this article...
  18. Mikaelochi

    I Understanding the Role of the Identity Map in Fundamental Group Theory

    So, this problem I sort of get conceptually but I don't know how I can possibly rewrite (idX)∗ : π1(X) → π1(X). Does this involve group theory? It's supposed to be simple but I honestly I don't see how. Again, any help is greatly appreciated. Thanks.
  19. L

    MHB Can You Help Prove This Combinatorial Identity?

    Dear All, I am trying to prove the following identity: \[\binom{n}{k}=\binom{n-2}{k}+2\binom{n-2}{k-1}+\binom{n-2}{k-2}\] My attempt was based on transforming the binomial coefficients into fractions with factorials, and then elimintating similar expressions. Somehow it didn't work out. I...
  20. MathematicalPhysicist

    I Question about this set-theory identity

    I am reading this book: https://web.stanford.edu/class/math285/ts-gmt.pdf on page 2 in remark 1.5(1), it's written that: ##\cap_{j=1}^\infty A_j = X\setminus (X\setminus \cup_{j=1}^\infty A_j)## this seems totally wrong, shouldn't it be ##X\setminus \cup_{j=1}^\infty (X\setminus A_j)## ? I...
  21. R

    Show the identity ##\vec{\nabla}(\vec{r} \cdot \vec{u})##

    First of all, sorry for the title I don't know the name of this formula and that's part of the problem, I can't find anything on google. I have to show the identity above. Here's what I did. I don't know if this is correct so far. ##\vec{u} + \vec{r}(\vec{\nabla} \cdot \vec{u}) + i(\vec{L}...
  22. U

    I Prove series identity (Alternating reciprocal factorial sum)

    This alternating series indentity with ascending and descending reciprocal factorials has me stumped. \frac{1}{k! \, n!} + \frac{-1}{(k+1)! \, (n-1)!} + \frac{1}{(k+2)! \, (n-2)!} \cdots \frac{(-1)^n}{(k+n)! \, (0)!} = \frac{1}{(k-1)! \, n! \, (k+n)} Or more compactly, \sum_{r=0}^{n} (...
  23. Astronuc

    Lingusitics (BBC) Bolze is more than a just a language: it’s a cultural identity

    Cool article by By Molly Harris (BBC), 23rd April 2019 https://www.bbc.com/travel/article/20190422-the-swiss-language-that-few-know I've wondered about places like Alsace and Lorraine that have moved back and forth among two nations/states/regions, or for that matter, the borders of nations...
  24. B

    What is the proof for the rare trig identity with tan/tan = other/other?

    Came across this trig identity working another problem and I've never seen it before in my life. I don't need to prove it myself, necessarily, but I would really like to see a proof of it (my scouring of the internet has yielded no results). If someone more trigonometrically talented than myself...
  25. S

    I Confused about identity for product of cosines into a sum of cosines

    What I mean is the way that a product of cosines in which the angles increment the same amount is equal, with some extra terms, of the sum of the cosines. It is discussed here...
  26. G

    I Strange result from Bianchi identity, me spot the error

    I have accidentally derived a very wrong result from the contracted Bianchi identity and I can't see where the error is. I'm sure it's something obvious, but I need someone to point it out to me as I've gone blind. Thanks! Start with the contracted Bianchi identity, $$ \nabla_a \left(...
  27. Arman777

    I Definition of Tensor Identity Simplification

    Is there a simplifcation of ##g^{\alpha \delta}g_{\beta \gamma} ## or what is equal to ?
  28. JD_PM

    Showing an identity involving Grassmann variables

    All we should need for this problem are the basic rules for the Grassmann algebra \begin{equation*} \{ \theta_i, \theta_j\} = 0, \quad \theta^2_i=0 \end{equation*} \begin{equation*} \int d\theta_i = 0, \quad \int d\theta_i \ \theta_i = 1 \end{equation*} Starting from left to right...
  29. larginal

    Proof of Electromagnetic Identity: Puzzling Last Expression

    I tried to understand proof of this identity from electromagnetics. but I was puzzled at the last expression. why is that line integral of dV = 0 ? In fact, I'm wondering if this expression makes sense.
  30. Kaguro

    Identity permutation as product of even number of 2-cycles

    The book I'm following (Gallian) basically says: r can't be 1 since then it won't map all elements to themselves. If r=2, then it's already even, nothing else to do. If r>2, Then consider the last two factors: ##\beta_{r-1} \beta_r##. Let the last one be (ab). Since the order of elements...
  31. M

    Showing that this identity involving the Gamma function is true

    My attempt at this: From the general result $$\int \frac{d^Dl}{(2\pi)^D} \frac{1}{(l^2+m^2)^n} = \frac{im^{D-2n}}{(4\pi)^{D/2}} \frac{\Gamma(n-D/2)}{\Gamma(n)},$$ we get by setting ##D=4##, ##n=1##, ##m^2=-\sigma^2## $$-\frac{\lambda^4}{M^4}U_S \int\frac{d^4k}{(2\pi)^4} \frac{1}{k^2-\sigma^2} =...
  32. L

    MHB Solve Trig Identity: Tips & Explanation

    How do I work this out? Can’t seem to get my head around it! Thanks
  33. brotherbobby

    To prove a trigonometric identity with tan() and cot()

    Attempt : I could not progress far, but the following is what I could do. $$\begin{align*} \mathbf{\text{LHS}} & = (\tan A+\tan B+\tan C)(\cot A+\cot B+\cot C) \\ & = 3+\tan A \cot B+\tan B \cot A+\tan A \cot C+\tan C \cot A+\tan B \cot C+\tan C \cot B\\ & = 3+\frac{\tan^2A+\tan^2B}{\tan A \tan...
  34. E

    B Understanding the Change of Variables in the Hannay Angle Proof

    We have some potential that depends on slowly varying parameters ##\lambda_a##. Using the angle-action variables ##(I, \theta)##, the claim is that we can define a two-form$$W_{ab} = \left\langle \frac{\partial \theta}{\partial \lambda_a} \frac{\partial I}{\partial \lambda_b} - \frac{\partial...
  35. LCSphysicist

    I Group and Identity: Proving (12)(34)² = (12)(34)

    I am probably missing a crucial point here, but what does it means that (12)(34) squares to the identity? How do we prove it? ((12)(34))² = (12)(34)(12)(34) = (12)(12)(34)(34) = (12)(34) ##\neq I ## Is not this the algorithm?
  36. E

    Bianchi and Ricci Identities: Understanding and Applying in Tensor Calculus

    Start with the Bianchi identity,$${\nabla_{[a} R_{bc]d}}^e = 0$$$${\nabla_{a} R_{bcd}}^e - {\nabla_{a} R_{cbd}}^e + {\nabla_{b} R_{cad}}^e - {\nabla_{b} R_{acd}}^e + {\nabla_{c} R_{abd}}^e - {\nabla_{c} R_{bad}}^e = 0$$Use definition of Ricci tensor$$ \left[ {\nabla_{a} R_{bcd}}^e + \nabla_b...
  37. G

    I Deriving Curl of B from Biot-Savart Law & Vector Identity

    $$\nabla \times B(r)=\frac{\mu _0}{4\pi} \int \nabla \times J(r') \times \frac{ (r-r')}{|r-r|^3}dV'$$ using the vector identity: $$\nabla \times (A \times B) = (B \cdot \nabla)A - B(\nabla \cdot A) - (A \cdot \nabla )B + A(\nabla \cdot B)$$ ##A=J## and ##B=\frac{r-r'}{|r-r'|^3}## since...
  38. Arman777

    I Proving an identity for a free variable

    Let us suppose we have a function such that $$z = e^{1/ab} - 1$$ Where we have two free parameters, a and b. Q1) Can we say that as ##b \rightarrow \infty##, ##z = 0##? Or, since ##a## is a free parameter, there is always some value for ##a## such that ##z \neq 0## for ##b \rightarrow...
  39. greg_rack

    B Super silly question about a polynomial identity

    Am I(always) legitimized to write ##-(a-b)^n=(b-a)^n##? I don't know why but it's confusing me... can't really understand when and why I can use that identity
  40. E

    Understanding Christoffel Identity and its Application in Differential Geometry

    We use ##g_{\alpha \beta} = \vec{e}_{\alpha} \cdot \vec{e}_{\beta}## to show that$$\partial_c g_{ab} = \partial_c (\vec{e}_a \cdot \vec{e}_b) = \vec{e}_a \cdot \partial_c \vec{e}_b + \vec{e}_b \cdot \partial_c \vec{e}_a$$then because ##\partial_{\alpha} \vec{e}_{\beta} := \Gamma_{\alpha...
  41. R

    I Computing F with Nabla Identity

    Hi! The topic is electrodynamic but it's a question about Nabla identity. Given $$ F = (p \cdot \nabla)E $$ How does one compute F? Is this correct? $$ F = \sum_{i} p_i \partial_{i} E_{i} e_{i} $$
  42. V

    Unique Identities: Proving O₁ = O₂ in Theorem for Proof of Identity

    Theorem “Identities of + are unique”: O₁ = O₂ Proof: O₁ = Left Identity of + O₁ + x I'm a little confused where to begin this proof, I don't know if that is the first step either I think it is. Proofs are not a strength of mine so I struggle to see how to show that O₁ = O₂. Any guidance would...
  43. Bright Liu

    How do I derive this vector calculus identity?

    ##(\nabla\times\vec B) \times \vec B=\nabla \cdot (\vec B\vec B -\frac 1 2B^2\mathcal I)-(\nabla \cdot \vec B)\vec B## ##\mathcal I## is the unit tensor
  44. Hiero

    How to derive this thermodynamic math identity

    So the Legendre transforms are straightforward; define ##S_1=S-\beta E## and ##S_2= S-\beta E + \beta \mu n## then we get: ##dS_1 = -Ed\beta - \beta \mu dn + \beta PdV## ##dS_2 = -Ed\beta + nd(\beta \mu) + \beta PdV## And so by applying the equality of mixed partials of ##S_1## and ##S_2## we...
  45. Hiero

    Thermodynamic identity (math) question: one component system

    I was just wondering what is wrong with the following logic; From the Gibbs-Duhem relation we get, ##\frac{\partial \mu}{\partial P}\Big\rvert_T = v## Now consider, ##\frac{\partial v}{\partial \mu}\Big\rvert_T = \frac{\partial }{\partial \mu}\Big (\frac{\partial \mu}{\partial P}\Big\rvert_T...
  46. E

    What is the derivation for the probability of energy in quantum mechanics?

    If we can identify ##|c_n|^2## as the probability of having an energy ##E_n##, then that equation is just the bog standard one for expectation. But the book has not proved this yet, so I assumed it wants a derivation from the start. I tried $$ \begin{align*} \Psi(x,t) = \sum_n c_n...
  47. anemone

    MHB Prove Trig Identity: $\sin^7 x=\dfrac{35\sin x-21\sin 3x+7\sin 5x-\sin 7x}{64}$

    Prove that $\sin^7 x=\dfrac{35\sin x-21\sin 3x+7\sin 5x-\sin 7x}{64}$.
  48. L

    Evaluate this trigonometric identity

    (Sinx-2cosx)/ (cotx - sinx) Substitute tan instead of cot (Tanx(sinx-2cosx)/(1-sinx) What do I do from here I don't think what I did there is correct That's why I didn't expand the tan to sin/cos
  49. E

    B A differential equation, or an identity?

    This is quite literally a showerthought; a differential equation is a statement that holds for all ##x## within a specified domain, e.g. ##f''(x) + 5f'(x) + 6f(x) = 0##. So why is it called a differential equation, and not a differential identity? Perhaps because it only holds for a specific set...
  50. victor01

    I Clebsch–Gordan coefficients: An Identity

    Hi, everyone. I'm trying to get the next identity It is in the format <j1, j2; m1, m2 |j, m>. I hope you can help me