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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    I Sum-difference trig identity help

    Hi, I am working on an engineering problem and I have an equation which takes the following form: x = (A * cosα * sinθ) + (B * sinα * cosθ) Can this be further simplified? It almost looks like one of the sum-difference formulas you find in tables of trigonometric identities. I'm not to sure...
  2. binbagsss

    General Relativity asymmetry identity

    Homework Statement I have ##R^{u}_{o b u } F^{o}_a - R^{u}_{oau}F^{o}_{b}## and I want to show that this equal to ##2R_{o[aF^{o}_b]}## where ## [ ] ## denotes antisymmetrization , and ##F_{uv} ## is a anitymstric tensor Homework Equations Since ##F_{uv} ##is antisymetric the...
  3. Derek Hart

    Proving ƒ(x) is the Identity Function

    Homework Statement I have been going through a textbook trying to solve some of of these with somewhat formal proofs. This is a former Putnam exam question. (Seemingly the easiest one I have attempted, which worries me). Consider a polynomial function ƒ with real coefficients having the...
  4. M

    Vector Calculus - Tensor Identity Problem

    Homework Statement Homework Equations The Attempt at a Solution I am really lost here because our professor gave us no example problems leading up to the final exam and now we are expected to understand everything about vector calculus. This is my attempt at the cross product and...
  5. Mr Davis 97

    Proving Set Identity: A ∪ (B - A) = ∅ Explanation

    Homework Statement The problem is to prove that ##A \cup (B - A) = \varnothing## Homework EquationsThe Attempt at a Solution The solution in the textbook is that ##A \cup (B-A) = \{x~ |~ x \in A \land (x \in B \land x \not\in A) \} = \{x~ |~ x \in A \land x \not\in A \land x \in B \} = \{x~ |...
  6. W

    I Directional derivative: identity

    Hi all, According to wikipedia: Can someone explain to me with a mathematical proof the following: $$ \frac {\partial f(x)} {\partial v} = \hat v \cdot \nabla f(x) $$ I don't get this identity except the special example where the partial derivative of f(x) wrt x is a special kind of a...
  7. FritoTaco

    Verify the Trigonometric Identity

    Homework Statement Problem 1: csc(tan^{-1}\dfrac{x}{2})=\sqrt{\dfrac{x^{2}+4}{x}} Problem 2: \sqrt{\dfrac{1-sinx}{1+sinx}}=\dfrac{|cosx|}{1+sinx} Homework Equations Quotient Identities tan\theta=\dfrac{sin\theta}{cos\theta} cos\theta=\dfrac{cos\theta}{sin\theta} Pythagorean Identites...
  8. binbagsss

    A Modular Forms: Non-holomorphic Eisenstein Series E2 identity

    Hi, As part of showing that ##E^*_{2}(-1/t)=t^{2}E^*_{2}(t)## where ##E^*_{2}(t)= - \frac{3}{\pi I am (t) } + E_{2}(t) ## And since I have that ##t^{-2}E_{2}(-1/t)=E_{2}(t)+\frac{12}{2\pi i t} ## I conclude that I need to show that ##\frac{-1}{Im(-1/t)}+\frac{2t}{i} = \frac{-t^{2}}{Im(t)} ##...
  9. P

    I Intuition for Euler's identity

    I read an intuitive approach on this website. You should read it, it's worth it: https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ I read that an imaginary exponent continuously rotates us perpendicularly, therefore, a circle is traced and we end up on -1 after...
  10. A

    Unsure if this is a trig identity or calculus

    Homework Statement $$sinx - cosx = 1/3$$ solve for $$sin(2x)$$ Homework Equations $$sin^2x + cos^2x = 1$$ $$sin2x = 2cosxsinx$$ The Attempt at a Solution I think you can square both sides and get: $$sin^2x - cos^2x = 1/9$$ But how can I use this information to solve for sin2x? Is there a...
  11. Z

    I Can Euler's Identity be used?

    I have a homework question and I am wondering if you can use Eulers identity in this case. If the equation is f(x)=constant*e^(-x^2) can this be rewritten as f(x)=consant*e^(ix)^2 and then, can you use the identity when it is in this form? Edit: Can it be put in the form cosx+isinx I am not...
  12. K

    I An identity of hyperbolic functions

    Prove: ##(\cosh(x)+\sinh(x))^n=\cosh(nx)+\sinh(nx)## Newton's binomial: ##(a+b)^n=C^0_n a^n+C^1_n a^{n-1}b+...+C^n_n b^n## and: ##(a-b)^n~\rightarrow~(-1)^kC^k_n## I ignore the coefficients. $$(\cosh(x)+\sinh(x))^n=\cosh^n(x)+\cosh^{n-1}\sinh(x)+...+\sinh^n(x)$$...
  13. E

    B Does the following cross product identity always work?

    Mod note: Reproduced contents of image with broken link: i = j x k j = k x i k = i x j Wikipedia says this about the standard basis vectors. Does this work for all (i.e, non basis) vectors? For example, if you know A = B X C does that mean C = A X B and B = C X A?
  14. zonde

    B Is identity matrix basis dependent?

    To me it seems basic question or even obvious but as I am not mathematician I would rather like to check. Is it true that these two matrices are both identity matrices: ##\begin{pmatrix}1&0\\0&1\end{pmatrix} ## and...
  15. D

    I Confusion on Bianchi Identity proof

    This is from a general relativity book but I think this is the appropriate location. The proof that \nabla_{[a} {R_{bc]d}}^e=0 is as follows: Choose coordinates such that \Gamma^a_{bc}=0 at an event. We have \nabla_a {R_{bcd}}^e = \partial_a \partial_b \Gamma^e_{cd} - \partial_a...
  16. 8

    MHB Trigonometric Identity: Tan^2-Sin^2 = Sin^2 Cos^2

    \tan\left({^2}\right)-\sin\left({^2}\right)=\tan\left({^2}\right) \sin\left({^2}\right) i keep on getting \sin\left({^2}\right)-\sin\left({^2}\right) \cos\left({^2}\right)=\sin\left({^2}\right) \sin\left({^2}\right) \cos\left({^2}\right)...
  17. 8

    MHB Home work help: proving a trigonometric identity

    1 ___________ =csc2\theta-csc\thetacot\theta 1+cos\theta
  18. U

    MHB Which of the following are equal to this identity?

    Hello, sorry for the constant questions. But here is a question asking which of these are equal to the identity cot(x)/sin(2x). I managed to find out that this is equal to the third option of the three, however, apparently this option on its own is not the right answer. I can't seem to get the...
  19. Anonymous Vegetable

    B Implications of e^i*pi = -1

    Before I start, there are only really two pieces of information this concerns and that is the idea that 1x = 1 and that ei*π = -1 So it would follow that (ei*π)i = -1i And so that would mean that i2i = e-π which doesn't seem to be right at all. Where is the issue here as there must be one but I...
  20. E

    I Is this a Trigonometric Identity?

    I have encountered this equation: ##\cos^2 \gamma = \cos^2 \alpha \cdot \cos^2 \beta## According to the paper, this is a trigonometric identity, but this is the first time I have encountered this. The angles ##\alpha## and ##\beta## are somewhat similar to the components of the distance...
  21. T

    Identity of metal from electrolysis

    Homework Statement A solution of a trivalent metal ion is electrolysed by a current of 5.0A for 10 minutes during which time 1.18g of metal was plated out. The identity of the metal is: A cobalt B chromium C indium D gallium E bismuth Relative atomic masses: 1 faraday = 96,486 coulombs...
  22. P

    Solving Harder Trig Identity - Peter's Question

    [mentor note] moved to homework forum hence no template. HI, I'm just having a bit of trouble with the numerator part of this identity ... Resolving the the denominator is fairly straightforward but .. Can anyone shed light on the final couple of steps (sin^3 x - cos^3 x)/(sinx + cosx) =...
  23. F

    B Vector Calculus Identity proof?

    The following identity is found in a book on Turbulence: Can someone provide a proof of this identity? It isn't listed in the list of vector calculus identities on Wiki. Thanks
  24. H

    Vector calculus identity using index and comma notation

    Homework Statement Use index and comma notation to show: \begin{equation*}\text{div }(\text{curl } \underline{\bf{v}}) = 0\end{equation*} Homework Equations \begin{align*} & \text{(1) div } \underline{\bf{v}} = v_{i,i} \\ & \text{(2) curl } \underline{\bf{v}} = \epsilon_{ijk} v_{j,i}...
  25. H

    E-permutation and Kronecker delta identity

    Homework Statement \text{Show that } \epsilon_{ijk} \epsilon_{mjk} = 2\delta_{im} Homework Equations \begin{equation*} \epsilon_{ijk} \epsilon_{mnp} = \left| \! \begin{array}{ccc} \delta_{im} & \delta_{in} & \delta_{ip} \\ \delta_{jm} & \delta_{jn} & \delta_{jp} \\ \delta_{km} &...
  26. Draconifors

    Quick Trigonometric Identity Question

    Hi! I have an integral to solve (that's not the point, though) and the inside of the integral is almost a trig identity: 1. Homework Statement ##sin\frac{(x+y)} {2}*cos\frac{(x-y)} {2} ## Homework Equations I noticed this was very similar to ##sinx+siny = 2sin \frac{(x+y)} {2} *...
  27. P

    B Are there multiple ways to verify a trig identity?

    Well, are there? I thought that problems involving the verification of identities pretty much checked themselves because you know whether the steps you’re doing are legitimate or not and, of course, you know whether you’ve reached the expression you want. However, I got one of these problems...
  28. N

    MHB How to Expand Algebraic Identities

    Hello! Please help me start solving this. I did expand the lhs but I still can't make it to be like the rhs. Any help would be appreciated!
  29. D

    Solution to this trigonometric equation

    Homework Statement ##tanx=\frac{(1+tan1)(1+tan2)-2}{(1-tan1)(1-tan2)-2}## find x Homework Equations 3. The Attempt at a Solution [/B] I tried multiplying through the paranthesis and arrived at ##tanx=\frac{(tan1tan2-1)+(tan2+tan1)}{(tan1tan2-1)-(tan2+tan1)}## and i don't know if this is any...
  30. N

    MHB Proving Algebraic Identity: How to Simplify Complex Equations

    Hello everyone. I need help on this one Prove that $ \left((a-b)^2+(b-c)^2+(c-a)^2\right)^2=2\left((a-b)^4+(b-c)^4+(c-a)^4\right)$I noticed that the leftside of the eqn when expanded would be like $(X^2+Y^2+Z^2+2XY+2XZ+2YZ)$ from here I cannot move forward.
  31. O

    MHB Is R an Identity Relation on A?

    Let A= {1,2,3}. Let R= {<1,1>,<2,2>}. I(A) (Identity Realtion) on A >(def)> {<x,x>|x \in A} So that mean : \forall <x,x> x \in A (That how I understood it) My question: Is R is identity relation on A ? Thank you !
  32. Enochfoul

    Need Help Proving Identities for Q1 and Q2 in Trigonometry

    Homework Statement Hi Everyone, Would somebody please be able able to check my working for the following problems: (Q1) Prove the identity of cos3θ - cos7θ/sin 7θ + sin3θ ≡ tan 2θ (Q2) Prove the identity of cos3θ ≡ 4 cos^3θ - 3 cos θ [hint: Express cos 3θ as cos (2θ+θ).] Homework...
  33. perplexabot

    A Solving Equation (21) to (49): A Guide

    Hey all. So I think I've been trying to figure this out longer than I should, that is why I am here now. I was reading an ieee paper and have been pondering a missing proof (the paper deems this proof too easy to show, literally... I must be really stupid or something). It is a simple question...
  34. S

    Uniqueness of identity element of addition

    Homework Statement Here, V is a vector space. a) Show that identity element of addition is unique. b) If v, w and 0 belong to V and v + w = 0, then w = -v Homework EquationsThe Attempt at a Solution a) If u, 0', 0* belong to V, then u + 0' = u u + 0* = u Adding the additive inverse on both...
  35. P

    MHB Proving Trig Identity: (Sin2x-tanx)/cos2x=tanx

    May someone kindly assist me to prove this trig identity (Sin2x-tanx) / cos2x = tanx Thank you for your assistance
  36. A

    Trigonometry Identity Question

    For the given triangle as below: I can obtain trigonometry identities as below: ##\sin α = \frac{y}{r} = \cos (90° - α)## ##\cos α = \frac{x}{r} = \sin (90° - α)## ##\tan α = \frac{y}{x} = \cot (90° - α)## ##\cot α = \frac{x}{y} = \tan (90° - α)## ##\sec α = \frac{r}{x} = \csc (90° - α)##...
  37. C

    Trig Identities: Simplifying Expressions with Cotangent, Secant, and Cosecant

    I have re-post this forum as I should have paid closer attention to rules. I apologized for that. Homework Statement 1) The expression tan^3 θ + sinθ/cosθ is equal to: (a) cot θ (b) tan θ sec^2 θ (c) tan θ (d) sin θ tan θ (e) tan θ csc^2 θ 2) Simplify (cos θ/1+ sin θ - cosθ/sinθ-1)^-1 (a)...
  38. H

    Confusion with the Gordon identity

    For the Gordon identity $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p}) $$ If I plug in $\mu$=5, what exactly does the corresponding $(p'+p)^{5}$ represent? 4 vectors can only have 4 components so...
  39. H

    Gordon identity manipulation?

    The Gordon identity allows us to solve using $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p}) $$ But how would we solve for $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}v_{s}(\textbf{p}) $$ Would a...
  40. karush

    MHB What is the relationship between secant and cosecant in terms of acute angles?

    If $$\tan\left({\alpha}\right)\tan\left({\beta}\right)=1$$ $\alpha$ and $\beta$ are acute angles Then $$\sec\left({\alpha}\right)=\csc\left({\beta}\right)$$ Again there's options, I tried the product to sum formulas but it went off in a bad direction
  41. karush

    MHB Trig Identity Theory: Show $\tan\left({\theta}\right)=\frac{q-p}{2\sqrt{qp}}$

    If $\sin\left({\theta}\right)=\frac{\left(p-q\right)}{\left(p+q\right)}$ And $p$ and $q$ are $90^o<\theta<180^o$ and $p>q$ Show that $\tan\left({\theta}\right)=\frac{q-p}{2\sqrt{qp}}$ I tried using $q=\frac{2\pi}{3 }$ and $p=\frac{5\pi}{6}$ But not... To do this but theory I'm clueless
  42. Clarence Liu

    Using Mathematica to solve for Jacobi Identity

    Hi everyone, I'm new to Physics Forums and to Mathematica, as well as Jacobi Identity. In any case, I was wondering on how I may use Mathematica to solve various Quantum Mechanics related problems through commutators. Like if it's possible to find out what is the form of a particular commutator...
  43. Brian T

    Finding the Origin of an Integral Identity | Numerical PDEs Homework

    Hey all, As I was working on my numerical PDEs homework, an identity came up which we used to solve a problem. I was able to answer the question, but my question here is where does the identity come from (I figured it has something to do with analysis) ? The identity is The integral of $$v^2$$...
  44. chi_rho

    Delta Function Identity in Modern Electrodynamics, Zangwill

    I am currently reading Modern Electrodynamics by Andrew Zangwill and came across a section listing some delta function identities (Section 1.5.5 page 15 equation 1.122 for those interested), and there is one identity that really confused me. He states: \begin{align*} \frac{\partial}{\partial...
  45. J

    Green's first identity at the boundary

    As required by the Green's identity, the integrated function has to be smooth and continuous in the integration region Ω. How about if the function is just discontinuous at the boundary? Actually, this function is an electric field. So its tangential component is naturally continuous, but the...
  46. evinda

    MHB Solve problem- Identity matrix

    Hello! (Wave) I want to solve the following linear programming problem: $$\min (5y_1-10y_2+7y_3-3y_4) \\ y_1+y_2+7y_3+2y_4=3 \\ -2y_1-y_2+3y_3+3y_4=2 \\ 2y_1+2y_2+8y_3+y_4=4 \\ y_i \geq 0, i \in \{ 1, \dots, 4 \}$$ $\begin{bmatrix} 1 & 1 & 7 & 2 & | & 3\\ -2 & -1 & 3 & 3 & | & 2\\ 2 & 2 & 8...
  47. Orange-Juice

    Applying binomial theorem to prove combinatorics identity

    Homework Statement Prove that \sum\limits_{k=0}^l{n \choose k}{m \choose l-k} = {n+m \choose k}Homework Equations Binomial theorem The Attempt at a Solution [/B] We know that (1+x)^n(1+x)^m = (1+x)^{n+m} which, by the binomial theorem, is equivalent to: {\sum\limits_{k=0}^n{n \choose...
  48. S

    Proof of ladder operator identity

    Homework Statement Define n=(x + iy)/(2)½L and ñ=(x - iy)/(2)½L. Also, ∂n = L(∂x - i ∂y)/(2)½ and ∂ñ = L(∂x + i ∂y)/(2)½. with ∂n=∂/∂n, ∂x=∂/∂x, ∂y=∂/∂y, and L being the magnetic length. Show that a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ a and a† are the lowering and raising operators of quantum...
  49. J

    Green's first identity at the boundary

    As required by the Green's identity, the integrated function has to be smooth and continuous in the integration region Ω. How about if the function is just discontinuous at the boundary? For example, I intend to make a volume integration of a product of electric fields, the field function is...
  50. ognik

    MHB Proving the Pauli Matrix Identity with Ordinary Vectors: A Simplified Approach

    I'm not sure I have the right approach here: Using the three 2 X 2 Pauli spin matrices, let $ \vec{\sigma} = \hat{x} \sigma_1 + \hat{y} \sigma_2 +\hat{z} \sigma_3 $ and $\vec{a}, \vec{b}$ are ordinary vectors, Show that $ \left( \vec{\sigma} \cdot \vec{a} \right) \left( \vec{\sigma} \cdot...
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