Identity Definition and 1000 Threads

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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    What Does the Floor Function Identity Mean?

    Hi all, I found this rather interesting formula online and I was wondering what it means. Could someone explain it to me? All help is appreciated: http://functions.wolfram.com/IntegerFunctions/Floor/16/03/0001/
  2. K

    Log Identity Proofs: Simplifying a^{log_{b}(c)}=c^{log_{b}(a)}

    Homework Statement a^{log_{b}(c)}=c^{log_{b}(a)} The Attempt at a Solution Take log_{a} of both sides: log_{a}(a^{log_{b}(c)})=log_{a}(c^{log_{b}(a)}) gives: log_{b}c=log_{b}alog_{a}c Looks like one more step for the RHS. I sort of see that the RHS should become log_{b}c and...
  3. Math Amateur

    MHB Principal Ideals - Need for a ring with identity or a unity

    On page 273 of Dummit and Foote the last sentence reads: (see attachment - page 273) "The notion of the greatest common divisor of two elements (if it exists) can be made precise in general rings." (my emphasis) Then, the first sentence on page 274 reads as follows: (see attachment - page...
  4. Math Amateur

    MHB Principal ideal in a ring without identity

    (Hungerford exercise 31, page 143) Let R be a commutative ring without identity and let a \in R Show that A = \{ ra + na \ | \ r \in R, n \in \mathbb{Z} \} is an ideal containing a and that every ideal containing a also contains A. (A is called the prinicipal ideal generated by a)
  5. P

    Prove the trigonometric identity

    Homework Statement (question attached) Homework Equations The Attempt at a Solution Checking solution.. pretty sure I did this wrong. (solution attached)
  6. C

    Differential Operator to prove identity

    Homework Statement Use ##D = \frac{d}{dx}##as a differential operator and the following $$(D - a)(D -b)[f(x)e^{\lambda x}] = e^{\lambda x} (D + \lambda -a)(D + \lambda -b)f(x)$$ to obtain $$(D^2 + D +1)[(Ax^2 + Bx + C)e^{ix}] = (iAx^2 + [iB + (4i + 2)A]x + 2A + (2i + 1)B + iC)e^{ix}$$ The...
  7. icystrike

    Solving Combinatorial Identity: Exploring a Curious Equation

    Homework Statement Hello PF! This is not a homework problem but I am curious to know if the following combinatorial identity exist: \sum^{r-1}_{k=0} (^{n-1}_{r-(k+1)}) \times (^{r}_{k}) = (^{n+r-1}_{r-1}) Much thanks :)
  8. A

    Mathematica Mathematica to recognize e−iθ as the eulers identity

    I just need to know how can Mathematica recognize e^{-i\theta} as the eulers identity. This is, e^{-i\theta} = cos \theta + sin \theta . When i plot a function like e^{i\theta}, nothings appear in the graph. Help is appreciated.
  9. A

    Proof of a vectoral differentation identity by levi civita symbol

    Homework Statement prove, ∇x(ψv)=ψ(∇xv)-vx(∇ψ) using levi civita symbol and tensor notations Homework Equations εijkεimn=δjnδkm-δknδjm The Attempt at a Solution i tried for nth component εnjk (d/dxj)εklm ψl vm εknjεklm (d/dxj) ψl vm using εijkεimn=δjnδkm-δknδjm...
  10. A

    Using Tensor Notations and Levi Civita Symbol to Prove Lagrange's Identity

    Dear all, Any idea for the proof of the Lagrange's identity using tensor notations and Levi Civita symbol? (a x b).(c x d)=(a.c)(b.d) - (a.d)(b.c) x: cross product a,b,c,d: vectors Thanks
  11. S

    Basic proof of units in a ring with identity.

    Homework Statement Let R be a ring with identity, and a,b are elements in R. If ab is a unit, and neither a nor b is a zero divisor, prove a and b are units. Homework Equations If ab is a unit then (ab)c=1=c(ab) for some c in R. The Attempt at a Solution Assume both a and b are...
  12. W

    How do you simplify trig identities with cosθ + sinθ = √2 cos(θ-∏/4)?

    cosθ + sinθ = √2 cos(θ-∏/4) what are the steps in between?
  13. I

    Trigonometry identity sin(pi)cos(wpi)+cos(pi)sin(wpi)

    Homework Statement Hi guys, How can sin(∏)cos(ω∏)-cos(∏)sin(ω∏) = sin(ω∏)? please guide me trigonometry identity to apply with this? Homework Equations The Attempt at a Solution
  14. A

    Proving the Identity for cosh Using Exponential Function Properties

    Show that cosh(x) = 1 => x = 0 I am only allowed to use the definition of cosh, the algebraic rules for the exponential function, that exp(x2)>exp(x1) for x2 > x1, and the fact that we have defined it with the requirement: exp(x) ≥ 1 + x The exp(x) term of course is not trouble. What...
  15. MarkFL

    MHB Mangoqueen54's question at Yahoo Answers involving a trigonometric identity

    Here is the question: Here is a link to the question: http://answers.yahoo.com/question/index?qid=20130130130636AAOqgvz I have posted a link there so the OP can find my response.
  16. L

    Gradient of a dot product identity proof?

    Gradient of a dot product identity proof? Homework Statement I have been given a E&M homework assignment to prove all the vector identities in the front cover of Griffith's E&M textbook. I have trouble proving: (1) ∇(A\bulletB) = A×(∇×B)+B×(∇×A)+(A\bullet∇)B+(B\bullet∇)A Homework...
  17. T

    How do you distinguish between an identity and an equation?

    If you're just given x2+y2=1, how would you know if it's an equation or an identity? Functions are identities, right?
  18. S

    MHB Lawyer's Bill - Mistaken Identity: $30

    Item on bill from lawyer: Crossed street to talk to you; it wasn't you: .$30.00 Fred was riding with his lawyer friend Jack. "Jack, you're a good guy, but you lawyers think of nothing but money." "That's not true," said Jack. "I'm only seeking justice for my clients." Just then a truck roared...
  19. P

    Complex Analysis - Fibonacci Identity

    Hey guys~ I was looking for a way to derive a formula for fn (the nth term in the fibonacci sequence). While looking for this, I came across a potential solution using the residue theorem. Using the generating function Ʃk≥0 fnzn, find the identity for fn. The problem looks like the right...
  20. G

    Prove that the equation is an identity. State any restrictions.

    Homework Statement cos(x)^2/(1+3sin(x)-4sin(x)^2)=(1+sin(x))/(1+4sin(x))Homework Equations We are taking a topic in math where you rearrange one side of the formula to match the otherThe Attempt at a Solution I have factor 1+3sin(x)-4sin(x)^2 to get (-sin(x)+1)(4sin(x)+1)
  21. U

    Prove: x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz

    Homework Statement If sin^{-1}x+sin^{-1}y+sin^{-1}z = \pi then prove that x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz Homework Equations The Attempt at a Solution I assume the inverse functions to be θ, α, β respectively. Rearranging and taking tan of both sides tan(\theta +...
  22. H

    Proving this trignometric identity

    Homework Statement Prove that : \frac{cos(x)-1}{(1-cos(x))^{3}} = -\frac{1}{4sin^{4}(0.5x)}Homework Equations None that I can think of. Maybe the double angle formula... The Attempt at a Solution I couldn't do much in this question : -\frac{1}{(1-cos(x))^{2}}
  23. caffeinemachine

    MHB Automorphism of order 2 fixing just identity. Prove that G is abelian.

    Let $G$ be a finite group, $T$ an automorphism of $G$ with the property that $T(x)=x$ if and only if $x=e$. Suppose further that $T^2=I$, that is, $T(T(x))=x$ for all $x\in G$. Show that $G$ is abelian. I approached this problem using the permutation representation afforded by $T$ on $G$. Its...
  24. M

    Power Series Identity for Bessel Functions

    Homework Statement Show e^{\frac{x}{2}(t-\frac{1}{t})}=\sum^{\infty}_{n=-\infty}J_n(x)t^n Homework Equations J_k(x)=\sum^{\infty}_{n=0}\frac{(-1)^n}{(n+k)!n!}(\frac{x}{2})^{2n+k} The Attempt at a Solution Power series product (\sum^{\infty}_{n=0}a_n)\cdot (\sum^{\infty}_{n=0}...
  25. J

    Can Proxy Servers Truly Protect Your Identity?

    Well a common question arises out of my mind that Local IP addresses assigned by ISP are stored...that's ok...But happens when I connect myself to a Proxy server...My identity is protected..isn't it...So even if I do something wrong I won't be prosecuted as because the convict is the proxy...
  26. J

    Help with Trig Identity Simplification

    Homework Statement Simplify (2cos2x-cos4x)/(2cos2x+cos4x) The Attempt at a Solution I let θ = 2x (2cosθ-cos2θ)/2cosθ+cos2θ) Since cos2θ= 1-2cos^2 (2cosθ-(1-2cos^2)/2cosθ+1-2cos^2 But I get lost when applying it and can't get beyond this, Do i have to use the quadratic...
  27. S

    Trig Identity Solutions: Solving csc^2(x/2) = 2secx | x Solutions

    Homework Statement Need some help finding all solutions for x... csc^2((x)/(2)) = 2secx The Attempt at a Solution Not sure what kind of approach to take but: 1/ sin^2(x/2) = 2/ cos x From here Not sure what to do i tried cross multiplying and got cos x = 2sin^2(x/2) but got...
  28. A

    Identity Operator: Vector Expressions in Basis A

    I was wondering about this: The identity operator writes a vector in the basis that is used to express the identity operator: 1 = Ʃlei><eil But if you are to apply it to a vector in a given basis A should the lei> then be expressed in terms of their own basis or in terms of A?
  29. G

    A Vector Calculus Identity for Characteristic Projections in PDEs

    In the notes it says that \text{v}\cdot \nabla \text{u} = |\text{v}|\frac{du}{dl} \text{v} = (a(x,y), b(x,y)) l is the arclength in the v-direction. Why is this? The LHS is the projection of v onto the gradient of u, the other thing is the magnitude of v, multiplied by the du/dl.
  30. M

    What identity is this? (Division to multiplication )

    This isn't a homework help issue, I just want to know what identity(?) this is. a/b to ab or A^2/B^2 to (A^2)(B^2)
  31. G

    Vector transformations that lead to the identity matrix

    Hi all, I have a question that seems very simple but I just do not see it;) Let α denote an r×1 vector with arbitrary entries; I'm trying to construct an 1×r vector m such that αm = I, where I is the r×r identity matrix... The first question is: is this possible? I tried the...
  32. B

    Powers of matrices equal to the identity matrix

    I am curious about under what conditions the powers of a square matrix can equal the identity matrix. Suppose that A is a square matrix so that A^{2} = I At first I conjectured that A is also an identity matrix, but I found a counterexample to this. I noticed that the counterexample...
  33. M

    Trig identity that I'm missing

    I am trying to integrate -tan(x)sec^2(x) and getting -tan^2(x) / 2. When I put it in wolfram alpha it gets the same answer when I press show solution, but without pressing it it shows -sec(x)/2. So I am wondering, is it the case tan^2(x) = sec(x)?? I don't remember this as a correct trig...
  34. A

    How to prove the following identity

    Homework Statement e_j=g_(jk)e^k where e_j is a covariant vector base e^k is a a contravariant vector base g_(jk) is the covariant metric Homework Equations The Attempt at a Solution
  35. Square1

    Prove the set of integers is a commutative ring with identity

    How should one prove that the integers form a commutative ring? I am not sure exactly where to go with this and how much should be explicitly shown. A ring is meant to be a system that shares properties of Z and Zn. A commutative ring is a ring, with the commutative multiplication property...
  36. K

    Trigonometric Identity Problem

    Homework Statement Prove the Identity sinθ/(1+cosθ) = 1-cos(θ)/sinθ Homework Equations sinθ/cosθ = tanθ sin^2θ + cos^2θ = 1 The Attempt at a Solution sinθ/(1 + cosθ) = LS cosθtanθ/(1+cosθ) = LS cosθtanθ/(sin^2θ + cos^2θ + cosθ) = LS cosθtanθ/(tan^2θcos^2θ +...
  37. B

    Proving the Combinatorial Identity for B_k(x)B_l(x)

    Let B_{k}(x)=\sum_{n\geq 0}\binom{n}{k}\frac{x^{n}}{n!}. Show that B_{k}(x)B_{l}(x)=\frac{1}{2^{k+l}}\binom{k+l}{l}B_{k+l}(2x). I'm having some trouble with this one. Does anyone have any hints? I've tried using Cauchy product and Chu-Vandermonde equality but I get...
  38. V

    Linear Algebra : Proving that Every map is an identity operator

    Suppose T belongs to L(V,V) where L(A,W) denotes the set of linear mappings from Vector spaces A to W, is such that every subspace of V with dimension dim V - 1 is invariant under T. Prove that T is a scalar multiple of the identity operator. My attempt : Let U be one of the sub spaces of V...
  39. A

    Proof of identity involving del

    Prove that ∇.(u×v) = v.(∇×u) - u.(∇×v), where "." means dot product and u,v are vectors. So by scalar product rule, A.(B×C) = C.(A×B) So applying same logic to above identity, shouldn't the left hand side just be equal to v.(∇×u)? Or just to -u.(∇×v), since A.(B×C) = -B.(A×C) ?
  40. M

    Assuming that the system (s,*) has an identity element ,prove that:

    assuming that the system (s,*) has an identity element. if the equation (a*b)*(c*d)=(a*c)*(b*d) holds for all a,b,c,d belongs to S , ,prove that:* is associative and commutative . I tried so much but with no good result ! any ideas ?
  41. S

    Prove the Identity by Using a Sign Reversing Involution

    Prove the Identity by Using a Sign Reversing Involution (See Attachment)
  42. R

    Help verifying a trig identity?

    (sin^3(x)-cos^3(x))/(sinx-cosx) = 1+(sinx*cosx) I'm following a path similar to the post on http://www.askmehelpdesk.com/mathematics/verify-identity-sin-3-x-cos-3-x-sin-x-cos-x-1-sin-x-cos-x-500483.html However, I keep getting 1-(sinx*cosx) when solving for mine as I end up with...
  43. M

    A possible more general form of Euler's identity

    Hi, I cannot find any other reference to this formula: sin(x)/cos(x-1) it seems to fit with Euler's identity as given by Wikipedia. Euler's identity is a special case of this identity equation. I've actually posted this on the Wikipedia page to see if I can get confirmation of this or...
  44. Feodalherren

    Trigonometric Identity Homework: Solving with Sin and Cos Formulas

    Homework Statement Homework Equations Any trig formulas The Attempt at a Solution The yellow paper is me switching everything to sin and cos to see if that helps but it doesn't. I'm completely stuck here.
  45. DeusAbscondus

    MHB Trig identity problem embedded in chain-rule myopia

    I'm having trouble understanding a trig identity and only include it here (rather than in trig forum) as it touches on a -broader- derivative problem. Here it is: $$\frac{d}{dx} \ e^{sin^2(x)}=e^{sin^2(x)}\cdot 2sin(x)cos(x)$$ $$=e^{sin^2(x)}\cdot \ sin(2x)$$ I have attached a proof of the...
  46. A

    How to Prove the Vector Identity Involving Curl and Dot Product Operations?

    Homework Statement Prove that: ∇×(a∙∇a) = a∙∇(∇×a) + (∇∙a)(∇×a) - (∇×a)∙∇a Homework Equations Related to the vorticity transport equation. The Attempt at a Solution Brand new to index/tensor notation, any suggestions on where to begin? For example, I am having trouble...
  47. D

    Proving the contracted epsilon identity

    proving the "contracted epsilon" identity in the wikipedia page for the Levi Civita symbol, they have a definition of the product of 2 permutation symbols as: ε_{ijk}ε_{lmn} = δ_{il}(δ_{jm}δ_{kn} - δ_{jn}δ_{km}) - δ_{im}(δ_{jl}δ_{kn} - δ_{jn}δ_{kl}) + δ_{in}(δ_{jl}δ_{km} - δ_{jm}δ_{kl}) and...
  48. P

    How Does the Scaling Property Affect the Derivative of the Dirac Delta Function?

    Hello! I should prove: \delta'(\lambda x) = \dfrac{1}{\lambda \vert \lambda \vert} \delta(x), where lambda is just a constant. If we make use of the scaling property and the definition of the distributional derivative, we find: \left( \delta'(\lambda x), f \right) =...
  49. A

    Proving the Vector Identity: a dot d(a)/dt = ||a|| x ||da/dt||

    Homework Statement Prove the following vector identity: Any vector a dotted with its time derivative is equal to the vector's scalar magnitude times the vector's derivative's scalar magnitude. Homework Equations (a)dot(d(a)/dt)=||a|| x ||da/dt|| The Attempt at a Solution I...
  50. J

    Prove Quadruple Product Identity from Triple Product Identities

    Homework Statement I need to prove the identity: (a×b)\cdot(c×d)= (a\cdotc)(b\cdotd)-(a\cdotd)(b\cdotc) using the properties of the vector and triple products: Homework Equations a×(b×c)=b(a\cdotc)-c(a\cdotb) a\cdot(b×c)=c\cdot(a×b)=b\cdot(c×a) The Attempt at a Solution I...
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