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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    Identity Function Clarification: Definition & Examples

    From what I was reading, the apparent definition goes as: The Identity Function on E is the function IE from E into E defined by IE(x) = x. Since IE is the set of all ordered pairs (x,x) such that x ϵ E, IE is also called the diagonal subset of E x E. If f is a function from E into F, clearly...
  2. G

    Linear Algebra - Identity matrices

    I am having some difficulty with identity matrices in linear algebra at the moment. I am sure it is fairly simple to solve, but I just cannot follow the logic behind this particular problem. I need to come up with a matrix B (2x2), such that B =/= I but B2 = I Since I = (1 0) (0 1)...
  3. T

    Arc length of a curve (trigonometric identity)

    Homework Statement find arc length of the segment of the 2space curbe that is defined by the parametric equations x(t) = t-sin(t) y(t) = 1+cos(t) 0 ≤ t ≤ 4π The Attempt at a Solution I've found dx/dt and dy/dt respectively and put them into the arc length equation, i.e...
  4. F

    How to Prove This Combinatorial Identity Involving Binomial Coefficients?

    Homework Statement For positive integers n, r show that C(n+r+1, r) = C(n+r, r) + C(n+r-1, r-1) + ... + C(n+2, 2) + C(n+1, 1) + C(n, 0) = C(n+r, n) + C(n+r-1, n) + ... + C(n+2, n) + C(n+1, n) + C(n, n) Homework Equations The Attempt at a Solution
  5. F

    What are the identity elements in S_3 for x^2=e and y^3=e?

    Homework Statement In S_3, show that there are four elements satisfying x^2=e and three elements satisfying y^3=e. The Attempt at a Solution I don't understand what the question is asking at all...
  6. B

    Topology - Gluing two handlebodies by the identity

    Hello all, I have a question I'm having a hard time with in an introductory Algebraic Topology course: Take two handlebodies of equal genus g in S^3 and identify their boundaries by the identity mapping. What is the fundamental group of the resulting space M? Now, I know you can glue two...
  7. Q

    Deriving Identity: A Proof for S^{p}_{n} = 1^p + ... + n^p

    deriving identity - need help! Homework Statement Derive for S^{p}_{n} = 1^p + ... + n^p the identity (p+1)*S^{p}_{n} + (p+1 choose 2)*S^{p-1}_{n} + ...+S^{0}_{n} = (n+1)^(p+1) - 1 Homework Equations Um, I know that the S^{1}_{n} = n(n+1)/2 S^{2}_{n} = n(n+1)(2n+1)/6 S^{3}_{n} =...
  8. K

    Can You Prove the Trig Identity: cos(3x)/cos(x) = 2cos(2x) - 1?

    Homework Statement Prove that \frac{cos 3x}{cos x} = 2cos (2x) - 1 Homework Equations The ones I used: cos 2x = cos^2 x - sin^2 x sin^2 x + cos^2 x = 1 The Attempt at a Solution I *think* that the left hand side cannot be manipulated so I only fooled around with the right hand side...
  9. Q

    Deriving Identity: Proving the Sum of Powers Identity with Step-by-Step Guide

    deriving identity - need help! Homework Statement Derive for S^{p}_{n} = 1^{p} + ... + n^{p} the identity (p+1)*S^{p}_{n} + (p+1 choose 2)*S^{p-1}_{n} + ...+S^{0}_{n} = (n+1)*^{p+1} - 1 Homework Equations Um, I know that the S^{1}_{n} = n(n+1)/2 S^{2}_{n} = n(n+1)(2n+1)/6...
  10. B

    Proving the Cosine Identity: 5/16 + 15/32(cos2x) + 3/16(cos4x) + 1/32(cos6x)

    yet another trig identity... Homework Statement prove: cos^(x)= 5/16+15/32(cos2x)+3/16(cos4x)+1/32(cos6x) Homework Equations The Attempt at a Solution i attempted to use the formula cos^2(x)=(1+cos2x)/(2), and square both sides, then use it again for the square roots, then...
  11. B

    Can't make sense of this trig identity

    Homework Statement im in first year differential calculas and i have no idea what my prof wrote down...i just copied it and thought ide figure it out later. but i can't fore the life of me. Homework Equations the identitie that he wrote is: sinC+sinB=2Sin (C+D)/2 cos (c-D)/2 The...
  12. S

    I evaluating this vector product identity

    Homework Statement The problem is written as: Del X (A X B) = (B*DEL)A- (A*DEL)B +A(DEL*B) -B(DEL * A) where * = dot. I don't know how to evaluate this because if the author meant for the standard mathematical order of operations to apply it makes since they wouldn't have worried about...
  13. pluviosilla

    Calculating a CDF Identity: Derivation and Explanation

    I ran across this identity in some actuarial literature: Pr( (x_1 \le X \le x_2) \ \cap \ (y_1 \le Y \le y_2) ) = F(x_2, y_2) - F(x_1, y_2) - F(x_2, y_1) + F(x_1, y_1) First of all, I am not certain this is correct. I think the expression on the LHS is equal to the following double...
  14. R

    How Do Trigonometric Identities Simplify Complex Equations?

    Homework Statement If \frac{(cos x)^{4}}{(cos y)^{2}}+\frac{(sin x)^{4}}{(sin y)^{2}}=1 prove that \frac{(cos y)^{4}}{(cos x)^{2}}+\frac{(sin y)^{4}}{(sin x)^{2}}=1 The Attempt at a Solution (cos x)^{4} (sin y)^{2}+(sin x)^{4} (cos y)^{2}=(sin y)^{2}-(sin y)^{4} On...
  15. S

    Trigonometric Identity Problem

    Homework Statement http://img206.imageshack.us/img206/9099/titleol2.jpg http://g.imageshack.us/g.php?h=206&i=titleol2.jpg Show the above statement is equivalent to : sec (2x) + tan (2x) Homework Equations The Attempt at a Solution First attempt in which I used the...
  16. G

    Solving Trig Identity: sin5xcos3x=sin4xcos4x+sinxcosx

    Homework Statement sin5xcos3x=sin4xcos4x+sinxcosx, solve the identity Homework Equations all the identities and formulas mentioned in my last thread. The Attempt at a Solution Alright so I thought I could use the product to sum formula on the left side which ended up being...
  17. J

    How Does Euler's Identity Simplify the Expression y = e^(x(1-i)) + e^(x(1+i))?

    How does y = e^(x(1-i)) + e^(x(1+i)) work out to y = (e^x)sinx + (e^x)cosx? Using Euler's identity I get, y = (e^x)e^-ix + (e^x)e^ix y = e^x(cosx - isinx + cosx + isinx) y = e^x(2cosx)
  18. J

    Prove this trigonometric identity

    Homework Statement Verify the possibility of an identity graphically. (Completed this part) Then, prove each identity algebraically. \dfrac{sinx+tanx}{cosx+1}=tanx Homework Equations tan\theta=\dfrac{sin\theta}{cos\theta} cot\theta=\dfrac{cos\theta}{sin\theta}...
  19. G

    Proving Identity: $(\stackrel{m + n}{l}) = (\stackrel{m}{l})(\stackrel{n}{0})$

    Homework Statement Let l, m, and n be positive integers with l \leq m and l \leq n. Prove the identity. (\stackrel{m + n}{l}) = (\stackrel{m}{0})(\stackrel{n}{l}) + (\stackrel{m}{1})(\stackrel{n}{l-1})+...+(\stackrel{m}{l})(\stackrel{n}{0}) 2. The attempt at a solution I have no clue, I...
  20. R

    Prove the following identity by mathematical induction

    Homework Statement Prove the following identity by mathematical induction: \sum_{i=1}^n \frac{1}{(2i - 1)(2i + 1)} = \frac{n}{(2n + 1)} Homework Equations The Attempt at a Solution Let P(n) = \sum_{i=1}^n \frac{1}{(2(1) - 1)(2(1) + 1)} = \frac{1}{(2(1) + 1)} P(1) =...
  21. P

    Difference between an Equation and an Identity?

    Can u guys tell me the difference b/w an Equation and an Identity? Thx
  22. L

    Proving Trigonometric Identities: Attempt and Solution

    Homework Statement I'm attempting to prove that 1 - sin^2 t /(1 + cos t) - cos^2/(1+tan t) = cos t sin t 2. The attempt at a solution I've tried various approaches. The most promising has the LHS reduced to: (sin t cos t (1 + cos t + sin t cos t))/((1 + cos t)(cos t + sin t))...
  23. M

    Matrix Invertibility: RREF to Identity

    Prove that a matrix A is invertible if and only if its reduced row echelon row is the identity matrix.
  24. L

    Proving a Trigonometric Identity

    Im supposed to verify that (1-sinx)/(1+sinx) = (secx-tanx)^2 RHS = (secx-tanx)^2 = (1/cosx - sinx/cosx)^2 = [(1-sinx) / cosx]^2 = [(1-sinx)(1-sinx)]/cosx^2 = (1-2sinx+sinx^2)/(1-sinx^2) From here, I'm feeling pretty confused. I'm not even sure if all my values are correct.
  25. T

    Are My Trigonometric Identity Solutions Correct?

    I'm having difficulties with a few identity problems and I wanted to make sure I'm doing the ones I believe I did correctly, correctly... 1. (cos^3x)+(sin^2x)(cosx) (cosx)(cos^2x)+(sin^2x)(cosx) 2cosx 2. (1+cosy)/(1+secy) (1+cosy)/(1+1/cosy) (1+cosy)/(1+cosy) 1 3. (tanx)/(secx)...
  26. C

    An Identity in SUSY sigma model

    I am struggleing in an identity, i.e. \nabla_m R_{ikjl}(\overline{\epsilon}\psi^m)(\overline{\psi^i}\psi^j)(\overline{\psi^k}\psi^l)=0 , where i,j,k,l,m are dummy indices, \nabla_m is covariant derivative, R_{ikjl} is Riemann-Christoffel curvature tensor, and it is known that, for any two...
  27. L

    Definition of Identity & Equation: Trig-Identity & Relation

    can anybody give me the definition of a trig-identity? And then the definition of an equation? Because i think that the relation \tan^2 x + 1 = \sec^2 x is not an identity.
  28. S

    What Are the Theoretical Forms for f(.) and g(.)?

    Given that 1/ f(cx) = k - g(x) and 2/ the above is an identity, where f(.) and g(.) are two functions and c, k are real valued constants. The problem is to infer upon the types of f(.) and g(.). I have a hunch that f(.) and g(.) are logarithimic functions. Can anyone provide...
  29. M

    Is the Fourier integral applicable to find b_n?

    for every sequence of numbers a_n E_n is this identity correct ? \sum_{n= -\infty}^{\infty}a_n e^{2\pi i E_{n}}= \sum_{n= -\infty}^{\infty}a_n \delta (x-E_{n})
  30. S

    Equivalent Statements: An Example

    Suppose we have a statement A that holds if and only if statement B holds. "A if and only if B" I'm fairly sure I read before that this does not necessarily mean that A and B are identical: in general, A <--> B does not imply A = B. I'm having difficulty determining how A and B could be...
  31. T

    Green identity, poisson equation.

    Suppose \phi is a scalar function: R^n\to R, and it satisfies the Poisson equation: \nabla^2 \phi=-\dfrac{\rho}{\varepsilon_0} Now I want to calculate the following integral: \int \phi \nabla^2 \phi \,dV So using Greens first identity I get: \int \phi \nabla^2 \phi \,dV = \oint_S \phi...
  32. E

    Is Identity Death Possible Through Brain Damage?

    Alright, I'll need some help formulating this, since my writing tends to be... well... just not very eloquent and representative of my thoughts. I don't believe in soul, afterlife, or other nonsense. I think our self, our consciousness, is a function of our complex brains. For what...
  33. K

    2-3 Pachner move and Biedenharn-Elliot identity

    Homework Statement Show that up to "fudge factors" (such as a few theta-nets an a loop) the 2-3 Pachner move is just the Biedenhard-Elliot identity between 6j symbols. If you go to the Quantum Gravity Seminar notes of Baez and Alvarez, you can see this problem here...
  34. E

    Proving the Divergence Theorem for Bounded Domains and Differentiable Fields

    Homework Statement Let the domain D be bounded by the surface S as in the divergence theorem, and assume that all fields satisfy the appropriate differentiability conditions. Suppose that: \nabla\cdot\vec{V}=0 \vec{W}=\nabla\phi with \phi = 0 on S prove...
  35. R

    Solving Strange Log Identity - Richard

    Hey folks, I'm reading the paper: http://arxiv.org/abs/hep-ph/0301168 and I'm trying to make sense of the first line of eqtn 44 where he states that we can write: \frac{1}{2}\sum \int\frac{d^{2n}k}{(2\pi)^{2n}}log(k^2+\frac{m^2}{L^2}) as...
  36. Orion1

    Resolving a Complex Identity: Collaborative Proof Approach

    I am having difficulty symbolically resolving the LHS of this identity algebraically: \frac{r}{2} \left[ \left(8 \pi P(r) + \frac{1}{r^2} \right) \frac{r}{r - 2u} - \frac{1}{r^2} \right] = \frac{4 \pi r^3 P(r) + u}{r(r - 2u)} \left(4 \pi r P(r) + \frac{1}{2r} \right) \frac{r}{r - 2u} -...
  37. A

    Algebraic Manipulation of Euler's Identity Leads to a Strange Result

    I was playing around with Euler's identity the other day. I came across something that seems contradictory to everything else I know, but I can't really explain it. I started with e^{i\pi} = -1. I rewrote this as ln[-1] = i\pi Multiplying by a constant, we have kln[-1] = ki\pi...
  38. M

    Mastering Identities: Solving Tricky Problems in Pre-Cal 2

    Hi, I'm new to this site and I'm very happy that I found it. My Pre-cal 2 teacher has been no help to me when it comes to explaining certain steps needed to solve a problem. Overall I'm having a hard time choosing the correct identity needed to solve the problems. However what I do not...
  39. S

    The identity theroem complex analysis

    Homework Statement Prove that there is no holomorphic function f in the open unit disk such that f(1/n)=((-1)^n)/(n^2) for n=2,3,4... Homework Equations The identity theorem: Let f and g be holomorphic functions in the connected open subset of C, G. If f(z)=g(z) for all z in a subset...
  40. C

    Proving the Identity in Quantum Mechanics: A Comparison of LHS and RHS

    Hi I am a Mech Engg student trying to study how stress is defined in quantum mechanics. I am referring to a paper where the following identity is given but i am not sure how to go about proving it The identity is \[ \left\{ {\hat A,\left[ {\nabla _i \nabla _i ,\delta \left( {{\bf{\hat r}} -...
  41. R

    Is (I+P) Always Invertible When P^2 = P?

    Homework Statement Suppose P \in L(V) and P^2 = P. Prove that (I+P) is invertible. Homework Equations The Attempt at a Solution Am I right to assume that since P^2 = P, P = I?
  42. J

    Determining the Identity of Irregular Solids

    well trying to help my little brother with some chem homework, and i believe i am just thinking too hard about this question anyways its a whole chem lab thingy about the composition of pennies and one of the thinking questions is now when it says "identity" I am assuming they are...
  43. quasar987

    Can R be a subring with identity different from 1_S?

    [SOLVED] Identity in a subring Homework Statement In Dummit & Foote on the section on tensor product of modules (10.4 pp.359), the authors write "Suppose that the ring R is a subring of the ring S. Throughout this section, we always assume that 1_R=1_S (this ensures that S is a unital...
  44. L

    Sigma Notation Question/Trig Identity

    [SOLVED] Sigma Notation Question/Trig Identity I posted this elsewhere but I think I put it in the wrong place so I'm going to post my question again here. Basically I have to deduce the second formula from the first. Both equations are the same except for the top of the right side...
  45. M

    Proving Identity: |a × b|² + (a•b)² = |a|²|b|²

    Homework Statement The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below. | a × b |² + (a • b)² = |a|²|b|²...
  46. R

    Derivative of metric and log identity

    Has anyone seen this identity: g^{ab}\nabla g_{ab}=\nabla ln|g| I've seen it used, but want to figure out where it comes from. Does anyone know a name or have any ideas??
  47. H

    To compare an integral with an identity

    Integral inequality and comparison Homework Statement Prove the inequality \frac{2}{(n+1) \cdot \pi} \leq a_n \leq \frac{2}{n \pi}} where a_n = \int_{0}^{\pi} \frac{sin(x)}{n \cdot \pi +x} dx and n \geq 1 The Attempt at a Solution Proof: If n increased the left side of...
  48. M

    Proving Injectivity and the Identity Map for Finite Dimensional Linear Maps

    The question is to prove for finite dimensional T: V to W, T is injective iff there exists an S: W to V such that ST is the identity map on V. I can't quite make the connection between injectivity and the identity map. any suggestions? thanks in advance.
  49. E

    Vector Analysis Identity derivation

    Homework Statement derive the identity: del((F)^2) = 2 F . del(F) + 2Fx (del x F) the dot is a dot product Homework Equations The Attempt at a Solution first i set F = <a,b,c>, making F^2 = a^2 + b^2 + c^2 I took the partial derivatives with respect to x, y, and z (to get the necessary parts...
  50. Y

    Prove a delta function identity

    Hi, I'm stuck with the last proof I need to do Homework Statement I need to prove that f(x)delta(g(x)) = f(x) delta (x-x0)/abs(g'(x)) By delta I mean the Dirac delta function here. (I'm new to this forum, so i don't know how to write it all nicely like so many of you do!) Homework...
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