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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    How Can We Prove the 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...
  3. 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...
  4. Y

    How Do You Prove the Bessel Identity J-3/2(x)?

    I have been working on this for a few days and cannot prove this: J-3/2 (x)=\sqrt{\frac{2}{\pi x}}[\frac{-cos(x)}{x} - sin(x) ] Main reason is \Gamma(n-3/2+1) give a negative value for n=0 and possitive value for n=1,2,3... I cannot find a series representation of this gamma...
  5. K

    Identity for the probability of a coin having an even number of heads

    Homework Statement Given that n independent tosses having probability of p of coming up heads are made, show that an even number of heads results is 0.5(1+(q-p)^n) where q is 1-p, by proving the identity Sigma from i=0 to n/2 of (n choose 2i) (p^2i)(q^(n-2i))=0.5(((p+q)^n)+(q-p)^n)...
  6. S

    How Do You Solve Trig Identities Using Basic Trigonometric Equations?

    Homework Statement (1 + cosθ) / (1 - cosθ) = (1 + secθ) / (secθ - 1) Homework Equations using only the quotient identities, pythagorean identities, and reciprocal identities The Attempt at a Solution didnt know where to start...
  7. E

    Proving Identity of S12^2 in Two Particle System

    I am trying to prove the identity S_{12} ^ 2 = 4S^2-2S_{12} where S12 is the tensor operator: S_{12} = 3(\vec{\sigma_1} \vec{r})(\vec{\sigma_2} \vec{r}) / r^2 - (\vec{\sigma_1} \vec{\sigma_2}) where sigmas are vectors made of the Pauli matrices in the space of particle 1 and 2, and \vec{S}...
  8. S

    Trouble finding the Linear Functions that satisfy the given Identity

    Homework Statement Given f[f(x)] = 2x + 1 find all linear functions that satisfy this identity. Given f[f[f(x)]] = 2x + 1 find all linear functions that satisfy this identity. 2. The attempt at a solution I have not started to attempt a solution at this because I have no idea how to...
  9. S

    Trig Identity Question Sort of

    Homework Statement Okay so the objective here is to express y(t) = cos(t - b) - cos(t) in the form y(t) = Asin(t - c) where A and c are in terms of b.Homework Equations For easy reference, here is a table of identities: http://www.sosmath.com/trig/Trig5/trig5/trig5.html The Attempt at a...
  10. A

    Hypergeometric identity proof using Pochhammer

    I'm trying to show that: F(a, b; z) = F(a-1, b; z) + (z/b) F(a, b+1 ; z) where F(a, b; z) is Kummer's confluent hypergeometric function and F(a, b; z) = SUMn=0[ (a)n * z^n ] / [ (b)n * n!] where (a)n is the Pochhammer symbol and is defined by: a(a+1)(a+2)(a+3)...(a+n-1)...
  11. Pengwuino

    How can Bessel functions be used to prove the expansion of a specific function?

    Homework Statement By appropriate limiting procedures prove the following expansion: J_0 (k\sqrt {\rho ^2 + \rho '^2 - 2\rho \rho '\cos (\phi )} ) = \sum\limits_{m = - \infty }^\infty {e^{im\phi } J_m (k\rho )J_m (k\rho ')} Homework Equations...
  12. L

    How do I simply this (there should be a trig. identity involved

    1. This was actually a center of mass problem, so I got the equation below: 2.[T_2*sin(theta2)] / [T_1*sin(theta1) + T_2*sin(theta2)][b] [b]3. This is part of a solution I obtained for a physics problem. I know there is some trick with a trig indentity that I can use to simplify...
  13. cepheid

    Arctan Identity: Solving t_0 for z=0

    I've encountered an equation in my textbook where a formula for t is given: t = \frac{2}{3H_0 \Omega_{\lambda}^{1/2}} \ln \left( \frac{1 + \cos \theta}{\sin \theta} \right ) where, \tan \theta = \left( \frac{\Omega_0}{\Omega_{\lambda}}\right)^{1/2} (1 + z)^{3/2} So, basically, t is...
  14. M

    Trig Identity: Verify a*sin Bx + b*cos Bx = sqrt(a^2 + b^2)sin(Bx + C)

    [b]1. Verify this identity: a*sin Bx + b*cos Bx = sqrt(a^2 + b^2)sin(Bx + C) where C= arctan b/a [b]2. a/sqrt(a^2+b^2)sin Bx + b/sqrt(a^2+b^2)cos Bx=cos C sin Bx + sin C cos Bx= [b]3.a*sin Bx + b cos Bx = sqrt(a^2 + b^2) sin(Bx + C) Homework Statement Homework Equations...
  15. P

    Solving Integral with Logarithm Identity

    I read the following expression in a book: \int_{-\infty}^{\infty} \dfrac{1}{t(1-t)} \log \left| \dfrac{t^{2} q^{2}}{(p-tq)^{2}} \right| ~ dt = - \pi^{2} p and q are both timelike four-vectors, so p², q² > 0 This integral was solved by using the identity \lim_{s \to \infty}...
  16. P

    What are the steps to simplify a trig identity with multiple angles?

    Homework Statement (sin 3α/sin α) - (cos 3α/cosα) =2 Homework Equations The Attempt at a Solution I know for sin 2 α I would put 2 sinαcosα, so for 3α, do I just put 3sinαcosα? for cos 3α, I'm sort of clueless because there's 3 we can use for cosine, Then after that step, I...
  17. P

    Solving the Cosine Identity: cos(α-β)cos(α+β) = cos2α - sin2 β

    Homework Statement cos(α − β)cos(α + β) = cos2α - sin2 β Homework Equations cos(α + β) = cos α cos β − sin α sin β cos(α − β) = cos α cos β + sin α sin β The Attempt at a Solution I worked out the LHS which makes it cos2α cos2β - sin2α sin2β=RHS Then, I'm stuck, however, i...
  18. C

    Prove jacobian matrix is identity of matrix of order 3

    If f(x,y,z) = xi + yj +zk, prove that Jacobian matrix Df(x,y,z) is the identity matrix of order 3. Because the D operator is linear, D1f(x,y,z) = i, D2f(x,y,z) = k, D3f(x,y,z) = k There is clearly a relationship between this and some sort of identity, but I'm not sure how to state it, and...
  19. F

    Expanding Vector Identity: ∆ x [(u.∆)u]

    Homework Statement Could someone please tell me how to expand: ∆ x [(u.∆)u] Homework Equations [b]3. The Attempt at a Solution thankyou
  20. S

    Euler's Identity: E^iπ=-1, Why e^iπ/3 ≠ -1?

    e^{i\pi}=-1 e^{i\frac{\pi}{2}}=i but e^{i\frac{\pi}{3}}\neq-1 I know there are infinitely many solutions here, but I would expect the third result should include -1 as the cube root of itself. However e^{\pm ix}=cos(x)\pm{isin(x)} would not seem to give -1 for any solution for...
  21. B

    Trigonometric Identity and Differential Equation question

    I'm looking over the differential equation describing a hanging cable in a textbook, and I probably need to review my trigonometric derivatives and integrals again because I'm not seeing how they got the following: \frac{dy}{dx} = tan(\phi) \frac{ws}{T_0} \frac{d^2y}{dx^2} =...
  22. D

    Identity for laplacian of a vector dotted with a vector

    Homework Statement I have $\int \nabla^2 \vec{u} \cdot \vec{v} dV$ where u and v are velocities integrated over a volume. I want to perform integration by parts so that the derivative orders are the same. This is the Galerkin method. Homework Equations The Attempt at a Solution I have...
  23. S

    Exploring Identity in Langston Hughes' "Theme for English B

    Hello, I have to write an essay on the poem "Theme for English B" by Langston Hughes. The topic is is it crippling to question one's identity or is it ultimately enabling? I have trouble understanding the topic. Could anyone give me a general idea on what to write about?
  24. S

    Trig Identity Limit: Solving Trig Identities with Difficulty

    Homework Statement lim t3/tan32t t->0 The Attempt at a Solution I am stuck I have a lot of trouble with trig identities
  25. S

    Solving Simple Trig Identities Homework Problem

    Homework Statement Simplify this expression: f(t) = sin(\betat)*cos(\betat) Homework Equations Identities The Attempt at a Solution I started out by doing sin(\betat)*sin(\betat+\pi/2) but I can't go anywhere from there. If I use the sin(a+b) formula it brings me back to the original...
  26. A

    2 Problems/Trig Function and Identity

    Hello everyone. I officially have the worst Trig teacher in America and I have never been so confused in a math class before. I have at least 5 problems (only 2 posted here) I'm struggling with and need to figure out before my exam tomorrow. Any help is much appreciated. 1. Homework Statement...
  27. R

    Vector calculus identity proof.

    Homework Statement Let f(x,y,z) be a function of three variables and G(x,y,z) be a vector field defined in 3D space. Prove the identity: div(fG)= f*div(G)+G*grad(f) Homework Equations For F=Pi +Qj+Rk div(F)=dF/dx + dQ/dy + dR/dz grad(F)=dF/dx i + dQ/dy j + dR/dz k The...
  28. G

    Is there a unique identity element for matrices?

    For a set S, there is an identity element e with respect to operation * such that for an element a in S: a*e = e*a = a. For a matrix B that is m x n, the identity element for matrix multiplication e = I should satisfy IB = BI = B. But for IB, I is m x m, whereas for BI, I is n x n. Doesn't...
  29. T

    Substitutionless first-order logic w/ identity

    I have been trying to familiarize myself with a particular system of first-order logic with identity, in which the process of substitution is achieved by replacing, one at a time, one occurrence of a variable with a term. (see axiom schemes 6) and 7)). I want to use these axioms to prove the...
  30. E

    Series Identity: Showing f_(a+b) is Equivalent to f_(a)f_(b)

    1. Homework Statement [/b] f _{a} (z) is defined as f(z) = 1 + az + \frac{a(a-1)}{2!}z^{2}+...+\frac{a(a-1)(a-2)...(a-n+1)}{n!}z^{n} + ... where a is constant Show that for any a,b f _{a+b} (z)= f _{a}(z)f _{b}(z) Homework EquationsThe Attempt at a Solution I've tried starting directly...
  31. C

    Trig Identity - Never Seen This Before

    Homework Statement http://carlodm.com/images/m.png Homework Equations sin2 et + cos2 et = 1 The identity above is foreign to me. Can anyone explain/have external links that explains this identity? I haven't seen anything like it and Google isn't showing anything useful. Thanks
  32. E

    Continuity of the identity function on function spaces.

    Homework Statement Show that if p\in (1,\infty) the identity functions id:C^{0}_{1}[a,b]\longrightarrow C^{0}_{p}[a,b] and id:C^{0}_{p}[a,b]\longrightarrow C^{0}_{\infty}[a,b] are not continuous. Homework Equations C^{0}_{p}[a,b] is the space of continuous functions on the [a,b] with...
  33. Z

    How Do Trig Identities Help Calculate Derivatives?

    1. Find the limit of [Cos(x+h)-Cos(x)]/h as h approaches 0 2. Solve using trig identity cos(A+B)= cos(A)cos(B)-sin(A)sin(B) 3. My first class using the actual definition of a derivative. My high school teacher just showed us the shorthand and said "good luck when you get to...
  34. O

    What is the validity of the vector identity Ax(BxC)?

    Homework Statement Regarding the identity Ax(BxC) Homework Equations Does this identity only hold when A != B != C?
  35. P

    Is the identity I came up with for sin(x) ^ 2 correct?

    I noticed that the graphs of sin(x) and sin(x) ^ 2 are very similar. So I offset sin(x) ^ 2 to exactly match sin(x): sin(x) = 2 sin^{2}\left(\frac{x}{2} +\frac{\pi}{4}\right) - 1 Is this right, or is it an illusion? I haven't been able to find any identity that this is based on. If it is...
  36. Pythagorean

    What Is a Lie Group Without an Identity Matrix Called?

    Is there a name for studying a Lie "group" that doesn't use the identity matrix as a member of the group? I know it's not technically a group anymore, but is there any mathematical work pertaining to the general idea... and what is the terminology so that I can research it better?
  37. P

    Is the Divergence of the Cross Product of Gradients Zero?

    Homework Statement div(grad f x grad g)=0. I need to prove this somehow. Homework Equations The Attempt at a Solution I don't really know where to even start this at >.< any help is greatly appreciated.
  38. M

    Derive the Pythagoream Identity

    Homework Statement Derive sin^2 + cos^2 = 1 Homework Equations Use cos 0 =1, cos (x+y) = cos x cos y - sin x sin y Earlier someone posted this same question, but I still don't understand it so please help
  39. J

    Trig identity question need checking

    1. cos(2x+y) = cos(a+b) = sinasinb + cosacosb = (2x+y) = sin2xsiny + cos2xcosy = sin2x = 2sinxcosx and cos2x = cos2x-sin2x = cos(2x+y) = (cos2x-sin2x)cosy - (2sinxcosx and cos2x)siny (is this correct) 2. evaluate the following exactly (use \sqrt{} in your answer where necessary) cos...
  40. J

    An identity involving a Dirac delta function.

    I have been reading papers for my research and I came across this equation twice: \lim_{\eta\to 0+}\frac{1}{x+i \eta} = P\left(\frac{1}{x}\right) - i \pi \delta(x) Where P is the pricipal part. It has been quite a while since I have had complex variables, but might it come from the...
  41. N

    Is This Tensor Identity Valid?

    Homework Statement I do not know if the following is correct;if it is,I will be able to save some calculation while doing a problem.Can you please let me know if it is true: \epsilon_{ijk}\*\epsilon_{lmn} = \left(\begin{array}{ccc}\ g_\ {11}&\ g_\ {21}&\ g_\ {31}\\ g_\ {12}&\ g_\...
  42. S

    Are equal sets always identical in mathematics?

    Two sets are equal iff they contain the same elements. I would argue that two sets that have the same elements are identical as well as equal and that there is a difference between identity and equality. In general {2,3}={3,2} if neither set is defined to be ordered. However obviously {5} \neq...
  43. R

    Question about cosine and Eulers identity

    I was doing a signals and systems problem and I think I might be screwing something up with the cosine function because I get cos(a+b) = cos(a)*cos(b) This is how cos(a+b)=Re\left\{ e^{j*(a+b)} \right\} =Re\left\{ e^{j*(a)}*e^{j*(b)} \right\} =cos(a)*cos(b) Can anyone point out my mistake...
  44. R

    Why Does This Polylogarithm Identity Have No Restrictions?

    I found this equation last night on Wolfram: http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/PolyLog/06/03/0001/ How is it possible this equation has no restrictions given that the gamma function has poles at the negative integers? Also, won't the zeta function portion run...
  45. mnb96

    Semigroup partitions and Identity element

    If I have a semigroup S, is it possible to partition the set of element S into two semigroups S_1 and S_2 (with S_1 \cap S_2 = 0), in such a way that S_1 has an identity element but S_2 has none?
  46. H

    Solving Trig Identities: Combining Cos(x) and Sin(x) Terms

    I forget how this one goes. A cos(x) + B sin (x) = C sin (x + invtan(?)) How do you go about condensing both these terms into 1 like the above?
  47. H

    Proving the Identity: sin2(x)-sin2(x)=sin(x+y)sin(x-y)?

    Homework Statement Prove this is an identity: sin2(x)-sin2(x)=sin(x+y)sin(x-y) Homework Equations N/A The Attempt at a Solution I have made a lot of attempts but can not get one side to equal the other. I know It's something really simple I am missing, but can't figure it out.
  48. S

    From Euler's identity: i^i=exp(-pi/2)= 0.2079 (rounded)

    From Euler's identity: i^i=exp(-pi/2)= 0.2079 (rounded). I've always thought of this as an interesting result although I don't know of any particular significance or consequence of it. Is there any?
  49. J

    Trying to prove a trig identity

    Homework Statement cos^2x-cotx --------------- = cot^2x sin^2x-tanx Homework Equations The Attempt at a Solution every solution I get gives me a zero, not cot^2
  50. A

    If x is a cycle of length n, x^n is the identity.

    Is it true that if \sigma \in S_n is a cycle of length k \leq n, then \sigma^k = \varepsilon, where \varepsilon is the identity permutation, and that k is the least nonzero integer having this property?
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