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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    Prove Trig Identity: A+B+C = 180 → 1+4 cosAcosBcosC

    Question Statement If A+B+C = 180, prove that cos (A+B-C) + cos (B+C-A) + cos (C+A-B) = 1+4 cosAcosBcosC My Attempt If A+B+C=180, Then A+B-C=180-2C cos (A+B-c)=cos(180-2C) (After some substitution and caculation) cos (A+B-C) = -cos 2C Similarily, I obtain the same expression for...
  2. P

    Boolean rings with identity can only take 2 elements?

    Using the theorem that in any boolean ring a+a=0 for all a in boolean ring R. Then 0 is in R. Make the multiplicative identity 1 is also in it. Therefore R can only take 0 and 1 and no more because 1+1=0. 0+0=0. 1+0=1 always. So 2 or other elements can never occur.
  3. happyg1

    Solving a Constructible Identity: 1+e to the 2pi/7i and Beyond

    Homework Statement hi, I'm working on constructible things again and in one of the proofs our prof threw out this identity and I just don't know where it came from...
  4. P

    What is the derivation of the identity (dS/dV)T=(dP/dT)V in thermodynamics?

    Homework Statement If dU=TdS-PdV then (dS/dV)T=(dP/dT)V the T and V at the end means that T and V are constant How did they get this identity? It came from a thermodynamics hence for their notations. I have tried ways like rearranging but it dosen't seem to work. I think it has something to...
  5. K

    Solving Vector Identity: {phi (grad phi)} X (n^)dS=0

    Homework Statement I am to show: closed integral {phi (grad phi)} X (n^)dS=0 Homework Equations The Attempt at a Solution I understand I am to use divergence theorem here.but cannot approach.Please help
  6. C

    Proving Identity: tan²θ - sin²θ = tan²θsin²θ

    Homework Statement Prove the Identity: tan²θ - sin²θ = tan²θsin²θ Homework Equations The Attempt at a Solution Well I got up to (sin²θ/cos²θ) - (sin²θcos²θ/cos²θ) = sin⁴θ/cos²θ I got the answer cause my calculator says sin²θ - sin²θcos²θ = sin⁴θ But I don't know how sin²θ - sin²θcos²θ =...
  7. U

    Does Parity Operator Squared Equal Identity Operator?

    just wondering... does the parity operator squared give the identity operator?
  8. C

    Proving this trigonometric identity

    Homework Statement Prove the following identity: (1 + cos \theta)^2 + sin^2\theta = 2(1 + cos \theta) Homework Equations cos^2 \theta + sin^2 \theta = 1 The Attempt at a Solution I've squared out the first bracket so that it becomes 1 + cos^2 \theta and multiplied out the second bracket so...
  9. R

    How to Prove This Fibonacci Identity Involving Squares and Products?

    Can someone guide me on how to prove that F_{4n+3} + F_{4n+6} = F_{2n+1}^2 + F_{2n+4}^2 either side of the above is the difference (F_{2n+2}*F_{2n+3} + F_{2n+4}^2) - (F_{2n}*F_{2n+1} + F_{2n+2}^2) I intend to post this sequence F_{2n}*F_{2n+1} + F_{2n+2}^2, with a comment re a few...
  10. K

    Solving Trig Problem: sin^2000(x) + cos^2000(x)=1 - Kirstin

    I'm trying to solve this trig problem: sin^2000(x) + cos^2000(x) = 1 I'm not sure how to go about it... I tried starting with sin^2(x) + cos^2(x) = 1 and build up to 2000 but I didn't get very far. Obviously any multiple of pi will be an answer since either sin^2000 or cos^2000 will be...
  11. D

    Proving a Trigonometric Identity Using Exponential Functions

    Hi. I need to prove the following identity \arccos{z} =i \ln { z + (z^2 -1)^\frac{1}{2} } I was given a hint to write \cos{A}=z, then rewrite \cos{A} in terms of the exponential. \cos{A}=\frac{\exp{iA}+\exp{-iA}}{2}=z I took the log on both sides and got stuck at that...
  12. H

    Bézout's identity and Diophantine Equation

    I am having problems with one exam question. Does this diophantine equation have a solution(s) 12a+21b+33c=6 as far as I know this is not a linear equation, and what I read online says that Bezout identity only applies for linear diophantine equations. The solution says gcd(12,21,33)...
  13. H

    [Identity relations] Need help at some odd identity relation problem

    Homework Statement On the set of Natural Numbers from 1 to 10000 are given the following identity relations. R1 ; n R1 m where m and n have the same remainder by division by 24, that is mod n 24 == mod m 24. R2 ; n R2 m where n and m have in decimal notation the same number of 2s R3; n...
  14. K

    Trigonometric Identity in My Book: Understanding (cos4x)^2 = 1+cos8x

    In my book, (cos4x)^2 is written 1+cos8x without referring to any formula. Which trig. identity is used here?
  15. K

    Trigonometric Identity Problems

    Can anyone help me solve the following problems? sec theta -1/1-cos theta = sec theta tan (pie/2 - theta) tan theta =1 Thanks
  16. S

    Proving Cartan's Identity: Tips & Hints

    Hi can someone help me prove this identity? I'm having trouble understand the role of the interior product or more precisely how to calculate with it. My professor uses the "cut" notation _| but i don't see this in any textbooks. Can someone give me some hints on how to prove the identity?
  17. A

    How to prove Chepyshev's polynomials generating function identity?

    (1-xt)/(1-2xt+t^2)=sum(Tn(x)t^n) How can i prove this equation? Could you give me a hint or suggestion?
  18. U

    Deriving heat capacity using thermodynamics identity

    Homework Statement Use the thermodynamic identity to derive the heat capacity formula C_V=T\frac{\partial{S}}{\partial{T}}_VHomework Equations C_V=\frac{\partial{U}}{\partial{T}} T=\frac{\partial{U}}{\partial{S}} dU=TdS-PdV+\mudN The Attempt at a Solution I used...
  19. B

    Proving Logarithm Identity for Nonzero Complex Numbers

    Homework Statement Show that, for any two nonzero complex numbers z_1 and z_2, \text{Log } (z_1 z_2) = \text{Log } z_1 + \text{Log } z_2 + 2 N \pi i \, , where N has one of the values -1, 0, 1. Homework Equations The logarithm on the principal branch is: \begin{align*}...
  20. D

    One More Trig Identity Problem

    There is one last problem i have on my trig assignment and i have no clue how to do it. The questions is: Find sinx, cosx, tanx, sin2x, cos2x, and tan2x from the given information: secx=5, sin is negative. If anyone could show me how to do this problem it would be soooo appreciated...
  21. D

    Proving the Trig Identity tanx+cotx=2csc2x

    Hey I've got an assignment on trig identities and can't figure this one out. Prove the Identity: tanx+cotx=2csc2x I got to tanx+cotx= 1/2 sin2x=1/4sinx2cosx but when i get to the point where i have numbers in front of the sinx or cosx i don't know what to do. Thanks for any help
  22. T

    Solving the Mystery of an Unfamiliar Trig Identity

    Today the professor wrote down the following for use in an integral: \frac{1}{2}cos(2\theta)=sin\theta cos\theta i am not sure is this is correct. i have tried to prove this and cannot, i have also not found it in an table of trig identities. Is this a valid identity? i am not sure since...
  23. K

    Prove $\hat{A}+\hat{B}$ Commutator $\lambda$ Complex Number Relation

    Question: If \hat{A} and \hat{B} are two operators such that \left[\hat{A},\hat{B}\right] = \lambda, where \lambda is a complex number, and if \mu is a second complex number, prove that: e^{\mu\left(\hat{A}+\hat{B}\right)}=e^{\mu\hat{A}}e^{\mu\hat{B}}e^{-\mu^{2}\frac{\lambda}{2}} What I...
  24. D

    Proving an Identity Involving Matrices and Inner Products

    Is there a non-ugly proof of the following identity: \langle Ax,y \rangle = \langle x,A^*y \rangle where A is an nxn matrix over, say, \mathbb{C}, A* is its conjugate transpose, and \langle \cdot , \cdot \rangle is the standard inner product on \mathbb{C} ^n.
  25. B

    Does \tan\frac{\theta}{2} equal \frac{\sin\theta}{1+\cos\theta}?

    This isn't a homework question, it's just for personal enrichment. I've been trying to prove that \tan\frac{\theta}{2}=\frac{\sin\theta}{1+\cos\theta} I tried starting off with \tan\frac{\theta}{2}=\frac{\sin\frac{\theta}{2}}{\cos\frac{\theta}{2}} is this even the right way to start the...
  26. R

    Could someone please prove this identity

    tan3A= 3tanA-tan3A/1-3tan^2 A
  27. R

    Difficulty proving another identity

    could anyone explain (no calculation) how to work the following identity so could get an understanding of it thank you tan(45+A)degrees tan(45-A)degrees=1
  28. R

    What's the Trick to Proving tan3A=3tanA-tan^3 A/ 1-3tan^2 A?

    can anyone help[ me prove the following identity i keep on ending up in a dead end tan3A=3tanA-tan^3 A/ 1-3tan^2 A thank you
  29. S

    Fourier series: Parseval's identity HELP

    Hey all, I am unsure how to do this problem... i find problems where i have to derive things quite difficult! :P http://img143.imageshack.us/img143/744/picture2ao8.png this is the Full Fourier series i think and so the Fourier coeffiecients would be given by...
  30. C

    Overcoming Roadblocks in Trigonometric Identity Proofs

    Hi, I am trying to prove \frac{tanx+1}{tanx-1}=\frac{secx+cscx}{secx-cscx} I am working on the right side and trying to get it to the same form as the left side. I get to \frac{1+2sinxcosx}{sin^{2}x-cos^{2}x} which I COULD apply the fact that sin2x=2sinxcosx as well as...
  31. C

    Lagrange Identity Sum Notation

    Hi, how do I interpret the last sum: http://planetmath.org/encyclopedia/LagrangesIdentity.html Sum (...) 1<=k < j <= n Is it the double sum: Sum( Sum( (a_k*b_j - a_j*b_k)^2 from k = 1 to n) from j = 2 to n ) ?
  32. D

    Proving the Identity: gcd(a, lcm(b,c))

    Is this identity true? gcd(a, lcm(b,c)) = lcm(gcd(a,b), gcd(a,c))
  33. C

    Trigonometric Identity for 1/2csc(THETA)sec(THETA)

    Hi, I have a question about a problem: 1/2csc(THETA)sec(THETA) I have to find the identity for it and I know that csc is 1/sin and sec is 1/cos but after that I don't see where it can lead to a simple answer. If anyone knows it would be helpful, thanks!
  34. P

    How can we combat the rising threat of spam and identity theft?

    It seems to me that this problem is going to become a major issue sooner than later. Not soon enough in my opinion considering no one is doing anything about it. Much as I would like these people summarily executed without trial, the problem will unfortunately have to get much worse before...
  35. mattmns

    How can the trig identity |cos(z)|^2 = cos^2x + sinh^2y be proven?

    I am asked to prove the following: (Note: z = x + iy) |cos(z)|2 = cos2x + sinh2y --------------- So I started the following way: |cos(z)|2 = |cos(x+iy)|2 = |cos(x)cosh(y) - i(sin(x)sinh(y))|2 = cos2(x)cosh2(y) + sin2(x)sinh2(y) [after having square root squared removed] once I got here I...
  36. E

    Identity Matrix: Does AB=BA for Other Matrices?

    Is the identity matrix (or multiple of) the only one that commutes with other matrices or are there other matrices that AB=BA? Thanks
  37. A

    Prove identity matrix cannot be product of an odd number of row exchanges

    Problem: #29 in Strang Linear Algebra Prove that the identity matrix cannot be the product of 3 row exchanges (or five). It can be the product of 2 exchanges (or 4). Now, to start, we try to count the number of rows that are different from the identity matrix. For the first row exchange, it's...
  38. kakarukeys

    Is there such an identity about SO(3)?

    T^i K_{ij} = K T^j K^{-1} repeated indices imply summation. T^i are the generators (Lie algebra elements) of SO(3). i.e.T^i_{jk} = - \epsilon_{ijk} T^i \in so(3) K \in SO(3) How to show it's true? Is there a universal formula for all Lie group?
  39. H

    Need a quick help with a simple identity

    Hi Where is the error is this 'identity'?: (-e^i)^{\frac{1}{2}} = (-1)^{\frac{1}{2}}*e^{\frac{i}{2}} My calculator says that the right side is minus one times the left but I can't see the mistake I'v made. Help me please, thanks.
  40. L

    Difference between Kronecker delta and identity matrix

    Hi, As in the title, what's the difference between the Kronecker delta and the identity matrix? They seem to have the exact same definition, so why are they differentiated? Thanks. Molu
  41. MathematicalPhysicist

    A nice identity, in need of a proof.

    how do i prove the next identity: 999/1000=1/(2!)+2/(3!)+3/(4!)+4/(5!)+5/(6!)+1/(7!)+7/(8!)+6/(9!)+1/(10!)+2/(11!)+2/(12!)+5/(13!)+2/(14!)+12/(15!)?
  42. M

    Proving an Identity from Differential Geometry

    One often encounters the following identitiy in Tensor Analysis/Differential Geometry: dx^j (partial/partial x^i) = partial x^j / partial x^i = delta ij It's easy to see why partial x^j / partial x^i = delta ij but how does dx^j (partial/partial x^i) = partial x^j/partial x^i ? I...
  43. B

    Another vector identity question

    Hi, I'm stuck another vector identity question. It's of a different kind to the other one I asked about and looks so much easier but I just can't see what I need to do. I am told to use standard identities to deduce the following result. The standard identities being referred to are listed in...
  44. B

    Proving Identity of $\nabla \times (\nabla \times F)$

    Hi, I am having an immense amount of trouble trying to show that the following identity is true. Q. Let F be a C^2 vector field. Prove that \nabla \times \left( {\nabla \times \mathop F\limits^ \to } \right) = \nabla \left( {\nabla \bullet \mathop F\limits^ \to } \right) - \nabla ^2...
  45. C

    How to Prove Complex Trigonometric Identity?

    how can i prove tan X/sinx+cosx=sin^2 X + sinXcosX/cos X - 2cos^3X so far I've tried using basic identities to figure it out, but i just end up getting confused. :confused:
  46. Apost8

    Proving the Pythagorean Identity: A Brief Analysis

    For homework, we were asked to prove that \cos^2 \theta + \sin^2 \theta = 1 is true for all angles \theta . Can someone please take a look at these and let me know if they are acceptable. I'm pretty sure the second one works, but I'm not sure of the first one, mainly because the premise of...
  47. T

    How Can Euler's Identity Be Applied to Write Phasor Equations v(t) and I(t)?

    for phasor, v = 20V e^(-j60) and i = 0.5A e^(-j30) how can i write them in v(t) and I(t) ?? pls help thanx
  48. J

    Trigonometric Identity? - Deriving the Double Angle Formulas for Sine and Cosine

    Trigonometric Identity?? I just can't figure this out. I don't think I've covered enough material to do this. Can anyone help? I've put the entire question but I am sure all i need is a little explanation and maybe the first answer and i could do the rest. :confused: Let z =...
  49. D

    Identity for |sinx-siny|

    does anybody know the identity for |sinx-siny| and |cosx-cosy|?
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