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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    How to Prove Gamma and Beta Function Identities?

    Homework Statement Need to prove these 2 identities of beta function & gamma function ? Homework Equations G(n)G(1-n)= pi/sin npi B(m,n) = (m-1)! / n (n+1)...(n+m+1) The Attempt at a Solution I tired using beta function in 1st one but did not get the solution .
  2. A

    Proving the triple curl identity

    Homework Statement Prove that \nabla \times (\nabla \times \vec{A}) = \nabla(\nabla \cdot \vec{A}) - (\nabla \cdot \nabla)\vec{A} using Einstein notation. Homework Equations \nabla \times (\nabla \times \vec{A}) = \nabla(\nabla \cdot \vec{A}) - (\nabla \cdot \nabla)\vec{A}...
  3. Q

    Help with a Trigonometric identity

    Help with a Trigonometric identity... Homework Statement (sin x + sin 2x + sin 4x) / (cos x + cos 2x + cos 4x) = tan 2x Homework Equations sin 2x = 2sinxcosx; cos 2x = cos^2x - sin^2x The Attempt at a Solution solving left side, =[sin x + sin 2x + sin (2x + 2x)]/[cos x + cos...
  4. T

    Prove that the Given Equation is an (Trig) Identity

    Homework Statement Prove that the Given Equation is an Identity: sin2A ------ = cotA 1 - cos2A Homework Equations sin(A+B) = sinAcosB + cosAsinB cos(A+B) = cosAcosB - sinAsinB tan(A+B) = (tanA + tanB) / (1 - tanAtanB) sin2A = 2sinAcosA cos2A = cos^{}2A - sin^{}2A...
  5. Q

    What trig identity did they use?

    Hi I'm having trouble understanding how they simplified this integration using trig substitutions...I really don't know what identities they used to make these substitutions or the strategy behind why this substitution was made(particularly the 3 steps in the red box). Obviously it works but I...
  6. V

    How to Simplify Trig Identity Proofs?

    More Trig Identity Proofs ... Homework Statement 1. cot^2x - 1 = cot2x ----------- 2cotx2. tanx + cotx = 2csc2x3. cos(A+B) = 1-tanAtanB --------- ---------- cos(A-B) 1+tanAtanB Homework Equations The Attempt at a Solution...
  7. E

    Proving Trig Identity for Odd n | Step-by-Step Solution

    [SOLVED] trig identity Homework Statement Can someone help me prove that \sum_{k=1}^{(n-1)/2}\cos(2 \pi k / n) = -1/2 where n is an odd number?Homework Equations The Attempt at a Solution I don't know where to start. You can easily verify it is true for n=3. But after that things get...
  8. quasar987

    Normed spaces and the parallelogram identity

    Homework Statement My professor stated the theorem "If (X,<,>) is an an inner product space and || || is the norm generated by <,>, then we have ||x+y||² + ||x-y||² = 2(||x||² + ||y||²)." But then she also said that the converse was true. I suppose this means that "Given (X, || ||) a normed...
  9. T

    Simplifying Trig Identity: cos^2x - cos^4x = cos^2x sin^2x

    Homework Statement cos^2x - cos^4x = cos^2x sin^2x Homework Equations N/A The Attempt at a Solution L.S. = cos^2x -(cos^2x)(cos^2x) = cos^2x -cos^2x(cos^2x) I'm stuck here. Am I doing something wrong during the first step? Thanks for your help.
  10. T

    Trig Identity Homework: Solving Equations with Sin and Cos Functions

    Homework Statement 1. (sinx - cosx)(sinx + cosx) = 2sin^2x-1 2. (2sinx + 3cos)^2 + (3sinx - 2cosx)^2 = 13 Homework Equations N/A The Attempt at a Solution For 1. L.S. = sinx^2+sinxcosx-sinxcosx-cosx^2, the sinxcosx cancels and I'm lost. I haven't a clue how to do the second...
  11. G

    Prove a sum identity for bessel function

    Hi This is one of the problems for my take home final exam on differential equations. I have been looking for a solution for this problem intensely for the last two days. This problem comes from Calculus vol 2 by Apostol section 6.24 ex 7. here it is Homework Statement Use the identities...
  12. M

    How can we prove a given identity?

    How can we proceed to prove the following identity ?
  13. P

    How can I prove this binomial identity?

    Homework Statement Prove that the following binomial identity holds: {n+k-1 \choose k} = \sum_{i=1}^k {k-1\choose i-1}{n\choose i} The Attempt at a Solution One of the methods I've tried is to use induction on the variable n, but while trying this I got stuk on rewriting the...
  14. W

    Lorentz's identity, relative speed

    Homework Statement start from: x = [x' + vt']/sqrt[1 - v^2/c^2] ct = [v/cx' +ct']/sqrt[1 - v^2/c^2] y = y' z = z' Homework Equations show that ( 1 - \frac{u^{2}}{c^{2}})(1+\frac{vux'^{2}}{c^{2}}) = ( 1 - \frac{v^{2}}{c^{2}})(1-\frac{u'^{2}}{c^{2}}) The Attempt at a Solution...
  15. C

    Double Sum Identity Problem Solution

    Hi. The problem is as follows: Homework Statement Let m and n be integers, we may assume that (if they are not equal), m is the smallest. Then \sum_{i=0}^m \sum _{j=0}^n f((m+n)-2 (i+j)) = \sum_{i=0}^m \sum _{j=0}^{-2 i+m+n} f((m+n)-2 (i+j)) for some sequence f(k)_k. Homework Equations...
  16. S

    Trig Identity problem (double angle formulas incl.)

    Homework Statement (1) (1+cosx)/(sinx)= cot (x/2) (2) 2 csc 2x= sec x csc x (3) cos^6 x- sin^6 x= cos 2x(1 - 1/4sin^2 2x) ( I think this has to do something with subtracting -3a^2b^2, since I need to get a-2ab+b to factor it..?) Homework Equations Addition and Subtraction...
  17. D

    Prove: Product of Sin Values = $\frac{\sqrt{n}}{2^{n-1}}$

    Homework Statement Show that \prod_{k=1}^{n-1}\sin\frac{k\pi}{2n}=\frac{\sqrt{n}}{2^{n-1}} The Attempt at a Solution I have no idea where to start.
  18. R

    Trig Identity: Solving a RHS LHS Problem with Cosine Functions

    [SOLVED] Trig Identity Homework Statement cos^4 (x) = (3/8) + (1/2)(cos(2x)) + (1/8)(cos(4x)) Homework Equations cos2x = 2cos^2 x - 1 cos^2 x = 1 - sin^2 x The Attempt at a Solution Can someone please give me hints? Thanks.
  19. M

    Weak/strong group identity axiom

    Hello all. While going back to group theory basics to make sure i understand rather than just know the fundamentals i came across for the first time ( having read many books ) the weak versus strong versions of the identity axiom. The strong version says that a group must have a unique...
  20. M

    Commutative rings with identity

    I have a trouble proving that a finate (nonzero) commutative ring with no zero divisors must have an identity with respect to multiplication. Could anybody please give me some hints? I do know all the definitions (of ring, commutative ring, zero divisors, identity) but have no idea how to go...
  21. R

    Have you seen this new recursive series identity?

    I derived the following identity after considering my thread "Recursive series equality" but the result is so clean and neat that I post it as a new topic. Let S_{0} = 0 \quad S_{1} = 1 \quad S_{n} = b*S_{n-1} - S_{n-2} Then S_{n}*(S_{n+b} -S_{b-2}) = (S_{n+1}+1)*(S_{n+b-1} -S_{b-1})...
  22. D

    Verifying and Proving z=cisθ Identity

    If z=cis\theta, verify that \tan \theta = \frac{{z - z^{ - 1} }}{{i(z + z^{ - 1} )}} . Use this result to prove that \cos (2\theta ) = \frac{{1 - \tan ^2 \theta }}{{1 + \tan ^2 \theta }} Ok, I've managed to verify the first equation given, but I am not really sure how to use it to...
  23. MathematicalPhysicist

    Proving the Binomial Identity: A Shorter Solution Approach

    problem prove that: \forall n \in N \forall 0<=k<=2^{n-1} (C(2^n,k)=\sum_{j=0}^{k}C(2^{n-1},j)C(2^{n-1},k-j)) attempt at solution induction seems to be too long I am opting for a shorter solution, so the sum that it's wrriten in the rhs is the square of the sum of the term C(2^(n-1),j) but...
  24. T

    Is there a unique multiplicative identity for all real numbers?

    Homework Statement Prove that there is at most one real number b with the property that br=r for all real numbers r. (Such a number is called a multiplicative identity) Note: to show there is a unique object with a certain property, show that (1) there is an object with the property and (2)...
  25. M

    The Bianchi Identity for p-Form Fields: Understanding Its Significance

    Dear All Does anyone have an online (preferably) source on the Bianchi identity on p-form fields (dF=0)? I would like to read more on the various cases, particularly the physical meaning of a violated Bianchi identity. Thanks ...
  26. I

    Finding a Trig Identity to Show a Relation

    I know that \frac{1-cos(x)}{2sin\left(\frac{x}{2}\right)} = sin\left(\frac{x}{2}\right) but is there a trig identity that states this? I've been manipulating a certain equation to try and fit a trig identity to make everything make sense. Actually, I started out with...
  27. A

    Poisson's Identity: Solving ((φλ)χ)+((λχ)φ)+((χφ)λ)=0

    please help me to solve this identity ((\phi\lambda)\chi)+((\lambda\chi)\phi)+((\chi\phi)\lambda)=0 where () = poisson bracket \phi=\phi(t,q_{i},p_{i}) \chi=\chi(t,q_{i},p_{i}) \lambda=\lambda(t,q_{i},p_{i}) for i=1,2,...,n
  28. rocomath

    Trigonometry, Prove the Identity and more

    Homework Statement Prove the identity 11. 1 - co5xcos3x - sin5xsin3x = 2sin^2x 50. ln |secx + tanx| = -ln |secx - tanx| 52. The following equation occurs in the study of mechanics: \sin\theta = \frac{I_1\cos\phi}{\sqrt{(I_1\cos\phi)^2 + (I_2\sin\phi)^2}}. It can happen that I_1 = I_2...
  29. malawi_glenn

    What is the Momentum Operator Identity in Modern Quantum Mechanics?

    Homework Statement I want to show: \langle x' - \triangle x' \vert \alpha \rangle = \langle x' \vert \alpha \rangle - \triangle x' \dfrac{\partial}{\partial x'}\langle x' \vert \alpha \rangle Homework Equations \vert \alpha \rangle is a state. The Attempt at a Solution i...
  30. L

    Help with identity for ideals

    I'm trying to prove this problem out of Allan Clark's Elements of abstract algebra. Given an epimorphism \phi from R -> R' Prove that: \phi^{-1}(a'b') = (\phi^{-1}a')(\phi^{-1}b') where a' and b' are ideals of R' I had no trouble showing that (\phi^{-1}a')(\phi^{-1}b') is a subset...
  31. R

    Tringular Number Identity

    Let T_{n} = n*(n+1)/2 and n and m are integers. I discovered that 2*n+1 = \frac{(T_{(n-1)} -m)*(T_{(n+2)}-m) - (T_{(n-2)}-m)*(T_{(n+1)}-m)}{(T_{n} - m - 1)} except for the case where the denominator is zero. Is there a simple way to prove this identity?
  32. E

    Vandermonde's Identity: Exploring a Special Case with Binomial Coefficients

    Homework Statement Is the identity C(m, a) + C(m,a+1) = C(m+1,a+1) (where C is the binomial coefficient function) a special case of Vandermonde's identity: \sum_{k=0}^r \binom{m}{r-k} * \binom{n}{k} = \binom{m+n}{r} Homework Equations The Attempt at a Solution n (or m) must...
  33. B

    Answer check, Hyperbolic trig identity (proof)

    Homework Statement Evaluate the integral: (int sign) Sech³xTanhx dxHomework Equations Derivative of Sechx = -(SechxTanhx)The Attempt at a Solution Rewrite as: Sech²xSechxTanhx U=sechx Du = -(SechxTanhx)dx -Du = SechxTanhx dx replace into integral -(integral sign) U²du Evaluate: -U³ / 3...
  34. C

    Understanding Vandermonde's Identity: Explanation and Proof

    Hey guys, Could someone give me a clear explanation of what Vandermonde's Identity is? I'm looking at the proof in my book and I'm having a difficult time understanding this. Fortunately I understand the rest of the section (which covers Binomial theorem, Pascal's identity and triangle)...
  35. D

    Reciprocal Derivative Identity

    Hi. I was just wondering, how can i prove the following identity: \frac{{dy}}{{dx}}\frac{{dx}}{{dy}} = 1 Its nothing that I am required to know, but i was just curious, so for all i know, it may be way out of anything that i can mathematically comprehend. The best I've been able to...
  36. K

    Is this Trig Identity really an identity?

    The textbook states something along the lines as prove the identity. 1 - ((sin^2x)/(1+cos x)) = cos x If you want you an work this out algebraically relatively easily to get cos x = cos x. But what if you put pi back into the original equation? You get 1 - undefined = cos x. So I graphed...
  37. C

    How to derive pythagorean identity?

    I got some precalc review to prepare for calc, and after hours of doing the packet, I'm on the last problem set...but it's all about derivatives which we never touched on last year. Homework Statement I'm supposed to derive sin^2 + cos^2 = 1 Homework Equations It says to use cos 0...
  38. N

    What is the proof for (∂u/∂T)_P=c_P – Pβv?

    Homework Statement To prove that (∂u/∂T)_P=c_P – Pβv where _P =>P constant;β=>co-eff. of vol exp. Homework Equations The Attempt at a Solution I proved it for ideal gases. Write d'Q=dh-vdP Now expand d'Q with 1st law and du(in 1st law) in terms of dP and dT.Since du is a total...
  39. H

    Deriving a trigonometric identity

    For a homework assignment I'm supposed to prove that sin(x)^2+cos(x)^2=1, using only the following identities (along with algebraic operations): sin(-x)=-sin(x) cos(-x)=cos(x) cos(x+y)=cos(x)cos(y)-sin(x)sin(y) sin(x+y)=sin(x)cos(y)+cos(x)sin(y) I can't figure this out, because as far...
  40. L

    Exploring John's Identity: Who Is He Really?

    Who am I, and what is it that give this identity to this daily life person that I know as me ? Should I say that I'm "John the taxi" driver or "John the teacher" or "John the neigbour", or what should I say ? What is that or those specific properties that gives John the identity of the...
  41. B

    Fundamental identity of SR valid in GR?

    From http://www.us.oup.com/us/catalog/general/subject/Physics/Relativity/?view=usa&ci=9780198567325" I learn that the fundamental identity c^2\text{d}{t'}^2 -\text{d}{x'}^2 -\text{d}{y'}^2 -\text{d}{z'}^2 = c^2\text{d}{t}^2 -\text{d}{x}^2 -\text{d}{y}^2 -\text{d}{z}^2 relates co-ordinates...
  42. J

    How to Prove contracted Bianchi Identity

    How to prove g^{im} \nabla_{\partial_j}R_{ilkm}=\nabla_{\partial_j}R_{lk}. of cause g^{im}R_{ilkm}=R_{lk}, but I don't know how the contraction can pass through the covariant derivative?
  43. N

    How to Use Vector Analysis Identity to Solve a Closed Loop Integral?

    Homework Statement we are to show a=(1/2) closed loop integral over [r x dl] Homework Equations The Attempt at a Solution I suppose this can be done formally from the alternative form of Stokes' theorem that can be obtained by replacing the vector field in curl theorem by VxC...
  44. K

    Verify that each equation is an identity

    The question is "Verify that each equation is an identity." Problem tan 8k - tan 8k tan^2 4k = 2 tan 4k The first thing I tried was to factor out the tangents. tan 8k (1 - tan^2 4k) then if I'm doing this correctly tan 8k (1 - tan 2k) (1 + tan 2k) But from here I'm stuck, that is if I'm on...
  45. K

    Transforming Trigonometric Identities: Solving 2(cosx)^2+2cosxsinx=0

    Which trigonometric identitiy are used to transform 2(cos(x))^2+2cos(x)sin(x) into 0?
  46. G

    Trigonometric identity forced oscillations

    Homework Statement http://www.jyu.fi/kastdk/olympiads/2004/Theoretical%20Question%203.pdf http://www.jyu.fi/kastdk/olympiads/2004/Solution%203.pdf Question A- (b) They use some trigomentric identity that I don't understand, which one is it? Thanks in advance. Homework...
  47. K

    Divided Identity: Hypothetical Separate Identities or One Person?

    Hypothetically- If you were able to split in two like a bacterium, would you be two people with separate identities, or would you be one person living in two bodies?
  48. I

    Can splitting in two create a divided identity?

    Hypothetically- If you were able to split in two like a bacterium, would you be two people with separate identities, or would you be one person living in two bodies?
  49. S

    Proof of Vandermonde's Identity by Induction

    Can someone point me in the right direction with vandermonde's identity, I'm seeking a algebraic proof. essentially it its the sum of (a ,k)(b ,n-k) = (a+b ,n) when summed over k = 0 to n. Could someone right this out in latex since it is probably incomprehensible. I used (a ,k) to denote...
  50. P

    Solving Parseval's Identity: Is This Correct?

    Homework Statement Is this correct (in the document)? The Attempt at a Solution I have a feeling it is not.
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