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 A later unpublished study by Carnegie Mellon University noted that "Most often, the causes of identity theft is not known", but reported that someone else concluded that "the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

    Proving Trig Identity: Secx - Tanxsinx = cosx Explained | One More Example

    Homework Statement I'm finally starting to understand proving trig identities, but I have just one more that I can't seem to figure out. secx - tanxsinx = cosx Homework Equations N/A The Attempt at a Solution Well first, I multiplied the tanx and sinx and came up with sin2x /...
  2. D

    What trig identity should i use for this

    0.15348=0.1415cosβ -0.291sinβcosβ how do i solve this equation with both sinβ and cosβ, i realize that i need to play with the identities but have had no luck, please help i tried squaring the whole thing, and saying cos2β=t, then i get 0.023556=0.02t - 0.582\sqrt{t-1}\sqrt{t}...
  3. C

    Prove Binomial Identity: Differentiation vs Subsitution

    Prove this using this identity: k\binom{n}{k}=n\binom{n-1}{k-1} \binom{n}{1}-2\binom{n}{2}+3\binom{n}{3}+...+(-1)n-1\binom{n}{n} I was able to do this via differentiation, but not using this substitution. Any hints would be great.
  4. C

    Can you explain the binomial identity \sumk=0n\binom{n}{k}2=\binom{2n}{n}?

    \sumk=0n\binom{n}{k}2=\binom{2n}{n} Could someone give me a hint as to how to start this. I'm not sure how to really interpret it. (n-k)\binom{n}{k}=n\binom{n-1}{k} Right Side: Suppose you create a committe from \binom{n}{k} , then to pick a leader who isn't in the committee but...
  5. D

    Trigonometric Identity Puzzle: Solving (1-cosx)/(1+cosx) = (cscx-cotx)^2

    Homework Statement (1-cosx)/(1+cosx) = (cscx-cotx)^2 Homework Equations cscx = 1/sinx, cotx = cosx/sinx, sin^2x + cos^2x = 1 The Attempt at a Solution I have tried many different attempts, but I can't seem to make one side like the other. I took the (cscx-cotx)^2 and expanded it...
  6. J

    Trigonometry Identity problem I been trying to solve all day

    Homework Statement solve 3cos(x) + 3 = 2 sin^2(x) where 0 <= x < 2piHomework Equations The Attempt at a Solution 3(cos(x) + 1) = 2 sin^2(x) 3(cos(x) + 1) = 2 (1- cos^2(x)) I've tried this variation, and a couple others but it just does not pan out. Please help. Oh yeah we have a real...
  7. C

    Proving this binomial identity

    \sum_{m=k}^{n-k}\binom{m}{k}\binom{n-m}{k}=\binom{n+1}{2k+1} I'm not sure how to prove it, I understand the combinatorial proof..i.e. putting it to an example...but i can't derive one side and get the other.
  8. Z

    How Can Ramanujan's Identity Simplify Summing Powers of Integers?

    i do not remember the webpage i watched this but i remember that they said ' IN chapter 1 of his notebook Ramanujan wrote ' \sum_{n=0}^{x}n^{r}= (r+1)^{-1}x^{r+1}+ \zeta (-r) - \sum_{k}B_{2k}\frac{\Gamma (r+1)}{\Gamma (k-2r+2)} does anyone knows how to get this ??
  9. K

    Homework Solution: Simplifying Trig Identity - cot2xsecx + 1/cosx

    Help please on trig identity Homework Statement Simplify cot2xsecx + 1/cosx The Attempt at a Solution Well so far i got: cot2xsecx + 1/cosx =(cos2x/sin2x)(1/cosx) + 1/cosx =((1+cos2x)/(1-cos2x))(1/cosx) + 1/cosx and from there I am stuck, I've tried playing around with it...
  10. C

    How to prove Lagrange's identity for real numbers?

    Homework Statement Prove Lagrange's identity for real numbers http://mathworld.wolfram.com/LagrangesIdentity.html The Attempt at a Solution I tried one of the methods used in proving the Cauchy-Schwarz inequality (Ax^2 + Bx + C is greater than or equal to zero, where a = the sum from...
  11. B

    Understanding the Relationship Between Ward Identity and Charge Conservation

    There are two things about this identity that I don't understand: 1. Why is it equivalent to a statement of charge conservation? 2. Wikipedia claims that it is like a quantum version of the classical noether's theorem. In what sense is this true? Thanks
  12. G

    Prove the following identity algebraically

    Homework Statement Must be proven algebraically, duh! Homework Equations trig identities The Attempt at a Solution I'm at a loss as what to do next. Any help would be appreciated.
  13. K

    Abstract - one sided identity question

    Homework Statement I'm trying to find what a a left and right identity element is. Also, I want to see if a one sided element for * exists, if it is unique. Homework Equations The Attempt at a Solution Ok, I just don't really know what a one sided element is. I'm using...
  14. T

    I: X'->X the identity function with topology

    Let X and X' denote a single set in the two topologies T and T', respectively. Let i:X'-> X be the identity function a. Show that i is continuous <=> T' is finer than T. b. Show that i is a homeomorphism <=> T'=T This is all I've got. According to the first statement... X \subset T and...
  15. P

    Gaussian Integral Identity with Grassmann Numbers

    Hi, I read the chapter "Anticommuting Numbers" by Peskin & Schröder (page 299) about Grassmann Numbers and now I would like to prove \int d \bar{\theta}_1 d \theta_1 ... d \bar{\theta}_N d \theta_N e^{-\bar{\theta} A \theta} = det A \theta_i are complex Grassmann Numbers...
  16. S

    Prove Identity: csc2@= 1/(1-(sin@-cos@)^2

    Homework Statement Prove: csc2@= 1/(1-(sin@-cos@)^2 Homework Equations The Attempt at a Solution I'm stuck can't seem to work this on out. I'm not seeing the relationship between the two
  17. S

    Find exact value difference identity

    Homework Statement Find the exact value of the expression Tan(3/4-12/5) Homework Equations tan(x-y)= (tan3/4 -tan12/5)/ (1+tan3/4tan12/5) The Attempt at a Solution I am not sure how to get exact values for these ratios. I haven't been able to get past this point
  18. N

    Vector cross product identity proof

    Homework Statement \bigtriangledown\times\\(v\times w)= v(\bigtriangledown\cdot w) - w(\bigtriangledown\cdot v)+ (v\cdot\bigtriangledown)w - (w\cdot\bigtriangledown) v I've tried expanding left side and get [v1(dw2/dy+dw3/dz)-w1(dv2/dy+dv3/dz)]i +...
  19. N

    A Generalized trigonometric identity for Cos(x_1++x_n)?

    Hi Everyone, Do there exist any explicit formula for Cos(x_1+x_2+...+x_n) as a sum of products of Sin(x_i) & Cos(x_i)? Or we need to expand using Cos(A+B), Sin(A+B) again & again? If it exists then what is about Sin(x_1+x_2+...+x_n)? [It is understood that there will be 2^(n-1) number of...
  20. M

    Differentiating the identity to develop another identity

    Homework Statement Differentiate the identity sin2x = 2sinxcosx to develop the identity for cos2x, in terms on sin x and cos x Homework Equations The Attempt at a Solution Im not sure where to start with this one. Should I find the derivative of both sides of the equation, and...
  21. K

    Identity element for group theory

    Homework Statement Show that (S, *) is a group where S is the set of all real numbers except for -1. Define * on S by a*b=a+b+ab The Attempt at a Solution Well I know that i have to follow the axioms to prove this. So I started with G1 which is associativity. This one I got to...
  22. C

    Nonsingular perturbed identity matrix

    Homework Statement If A = I + uv*, where u and v are m vectors and A is known to be nonsingular, show that the inverse of A = I + \alphauv* where \alpha is a scalar value Homework Equations The Attempt at a Solution Since A is nonsingular, we know the rank of A is m. Since both...
  23. C

    Can I prove that I-S is a nonsingular matrix?

    Homework Statement Given S is a Skew-Hermitian (S*=-S), Prove that I - S is a nonsingular matrix Homework Equations If a matrix A is nonsingular, for Ax=0, x={0} The Attempt at a Solution (I-S)x=0, and I have been trying to show that the solution for x is always zero. Is this the...
  24. P

    Identity for exponential function with imaginary arguments

    I have seen the following identity used. Exp[iw/2]-Exp[iw/2]=Exp[iw]-1 I can't find this in any book and I can't prove it myself. The left side equals 2isin(w/2) The right side equals cos(w)+isin(w)-1 On the face of it, that seems to make the identity absurd How can one go about proving...
  25. U

    Proving a trig identity: set theoretic ideas?

    Hi everyone, Any assistance with this following problem would be greatly appreciated. I'm in Year 11 and working through Apostol volume 1. Homework Statement sin n*pi = 0, where n is an integer sin n*pi =/= 0, where n is not an integer. Prove these statements... Homework...
  26. F

    Unravelling the Identity of k_RP Expression

    I am reading some notes and I can't understand a specif bit: the expression of the constant k_RP (RP means Reagents->Product) is as follows (Ξ is the heavyside function and C(t) the conditional probability): k_RP=dC(t)/dt=<Ξ_R[0]*(dΞ_P[t]/dt)>/<Ξ_R[0]> then for the following identity...
  27. Ed Aboud

    Trig Identity Question: Finding theta in Projectile Problem

    Homework Statement Basically I am finishing of a projectile question and I get stuck here: Trying to find \theta \frac{1}{2} (sin2 \theta) tan^2 \theta -tan \theta + \frac{1}{2} sin2 \theta = 0 Homework Equations The Attempt at a Solution I tryed spliting tan \theta into \frac{sin...
  28. M

    Help solving by using trig identity

    Homework Statement sinx cos2x=1 x is greater than or equal to 0 and less than 2pi Homework Equations What I used: 1-2sin2x cos2x-sin2x but there might be one that I didn't and should have... The Attempt at a Solution Basically I have...
  29. J

    What is so beautiful about Euler's Identity?

    I'm a pretty novice Physicist/Mathematician, but I've got a few offers for good universities, to show you my general level of knowledge. Could someone please explain in terms I will understand why this equation is considered so perfect and beautiful?
  30. M

    Integration that leads to a inverse trig identity

    Ok, so a teacher showed an example in class awhile back. So I am going over my notes right now, and I don't understand a certain part of the problem. Also I am new to the forums and its my first time posting here, so please push me in the right direction if i make a mistake. integration of...
  31. M

    Identity of Zeta function

    it is true in general that the sum (density of states for a physicst) \sum_{n=0}^{\infty} \delta (x- \gamma _{n}) is related to the value \frac{ \zeta '(1/2+is)}{\zeta (1/2+is)}+\frac{ \zeta '(1/2-is)}{\zeta (1/2-is)} here the 'gamma' are the imaginary parts of the non-trivial...
  32. F

    Identity Relation and Function

    Homework Statement I am reading a book on relations on function and I am very confused with identity relation and function. Any help on understanding I relation and I function will be appreciated. Homework Equations A function from A to B is a relation f from A to B such that a) the...
  33. I

    Prove Spinor Identity in Arbitrary Dimension

    Actually, the original motivation is to check the closure of SUSY \delta X^\mu = \bar{\epsilon}\psi^\mu \delta \psi^\mu = -i\rho^\alpha\partial_\alpha X^\mu\epsilon where \rho^\alpha is a two dimensional gamma matrix, and \psi^\mu ia s two dimensional Majorana spinor, the index \mu in the...
  34. M

    Vector Analysis: Seeking Guidance on Identity and Calculation

    hi there! I´m doing vector analysis the last two weeks and I feel unsure about this identity. Can anyone of you say if I´m on the right way, and if not where my mistakes lie :) A_i(\vec r)=\sum_{j=1}^3R_{ij}x_j, R constant 3x3 matrix I have to calculate rot\vec A, rotrot\vec A...
  35. A

    Difficult Trig Identity (no double ange, power reducing formulas)

    Homework Statement sin^3(x) - cos^3(x) / sin(x) + cos(x) = csc^2(x) -cot(x) - 2cos^2(x) / 1 - cot^2(x) Homework Equations The Attempt at a Solution I have attached one of my many attempts. Any input?
  36. happyg1

    O"Proving a Trig Identity: Sec^6x-Tan^6x = 1+3Sec^2xTan^2x | Tips & Tricks

    Homework Statement Show that the LHS can be changed into the RHS. sec^6 x-tan^6x=1+3sec^2x tan^2x Homework Equations Trig identities. The Attempt at a Solution I tried factoring the LHS: (sec^2-tan^2)(sec^4+sec^2tan^2+tan^4) sec^2-tan^2=1 so that leaves me with the other...
  37. T

    How Can I Prove This Hyperbolic Identity?

    \equivHomework Statement Hi, I've been given a hyperbolic identity to prove: 2sinhAsinhB \equiv Cosh(A+B) - Cosh(A-B) Homework Equations Cos(A\pm B) \equiv CosACosB \mp SinASinB The Attempt at a Solution I have Cosh(A+B) and - Cosh(A-B) so i can kind of see that there will be...
  38. S

    How to Prove a Difficult Trig Identity?

    Homework Statement I need help proving this identitiy. ...cos2A-cos4A tan3A = -------------- or tan3A = cos2A-cos4A/sin4A-sin2A ....sin4A-sin2A there both the same, just different way of writing it. please help! :) Homework Equations The Attempt at a Solution I honestly...
  39. J

    Thermodynamic identity (non-quasistatic?)

    Homework Statement A cylinder contains one liter of air at room termperature and atmospheric pressure. At one end of the cylinder is a massless piston, whose surface area is 0.01 m^2. Suppose that you push the piston _very_ suddenly, exerting a force of 2 kN. The piston moves only one...
  40. D

    Proving Identity: cos2A/1 + sin2A = cotA - 1 / cotA + 1

    Homework Statement Prove the following identity: cos2A/1 + sin2A = cotA - 1 / cotA + 1 Homework Equations The Attempt at a Solution I proved the right side, which eventually lead up to cosA - sinA / cosA + sinA I have NO idea how to do the left side. I have wasted...
  41. H

    How Do Trigonometric Identities Relate to Each Other?

    Does CSC(\pi/2 - x) = SinX OR 1 / SinX? What about CSC2(\pi/2 -x)? Does COT(\pi/2 + x) = -TanX or 1/-TanX?
  42. R

    Find Product Identity with ABCD & Triangular Variables

    Challenge to find a identity for the product abc, wherein each term contains a triangular variable as a factor and a, b, c are each separately used as the sole variable of the argument in at least one of the variable triangular numbers. My solution is abc = T_{(c+ab)} - aT_{b} - T_{c} -...
  43. M

    Prove Euler Identity without using Euler Formula

    Is it possible to prove Euler's identity (e^i*pi = -1) without simply taking it as a special case of Euler's formula (e^i*x = cos(x) + i sin(x))?
  44. L

    Verifying Identity: sinX(1-2cos^2x+cos^4x)=sin^5x

    Homework Statement sinX(1-2cos^2x+cos^4x)=sin^5x
  45. L

    Are the given trigonometric identities correct?

    Homework Statement tanX+tan Y / 1-tanXtanY= cotX+cotY/cotXcotY-1 Homework Equations tan= sin/cos cot= cos/sin The Attempt at a Solution
  46. L

    Can This Trigonometric Identity Be Verified?

    Homework Statement verify the identity : 1+sec(-∅)/sin(-∅+tan(-∅) = -csc ∅ Homework Equations The Attempt at a Solution 1+sec∅/-sin-tan∅ = -csc∅ I don't know where to start from, does anyone have any idea?
  47. B

    Proving Trigonometric Identity: cosx/1-sinx + 1-sinx/cosx = 2secx + 2tanx

    cosx/1-sinx + 1-sinx/cosx = 2secx + 2tanx I can get to 2secx + tanx - tanx, any help is appreciated
  48. B

    Does Subring Inherit Same Multiplicative Identity?

    should the subring inherit the same multiplicative identity of the original ring? assuming multiplicative identity is required in the definition of ring. according to the book (Rotman's), 1\in S is required. But, does it mean S contains the same multiplicative identity, or contains its own...
  49. Z

    Troubleshooting Trig Identities and Equations

    Homework Statement cos(squared)x = sinx-1/2 Homework Equations cos(squared)x= 1-sin(squared)x The Attempt at a Solution I tried everything but my answer does not match my answers in calculator
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