What is Continuity: Definition and 899 Discussions

In fiction, continuity is a consistency of the characteristics of people, plot, objects, and places seen by the reader or viewer over some period of time. It is relevant to several media.
Continuity is particularly a concern in the production of film and television due to the difficulty of rectifying an error in continuity after shooting has wrapped up. It also applies to other art forms, including novels, comics, and video games, though usually on a smaller scale. It also applies to fiction used by persons, corporations, and governments in the public eye.
Most productions have a script supervisor on hand whose job is to pay attention to and attempt to maintain continuity across the chaotic and typically non-linear production shoot. This takes the form of a large amount of paperwork, photographs, and attention to and memory of large quantities of detail, some of which is sometimes assembled into the story bible for the production. It usually regards factors both within the scene and often even technical details, including meticulous records of camera positioning and equipment settings. The use of a Polaroid camera was standard but has since been replaced by digital cameras. All of this is done so that, ideally, all related shots can match, despite perhaps parts being shot thousands of miles and several months apart. It is an inconspicuous job because if done perfectly, no one will ever notice.
In comic books, continuity has also come to mean a set of contiguous events, sometimes said to be "set in the same universe."

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  1. R

    Is h Continuous and Increasing?

    Homework Statement We have a worksheet with practice final questions and I'm really stuck on this one on continuity: Suppose h: (0,1) -> R has the property that for all x in (0,1), there exists a delta>0 such that for all y in (x, x+delta)\bigcap(0,1), h(x) <= h(y) a) prove that if h...
  2. B

    Problems relating to Absolute Continuity

    Hi, it's been awhile since I have studied Lebesgue measure so I'm trying to re-learn the material on my own. Most of my friends don't remember much as well so it's been a bit of a struggle trying to work on these problems on my own. Thank you for any kind of help! OMIT Question 1. If...
  3. R

    Is the series of sin(nx)/n^2 continuous on R?

    Homework Statement Show that \Sigma (from n=1 to infinity) of sin(nx)/n^2 is continuous on R Homework Equations The Attempt at a Solution No idea, any help would be greatly appreciated.
  4. Loren Booda

    Quantum to Classical: Exploring Intermediate States through Varying Uncertainty

    A rule of thumb seems to be that a quantum equation converts to its classical correspondent by replacing h (Planck's constant) in the former with zero for the latter. What do you think about the possibility for a continuum of intervening equations, wherein h eventually decreases to zero? Would...
  5. daniel_i_l

    Uniform Continuity of Integral Functions in (0,1)

    Homework Statement Prove that the function \int^{1}_{x}\frac{sin t}{t}dt is uniformly continues in (0,1). Homework Equations The Attempt at a Solution First if all, I defined f(x) as sin(x)/x for x=/=0 and 0 for x=0. So f is continues in [0,1]. Now G(x) = \int^{x}_{1}f(t) dt...
  6. P

    Differentiability and continuity confusion

    Hi there just a general question: this involves continuity and differentiability suppose: f(x) = sin 1/x if x not equal to 0 f(0) = 0 PROVE F IS NOT DIFFERENTIABLE AT 0 i understand if it is not differentiable at 0 then it may not be continuous at 0. however is there...
  7. daniel_i_l

    Uniform continuity and derivatives

    Homework Statement 1) f is some function who has a bounded derivative in (a,b). In other words, there's some M>0 so that |f'(x)|<M for all x in (a,b). Prove that f is bounded in (a,b). 2) f has a bounded second derivative in (a,b), prove that f in uniformly continues in (a,b)...
  8. daniel_i_l

    Prove Uniform Continuity: y^2 arctan y - x^2 arctan x

    Homework Statement Prove that if y>=x>=0: a) y^2 arctan y - x^2 arctan x >= (y^2 - x^2) arctan x b) \ | \ y^2 arctan y - x^2 arctan x \ | \ >= (y^2 - x^2) arctan x c) use (b) to prove that x^2 arctan(x) isn't UC in R. Homework Equations The Attempt at a Solution a) We...
  9. P

    Explaining Continuity Equation for Jet Engines

    I have this one as well, using the continuity equation to explain how a jet engine provides a foward thrust for an airplane. I have the equation but can some one explain this to me in laymen's terms. \frac{\partial\rho\left(\vec{r},t\right)}{\partial...
  10. P

    Continuity Equations and Bernoulli's Equation

    I have this question that I have stumped on for quite some time, discuss how the continuity equation and bernoulli's equation might relate to one another? Please post if you can explain this to me? Thx
  11. daniel_i_l

    Uniform continuity with bounded functions

    Homework Statement True or false: 1)If f is bounded in R and is uniformly continues in every finate segment of R then it's uniformly continues for all R. 2)If f is continues and bounded in R then it's uniformly continues in R. Homework Equations The Attempt at a Solution 1) If...
  12. S

    Definition of limit n continuity

    I am trying to understand the concept of limit for a single variable case. I don't understand why while defining a limit a function may not be defined at the point? For a function to be continous, why should we care about the existence of limit when we can define the function at every point on...
  13. M

    Differentiation and continuity

    Can anyone tell me whether sin|x| and cos|x| is differentiable at x=0 ? As far as i know, cos(x) and sin(x) is differentiable at all x. If i try to solve this, lim h->0 (f(x+h) - f(x))/h when x=0, and substitute cos|x| for f(x). lim h->0 (cos|h| - cos|0|)/(h) = 1, so cos|x| is...
  14. R

    Uniform continuity, bounded subsets

    Homework Statement Show that if f: S -> Rn is uniformly continuous and S is bounded, then f(S) is bounded. Homework Equations Uniformly continuous on S: for every e>0 there exists d>0 s.t. for every x,y in S, |x-y| < d implies |f(x) - f(y)| < e bounded: a set S in Rn is bounded if it is...
  15. A

    What is the physical meaning of the continuity equation

    Homework Statement I'm new here and I would like to ask a simple Q: what is the physical meaning of the continuity equation from (electrodynamic 1) I mean it's related to the electromagnatic problems Homework Equations The Attempt at a Solution I know the answer in my language...
  16. M

    Continuity of Integral with Fixed Variables in Lebesgue Integration

    Homework Statement For reference, this is chapter 11, problem 12 of Rudin's Principals of Mathematical Analysis. Suppose |f(x,y)| \leq 1 if 0 \leq x \leq 1, 0 \leq y \leq 1 ; for fixed x, f(x,y) is a continuous function of y; for fixed y, f(x,y) is a continuous function of x. Put g(x) =...
  17. C

    Analyzing Continuity and Differentiability of f(x) at x=1 & x=3

    Homework Statement f(x) is a piecewise function defined as: |x-3| x>=1 \frac{x^2}{4}-\frac{3x}{2}+\frac{13}{4} x<1 Discuss the continuity and differentiability of this funtion at x=1 and x=3 Homework Equations The Attempt at a Solution At x=3, this function is continuous...
  18. R

    Bernoulii's Principle and Equation of Continuity help

    Homework Statement A liquid with a specific gravity of 0.9 is stored in a pressurized, closed storage tank to a height of 7 m. The pressure in the tank above the liquid is 8700 Pa. What is the intial velocity of the fluid when a 5 cm valve is opened at a point 0.5 m from the bottom of the...
  19. W

    Continuity of Non-Fundamental Functions: A Theorem?

    For non-fundamental functions obtained by a set of fundamental functions (either by multiplication, addition, division, compound or all together), and given those fundamental functions are all continuous on the desired intervals, will those non-fundamental functions also be continuous? I know...
  20. J

    Derivation of Continuity Equation in Cylindrical Coordinates

    Help! I am stuck on the following derivation: Use the conservation of mass to derive the corresponding continuity equation in cylindrical coordinates. Please take a look at my work in the following attachments. Thanks! =)
  21. K

    Continuity and Differentiability of g Defined by Integrals

    Theorem: Let f be continuous on [a,b]. The function g defined on [a,b] by http://tutorial.math.lamar.edu/AllBrowsers/2413/DefnofDefiniteIntegral_files/eq0051M.gif is continuous on [a,b], differentiable on (a,b), and has derivative g'(x)=f(x) for all x in (a,b) 1) Given that g is defined...
  22. MathematicalPhysicist

    Proving the Existence of a Maximum or Minimum for a Continuous Function

    i have a continuous function f:R->R and we are given that lim f(x)=L as x approaches infinity and limf(x)=L as x approaches minus infinity, i need to prove that f gets a maximum or minimum in R. obviously i need to use weirstrauss theorem, but how to implement it in here. i mean by...
  23. S

    Limits & Continuity of xsin(1/x) and Removable Discontinuity: Explained

    Homework Statement 27. limit as x head towards infinity of xsin(1/x) is A 0 B infinity C nonexistent D -1 E 1 from barron's ap calc 7ed, Chapter two review questions p.37 how come the answer is E? Isn't it A b/c the limit equals infinity or neg infinity times zero? the Book explains...
  24. Repetit

    Why is the continuity equation called the continuity equation?

    Most of you are probably familiar with the continuity equation, but what does the term "continuity" mean? I mean, what is continuous in the context of the continuity eq.? Just wondering...
  25. L

    How to derive continuity eqn. in polar form?

    pleasezzzzzzzzzzzzzzzz
  26. radou

    Proof of continuity of f(x) = 1/x

    I just spent about an hour going through the proof that f(x) = 1/x is continuous at every point in R\{0}, and I'm still not completely sure if I understood the proof. I wonder if someome could perhaps present a more elegant and easy way to proove this, or is this the only way? I should actually...
  27. MathematicalPhysicist

    A few questions on continuity.

    1) let f:[a,b]->R be a continuous function, for every a<=t<=b we define: M(t)=sup{f(x)|a<=x<=t} prove that M(t) is a continuous function on [a,b]. 2) let f be a continuous function on [a,b], and we define that A={x in [a,b]| f(x)>=0} where f(a)>0>f(b). i need to show that the supremum of A...
  28. B

    Lipschitz Continuity and measure theory

    Hi, this is not a homework problem because as you can see, all schools are closed for the winter break. But I'm currently working on a problem and I'm not sure how to begin to attack it. Here's the entire problem: Let f be bounded and measurable function on [0,00). For x greater than or...
  29. mbrmbrg

    Power of Water Pump (from continuity?)

    Homework Statement Water is pumped steadily out of a flooded basement at a speed of 5.5 m/s through a uniform hose of radius 1.2 cm. The hose passes out through a window 2.9 m above the waterline. What is the power of the pump? Homework Equations R_v=Av R_m=\rho Av where P is...
  30. B

    Lipschitz Continuity & Uniform Continuity: Showing sinx & cosx in R

    Homework Statement Show that Lipschitz continutity imples uniform continuity. In particular show that functions sinx and cosx are uniformly continuous in R. The Attempt at a Solution I said that if delta=epsilon/k that Lipschitz continuity imples continuity. Now I am stuck as to how to...
  31. mattmns

    Continuity of exponential functions (epsilon-delta)

    Here is the question: -------- Show the following: Let a>0 be a real number, then f:R->R defined by f(x) = a^x is continuous. ----------- First we have the following definitions of continuity: ---------- Let X be a subset of R, let f:X->R be a function, and let x_0 be an element of X. Then...
  32. B

    Convergence and continuity question

    Can anyone help with this question? Let (f_n) be a sequence of continuous functions on D a subset of R^p to R^q s.t. (f_n) converges uniformly to f on D, and let (x_n) be a sequence of elements in D which converges to x in D. Does it follow that (f_n(x_n)) converges to f(x)? My proof goes...
  33. quasar987

    Does Showing F(x+1/n)--->F(x) Prove Continuity to the Right for Any Sequence?

    My probability professor proved the property of "continuity to the right" of the repartition function F by showing that F(x+1/n)--->F(x). But as I remember it, continuity to the right means that for any sequence {a_n} of elements of (x,+infty) that converges to x, F(a_n) converges to F(x). Is...
  34. B

    Proving Piecewise Continuity of f(x)=x^2(sin[1/x]) in (0,1)

    I have a question that asks to show that f(x)=x^2(sin[1/x]) is piecewise continuous in the interval (0,1). I need to show that I partition the interval into finite intervals and the function is continuous within the subintervals and have discontinuities of te first type at the endpoints. I tried...
  35. C

    Proving Function Continuity in [-1,30]: Understanding the Example

    I am trying to fully understand this example from a textbook I am reading: http://img59.imageshack.us/img59/9237/continuityyn8.jpg What I am not understanding is how they are proving it for [-1,1].. The way I see it is they proved that the function is continuous for all values in it's...
  36. N

    Are all functions from a discrete topological space to itself continuous?

    I need to show all fxn f: X -> X are cts in the discrete top. and that the only cts fxns in the concrete top are the csnt fxns. Let (X,T) be a discrete top with T open sets. Let f: X->X. WTS that f:X->X is cts if for every open set G in the image of X, f^-1(G) = V is an open in X when V...
  37. B

    Yet another proof function continuity related

    http://www.uAlberta.ca/~blu2/question1.gif hey guys, I've tried this question and here's what I come up with, however I don't think this is anywhere near the right answer, but it does show the direction that I'm trying to work toward, I would appreciate any tips/help on how should I...
  38. D

    Continuity Relay: Prevent Elevator Accidents with Relays

    Just curious about something. I work on elevators and there are countless safety circuits to prevent accidents. One example is an elevator hatch door. There are contacts that have to "make" in order for the elevator to run, to prevent the elevator from taking off with the door open. These...
  39. Oxymoron

    Continuity of Integrals in L^1 Spaces

    Question: Prove that if f \in L^1(\mathbb{R},\mathcal{B},m) and a \in \mathbb{R} is fixed, then F(x):=\int_{[a,x]}f\mbox{d}m is continuous. Where \mathcal{B} is the Borel \sigma-algebra, and m is a measure.
  40. B

    Proof Uniform Continuity: Epsilon-Delta & Sequential Equivalents

    I'm working on a proof that is not a homework assignment - that's why I'm posting it here. My question is simple. The epsilon-delta definition of continuity at a point a in an open subset E of the Complex plane is: \forall a \in E, \ \forall \ \varepsilon > 0 \ , \exists \ \delta > 0 \...
  41. J

    Continuity with piecewise functions.

    I have two problems.. I'll put them both here, and show my work on both of them. 1. Is this function continuous on [-1, 1]? f(x) = x / |x| , x does not equal 0 0 , x = 0 After graphing this function, the first statement gives y = -1 for all x < 0, and y = 1 for all x > 0...
  42. B

    Finding the Interval for Function Values within a Small Range

    I'm having trouble understanding the problem: Find the largest open interval, centered at x=3, such that for each x in the interval the value of the function f(x) = 4x - 5 is within 0.01 unit of the number f(3)=7 The solutions manuel goes on to say that the abs[f(x)-f(3)] = abs [(4x - 5) -...
  43. H

    Testing Continuity with a Voltmeter

    Please excuse my ignorance, but I could use some assistance. I need to get a device that will test if current can pass from an electrode through a connected wire on down to a pin that connects to a computer port. (Sometimes the electrical connection fails because of a poor connection between the...
  44. A

    Continuity in weak field approx.

    Given c=1, weak field approx for g: g(/mu,mu)=eta(/mu,mu)-2phi Derive eqn contiuity: d(rho)/dt+u(j)rho,j=-rho u(j/),j (all der. partial) Given T(mu,nu/)=(rho+p)u(mu/)cross u(nu/)+pg(mu,nu/) using divergenceT =0 i.e.T(mu,nu/;nu)=0: Step in the proof is Gamma(0/mu,j)u(mu)=-phi,j I get...
  45. W

    Associating Abstract Spaces with Real Intervals: A Puzzling Continuity

    It roughly says there exists a continuous function from a normal space X to some interval [a,b] Since the the space is a normal space, there exist two disjoints closed subsets A and B. What I don't understand is how can you associate some abstract space with a real interval and is...
  46. A

    Lipschitz continuity problem

    Let the function f:[0,\infty) \rightarrow \mathbb{R} be lipschitz continuous with lipschits constant K. Show that over small intervalls [a,b] \subset [0,\infty) the graph has to lie betwen two straight lines with the slopes k and -k. This is how I have started: Definition of lipschits...
  47. S

    Liquids involving continuity equation

    Any help would be appreciated - The water flowing through a 1.9 cm (inside diameter) pipe flows out through three 1.3 cm pipes. (a) If the flow rates in the three smaller pipes are 28, 15, and 10 L/min, what is the flow rate in the 1.9 cm pipe? The basic continuity idea is A1v1 = A2v2...
  48. U

    Finding function continuity and derivatives

    I'm not sure where to start with this question. If a limit was given, I could solve it but without it given, I am completely lost... State on which intervals the function f defined by f(x) = \left\{\begin{array}{cc}|x + 1|,&x < 0\\x^2 + 1,&x \geq 0\end{array}\right. is: i) continuous ii)...
  49. H

    Uniform convergens and continuity on R

    Hello people, I'm tasked with showing the following: given the series \sum_{n=1} ^{\infty} \frac{1}{x^2 + n^2} (1) show that it converges Uniformly f_n(x) :\mathbb{R} \rightarrow \mathbb{R}. (2) Next show the function f(x) = \sum_{n=1} ^{\infty} \frac{1}{x^2 + n^2} is continious on...
  50. T

    Deriving the 4d continuity equation

    Well we start out with -\frac {d} {dt} \int_{V}^{} \sigma dV = \int_{\Pi}^{} \vec{J} \cdot d\vec{\Pi} Using the Gauss theorem \int_{V}^{} (\frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J}) dV = 0 so \frac{ \partial {\sigma}}{ \partial {t}} + div \vec{J} = 0 and written in 4D...
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