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 The use of a Polaroid camera was standard but has since been replaced by digital cameras.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."

View More On Wikipedia.org
Recent contents Top users
  1. J

    How can I prove the continuity of sin(x) using common properties?

    I’m having trouble showing that Sin(x) is a continuous function. I’m try to show it’s continuous by showing: 0<|x - x_0| < d => |sin(x) - sin(x_0)|<\epsilon Here is what I have done |sin(x)| - |sin(x_0)|<|sin(x) - sin(x_0)|<\epsilon and |sin(x)|<|x| so -|x| < -|sin(x)| => |sin(x)|-...
  2. R

    Are Functions Continuous at a Cusp or Corner?

    I'm just working through some differentiability questions and have a quick question - are functions continuous at a cusp or corner? I know that functions are not differentiable at cusps or corners because you cannot draw a unique tangent at these points, but I'm not sure about continuity. From...
  3. B

    Can the Product, Sum, and Quotient of Continuous Functions be Continuous?

    Hi, I would like to know if I can say that products, sums, and quotients of continuous functions are continuous. From what I can tell, what I've asked is the same as asking if the product, sums, quotients of limits 'work' and of course they do. For example if lim(x->a)g(x) = c and...
  4. B

    Continuity of multivariable function

    Hi, I'm having trouble with the following question. I would like some help with it. Q. A function f:A \subset R^n \to R^m is continuous if and only if its component functions f_1 ,...,f_m :A \to R are continuous. Firstly, is there a difference between C \subset D and C \subseteq D? Anyway...
  5. S

    Definition Continuity

    Hi! Please, give me some guidance in solving this problem. Let f:{\mathbb{R}}^n\longrightarrow{\mathbb{R}}^m. Show that f is continuous iff for all M\subset{\mathbb{R}}^n the inclusion f(closM)\subseteq{clos{}f(M)} holds.(closM denotes the closure of the set M) Please, ask me some guiding...
  6. benorin

    Def. Continuity in terms of sequences: How do I generalize to multivariate fcns?

    Working from "Principles of Mathematical Analysis", by Walter Rudin I have gleaned the following definition of continuity of a function (which maps a subset one metric space into another): Suppose f:E\rightarrow Y, where \left( X, d_{X}\right) \mbox{ and } \left( Y, d_{Y}\right) are metric...
  7. I

    Proving Hölder Continuity of f(u)=-1/(1+u)^2

    Hello guys, I am trying to prove that the function f(u)=-\frac{1}{(1+u)^2} is Hölder continuous for -1<u \le 0 but I am stuck. Here is what I have done: If |u_1-u_0| \le \delta then \left|-\frac{1}{(1+u_1)^2}+\frac{1}{(1+u_0)^2}\right| \le...
  8. T

    How to Prove the Continuity of a Derivative?

    If f is differentiable on (a,b), does it imply that f' is continuous on (a,b)? If so, is there a way of proving it?
  9. T

    Proving continuity of two-variable function

    Hello to everybody. Yesterday we wrote a fake test, in which I encountered problem I haven't benn able to solve so far. The problem is given this way: Let f(x,y) := \left\{\begin{array}{cc}\frac{xy^3}{x^2+y^4} - 2x + 3y,&[x,y] \neq [0,0]\\0, &[x,y] = [0,0]\end{array}\right. Find out...
  10. T

    Show Uniform Continuity: Let f:R->R be Differentiable with |f'|<=15

    "Let f:R->R be differentiable such that |f'|<= 15, show that f is uniformly continuous." I can't solve it. I tried writing down the definition, but it got no where.
  11. F

    Exploring Limits and Continuity of Functions with Illustrative Examples

    1a)Do these functions have limits.If the limit exists, find it with justification, if not explain why not i) f(x,y) =x²-y²/x²+y² ii) f(x,y) =x³-y³/x²+y² iii) f(x,y) =xy/|x|+|y| iv) f(x,y) =1-√(1-x²)/x²+ xy+y² v) f(x,y) =y³x/y^6+x² im having problems finding the limits especially iii)...
  12. T

    Negating Limits and Continuity

    Let f:I->R and let c in I. I want to negate the statements: "f has limit L at c" and "f is continuous at c". Are these correct? f does not have limit L at c if there exists e>0 such that for some sequence {x_n} converging to c, |f(x_n)-L|>e for every n. f is not continuous at c if there exists...
  13. N

    Prove: Absolute Continuity Let f in AC[0,1] Monotonic

    Let f in AC[0,1] monotonic,Prove that if m(E)=0 then m(f(E))=0
  14. 1

    Uniform continuity and bounded

    Prove that if f is uniformly continuous on a bounded set S then f is bounded on S. Our book says uniform continuity on an interval implies regular continuity on the interval, and in the previous chapter we proved that if a function is continuous on some closed interval then it is bounded...
  15. T

    Question about continuity postulates

    I had a search for an answer but I turned up nothing, if this has been covered before could someone point me in the right direction? To the question. I'm studying QM at the moment but I'm having trouble with two of the postulates. Is the constraint that the wavefunction must be continuous...
  16. I

    Proving Uniform Continuity for Functions with a<1

    "Let f:[a,b]\rightarrow [a,b] be defined such that |f(x)-f(y)|\leq a|x-y| where 0<a<1. Prove that f is uniformly continuous and (other stuff)." Let e>0 and let d=e/a. Whenever 0<|x-y|<d, |f(x)-f(y)|\leq a|x-y|<ad=e. f is therefore by definition uniformly continuous. Did I do this right? It...
  17. I

    Is f(x) uniformly continuous on [0, inf)?

    "Suppose f:[0, inf) -> R is such that f is uniformly continuous on [a, inf) for some a>0. Prove that f is uniformly continuous on [0, inf)." But this is not true, is it? Consider the function f(x)=\left\{\begin{array}{cc}x &\mbox{ if }x\geq 1\\ \frac{1}{x-1} &\mbox{ if }x<1\end{array}\right
  18. T

    Continuity of two-variable function

    Hi, I have some troubles understanding the basic facts about investigating the continuity of two-variable functions. Our professor gave us very simple example to show us the basic facts:Very important is that projections are continuous, it means \pi_1 :[x,y] \longmapsto x \pi_2 :[x,y]...
  19. quasar987

    Continuity of a Function Around a Point

    Is it true that is f is continuous at t, then there exists an interval around t for each point of which f is continuous also? Edit: In case it is false, is it true however on a set of measure zero? P.S. Please just feed me the answer; I know nothing about measure except that a function is...
  20. A

    Topology and Continuity question

    Let \mathbb{R}_{l} denote the real numbers with the lower limit topology, that is the topology generated by the basis: \{[a, b)\ |\ a < b,\ a, b \in \mathbb{R}\} Which functions f : \mathbb{R} \to \mathbb{R} are continuous when regarded as functions from \mathbb{R}_l to \mathbb{R}_l? I...
  21. T

    Proving Continuity in Metric Spaces Using Open Sets

    Suppose f is a function from a metric space (X,D) into another metric space (Y,D') such that D(x,x') >= kD'(f(x),f(x'), where k is a constant positive real number. Prove that f is continuous. Okay, I know that there is a theorem that says "pre-images of open sets are open" so I suppose I can...
  22. V

    Solving Limits and Continuity Problems with Examples and Proofs

    I'm having a little trouble trying to figure out these problems. Any help would be appreciated. g(x) = (x^2 - a^2)/(x-a) when x≠a but 8 when x=a... how do i find the constant a so that the function will be continuous on the entire real line? f(x)= x^3 - x^2 + x - 2 on closed interval...
  23. S

    Continuity and Intermediate Value Theorem

    Hello everyone, I have come across two questions that I have solved, but unfortunately am quite sure I've done them incorrectly. They are related to continuity and the intermediate value theorem. Find the constant c that makes g continuous (-infinity,infinity). g(x){ x^2-c^2 if x<4...
  24. A

    Prove Determinant of Rotation Matrix is 1 w/Continuity Argument

    What's a continuity argument? For example, a question asks to prove that the determinant of a rotation matrix is always 1 using a continuity argument?
  25. D

    Finding Roots and Continuity of Functions

    I recently finished a homework assignment with the exceptions of the following: 1.) f(x) =x^3 - x^2 + x, show there is a number c such that f(c)=10. f(x) can be equated to 10, but I'm not quite sure how to solve the equation from that point. 2.) Prove that the equation has at least...
  26. A

    [calculus] Continuity of partial derivatives

    Hello, If I am given a function of several variables and a parameter. Such as: f(x,y,z)=\frac{x y z^2}{(x^2+y^2+z^2)^k} This function is defined to be 0 where it is incontinuous (in (0,0,0)). How can I conclude for which values of k the function has three continuous partial derivatives? I...
  27. K

    Lipschitz Continuity and Uniqueness

    Dear all, If a differential equation is Lipschitz continuous, then the solution is unique. But what about the implication in the other direction? I know that uniqueness does not imply Lipschitz continuity. But is there a counterexample? A differential equation that is not L-continuous, still...
  28. M

    Can you help me understand limits and continuity in Calculus?

    Hello everyone: I am a new member of this forum and this is my first post. I was referred by an Astronomy.com member and so I decided to check it out. First I would like to introduce myself. My name is John and I am seventeen years of age and a senior in High School. My Calculus teacher...
  29. S

    How Can You Prove Uniform Continuity on a Closed Interval?

    hello all i have been working on this problem, see i can see how it could be true but i don't know how to prove it,would anybody have any ideas on how to prove this ? let [a,b] be a closed interval in R and f:[a,b]->R be a continuous function. prove that f is uniformly continuous...
  30. K

    Can Catmull-Rom Spline Be Used for Physical Interpolation in Game Development?

    Hi all, first post here.. I hope you guys can point me in the right direction. I am writing a multiplayer game and I need to interpolate through some position points in time that the client receives from other players. What I am doing right now is just using a Catmull-Rom interpolation to...
  31. S

    Is a Continuous and Periodic Function Bounded and Uniformly Continuous on R?

    hello all, i have been working on problems with continuity and i have come across some question in which i understand generally what i have to do but i just don't know where to start and how to put it together a function f:R->R is said to be periodic if there exists a number k>0 such...
  32. K

    Solving the Continuity Equation: A Guide

    i do not understand how the continuity equation works?
  33. D

    Having trouble with limits and continuity? Let's clear things up!

    I'm having trouble with limits that involve 0+ and 0-. Can someone show me how the answers to the following limits are obtained? f(x) = \frac{1}{1+e^{\frac{1}{x}}} \lim_{x\rightarrow0^{+}} = 0 \lim_{x\rightarrow0^{-}} = 1 Now, my second query involves continuity. I understand that...
  34. M

    Can You Find a Continuous Function That Takes Each Value Exactly Three Times?

    I am having great, great difficulties in solving this problem, its asking me to find a function that is continuous everywhere which takes each of its values exactly 3 times(like give an example of a function, no proving). This part, i have a little imagination of my own to start, but the second...
  35. M

    Continuity & Uniform Continuity

    I'm seeking a bit of affirmation or correction here before i try to solidify this to memory... I know continuity to mean: Let f:D -> R (D being an interval we know to be the domain, D) Let x_0 be a member of the domain, D. This implies that the function f is continuous at the point...
  36. S

    Can Two Discontinuous Functions Become Continuous When Added Together?

    just a basic question, so if I'm asked to find 2 functions that are discontinus, but when added together, becomes continuous, how do I approach that? can I say like, let F(x) = 1 for x =< 0, and f(x) = 0 for x > 1. G(x) = 1 for x =<0 and g(x) = 0 for x = 1. can I just somehow "add" f...
  37. M

    Calc Proof(s): Uniform Continuity

    There are two proofs which I have attempted to work on that have beein somewhat trifling. The first of which is : prove that the function f: [0,infin) -> R defined by f(x) = 1/x is not uniformly continuous on (0,infin). im thinking that the way in which i should probably attempt to solve...
  38. D

    Continuity of a Function of Two Variables

    Question: Is the function f(x,y) = (x^2 - y^2)/(x-y) continuous at (1,1) if we set f(1,1) = 0? Why or why not? So far, I've just plugged 1 in for x and y and found the limit to equal 0. I guess that means that the limit is not continuous at (1,1)? And what do they mean by set f(1,1) =...
  39. T

    Proving Continuity with Epsilon-Delta: How to Approach a Challenging Function?

    Hi I am trying to prove the continuity of a function. I do understand the definition and I can do it for "smaller" functions. However, for this "larger" function I am having troubling bounding it and thus can't find a prove. Any suggestions would be greatly appreciated! Show, using the...
  40. Z

    Uniform Continuity (and Irrationals)

    I am a little shaky with the concept of proving uniform continuity vs regular continuity. Is the difference when proving through epsilon-delta definition just that your delta can not depend on "a" (thus be defined in terms of "a") (when |x-a|<delta) for uniform continuity? Also to the more...
  41. U

    Find Value of K for Continuity of f(x) at x=1

    let f be a function defined by f(x)=4-x^2 when x=<1 and k+x when x>1 What value of k will f be continuous at x=1? I know the answer is k=2, however, I don't know how to show to correct work. I got 2 when I sketched a graph of 4-x^2 and plugged in some numbers but I don't know how to show it...
  42. E

    Help on Continuity - Finding Nonremovable & Removable Discontinuities

    Help on continuity! 1) Ok, i know how to find x, but how do you know if something is nonremovable or removable discontinuity? like for this: f(x)=|x+2|/(x+2) i knoe its x=-2, but is it nonremovable or removable? 2) How do u do the continuity stuff with there: f(x)=csc2x...
  43. H

    Solve for K for Continuity of f(2) at @=0

    Hi, I have just one more problem :) here it is: (because I don't know how to do theta, "@" will equal theta) Find a value of K so that f(2) is continuous at @=0 ( != means "not equal") f(@) = ( (2sin@)/@ , @ !=0 ) ( 5k , @=0 ) f(@) is a piecewise function I don't know...
  44. Clausius2

    What is the solution for the Continuity Equation at r=0?

    Hi guys. I am solving the axisymmetric free jet of an incompressible fluid. But I have troubles at r=0. Continuty equation can be written in cylindrical coordinates as: 1/r*d(rv)/dr + du/dz=0 v=radial velocity (v=0 at r=0) u=axial velocity. hz=delta(z) hr=delta(r) What happens at...
  45. D

    Proving continuity at a point

    How do I show that f(x)=x^2 is continuous at any given point, say x=3. Thank you.
  46. himanshu121

    Continuity And Differentiability

    Consider f(x)=x^3-x^2+x+1 g(x)=\left\{\begin{array}{cc}{max\{f(t),0\leq t \leq x\}}\;\ 0\leq x \leq 1 \\ 3-x\;\ 1< x \leq 2\end{array}\right Discuss the continuity and differentiability of g(x) in the interval (0,2) I know how to do it As f(x) is increasing function therefore max...
  47. phoenixthoth

    The notion of continuity applied to sets

    i'm trying to define what it would mean for a set to be continuous. what i'd like to say is that S is continuous if it is homeomorphic to [0,1], (0,1], or (0,1). (perhaps that's redundant already?) but I'm not sure if that captures all the sets i'd like to think of as continuous. my...
  48. T

    Time and Indeterminacy vs. Continuity

    'Time and Indeterminacy vs. Continuity' Sorry; I couldn't resist that. (Peter Lynds theory) What is time? Dictionary.com/time: 'Time is a nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future. An interval separating...
  49. P

    Understanding Continuity and Discontinuity in Calculus

    Is it just me or is it the text didn't explain well enough about continuity? I totally don't understand it. Not only that, when it covers about derivatives it first introduced another defination of slope. Then it says that the derivative of x^2 is 2x. How does slop relate to derivative? Can...
Back
Top