Mathematical analysis | Topology | Types of functions

Nowhere continuous function

In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f is a function from real numbers to real numbers, then f is nowhere continuous if for each point x there is an ε > 0 such that for each δ > 0 we can find a point y such that 0 < |x − y| < δ and |f(x) − f(y)| ≥ ε. Therefore, no matter how close we get to any fixed point, there are even closer points at which the function takes not-nearby values. More general definitions of this kind of function can be obtained, by replacing the absolute value by the distance function in a metric space, or by using the definition of continuity in a topological space. (Wikipedia).

Video thumbnail

Determine Where the Function is Not Continuous

In this video I will show you how to Determine Where the Function is Not Continuous.

From playlist Continuity Problems

Video thumbnail

Calculus - Continuous functions

This video will describe how calculus defines a continuous function using limits. Some examples are used to find where a function is continuous, and where it is not continuous. Remember to check that the value at c and the limit as x approaches c exist, and agree. For more videos please

From playlist Calculus

Video thumbnail

Explaining if the tangent function is a continuous function or not

👉 Learn all about the Limit. In this playlist, we will explore how to evaluate the limit of an equation, piecewise function, table and graph. We will explore continuity as well as discontinuities such as holes, asymptotes and jumps and how they relate to the limit. We will evaluate the g

From playlist Is the Functions Continuous or Not?

Video thumbnail

Pre-Calculus - Where is a function continuous

This video covers how you can tell if a function is continuous or not using an informal definition for continuity. Later in the video, we look at a function that is not continuous for all values, but is continuous for certain intervals. For more videos visit http://www.mysecretmathtutor.

From playlist Pre-Calculus

Video thumbnail

Is the function continuous or not

👉 Learn how to determine whether a function is continuos or not. A function is said to be continous if two conditions are met. They are: the limit of the function exist and that the value of the function at the point of continuity is defined and is equal to the limit of the function. Other

From playlist Is the Functions Continuous or Not?

Video thumbnail

Ex 2: Find the Value of Constant to Make a Piecewise Defined Function Continuous Everywhere

This video explains how to determine the value of a constant in a one of the function rules of a piece-wise defined function in order for the function to be continuous everywhere. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Continuity Using Limits

Video thumbnail

Introduction to Discrete and Continuous Functions

This video defines and provides examples of discrete and continuous functions.

From playlist Introduction to Functions: Function Basics

Video thumbnail

Unusual Properties: Nowhere Monotonic/ Discontinuous Inverse

This video is about a nowhere monotonic functions and a function with a discontinuous inverse.

From playlist Basics: Unusual Properties in Math

Video thumbnail

Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function

MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw We can show that differentiability implies

From playlist MIT 18.100A Real Analysis, Fall 2020

Video thumbnail

Math research I have been working on: (Partial Derivative Of Okamoto’s Functions)

One of the math research projects I have been working on is now a preprint on the arxiv and on ResearchGate. I helped mentor two undergraduate students as our group investigated different properties of the partial derivative of Okomoto's functions with respect to the parameter. Even though

From playlist Academic Talks

Video thumbnail

A Function that is Nowhere Analytic but Complex Differentiable Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A Function that is Nowhere Analytic but Complex Differentiable Proof. An example of a function that is nowhere analytic but differentiable on the coordinate axes.

From playlist Complex Analysis

Video thumbnail

Math 131 112816 Uniform Convergence and Differentiation, Nowhere differentiable continuous function

When can one commute limit and differentiation? (continued from previous lecture). Construction of a continuous, nowhere-differentiable function. Question: what is "sequential compactness" for a set of functions? Definitions: pointwise bounded set of functions, uniformly bounded set of

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis

Video thumbnail

Understanding if a logarithmic function is continuous or not

👉 Learn all about the Limit. In this playlist, we will explore how to evaluate the limit of an equation, piecewise function, table and graph. We will explore continuity as well as discontinuities such as holes, asymptotes and jumps and how they relate to the limit. We will evaluate the g

From playlist Is the Functions Continuous or Not?

Video thumbnail

Math 131 Spring 2022 041822 Continuous nowhere-differentiable function, Sequential compactness

Construction of (fractal) continuous, nowhere-differentiable function (along the lines of Weierstrass). New section: sequential compactness-type results for function spaces. Notions of boundedness: pointwise bounded sequences of functions, uniformly bounded sequences of functions. Examp

From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)

Video thumbnail

Determine the Intervals on which the Function is Continuous Four Examples

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determine the Intervals on which the Function is Continuous Four Examples

From playlist Calculus 1 Exam 1 Playlist

Video thumbnail

Takako Nemoto: Baire category theorem and nowhere differentiable continuous function...

Full title: Baire category theorem and nowhere differentiable continuous function in constructive mathematics The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In Bishop's constructive mathematics, it is known that Bair

From playlist Workshop: "Constructive Mathematics"

Video thumbnail

Hölder Continuity

Hölder Continuity Definition and Properties In this video, I define the notion of Hölder continuity and show that any Hölder continuous function must be uniformly continuous. I then give some interesting properties of Hölder continuity Uniform Continuity: https://youtu.be/PA0EJHYymLE Wea

From playlist Limits and Continuity

Video thumbnail

Satz von Baire

Abonniert den Kanal, damit er auch in Zukunft bestehen kann. Es ist vollkommen kostenlos und ihr werdet direkt informiert, wenn ich einen Livestream anbiete. Hier erkläre ich den Satz von Baire.

From playlist Funktionalanalysis

Video thumbnail

Jens Kaad: Differentiable absorption of Hilbert C*-modules

The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C^*-module is isomorphic to a direct summand in a standard module. In this talk, I will generalize this result by incorporating a densely defined derivation on the base C^*-algebra. The extra com

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

Video thumbnail

Finding the domain by investigating continuity (KristaKingMath)

► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course In order to find the domain of a function, you have to be able to say where a function is continuous and discontinuous. A function will be continuous wherever it isn't discontinuous, so to figure

From playlist Calculus I

Related pages

Dirichlet function | Infinitesimal | Metric space | Topological space | Domain of a function | Absolute value | Mathematics | Rational number | Function (mathematics) | Weierstrass function | Hyperreal number | Real number | Indicator function | Codomain | Thomae's function | Blumberg theorem | Continuous function | Peter Gustav Lejeune Dirichlet