Real analysis | Complex analysis | Types of functions

Bounded function

In mathematics, a function f defined on some set X with real or complex values is called bounded if the set of its values is bounded. In other words, there exists a real number M such that for all x in X. A function that is not bounded is said to be unbounded. If f is real-valued and f(x) ≤ A for all x in X, then the function is said to be bounded (from) above by A. If f(x) â‰Ĩ B for all x in X, then the function is said to be bounded (from) below by B. A real-valued function is bounded if and only if it is bounded from above and below. An important special case is a bounded sequence, where X is taken to be the set N of natural numbers. Thus a sequence f = (a0, a1, a2, ...) is bounded if there exists a real number M such that for every natural number n. The set of all bounded sequences forms the sequence space . The definition of boundedness can be generalized to functions f : X → Y taking values in a more general space Y by requiring that the image f(X) is a bounded set in Y. (Wikipedia).

Bounded function
Video thumbnail

What are bounded functions and how do you determine the boundness

👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi

From playlist Characteristics of Functions

Video thumbnail

When is a function bounded below?

👉 Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi

From playlist Characteristics of Functions

Video thumbnail

Functions of equations - IS IT A FUNCTION

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

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

Determine if the equation represents a function

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Video thumbnail

Determine the domain, range and if a relation is a function

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Video thumbnail

How to determine if an ordered pair is a function or not

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

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

Using the vertical line test to determine if a graph is a function or not

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Video thumbnail

Bounds for L-functions by Ritabrata Munshi

PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla

From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

Video thumbnail

The subconvexity problem for L-functions – Ritabrata Munshi – ICM2018

Number Theory Invited Lecture 3.7 The subconvexity problem for L-functions Ritabrata Munshi Abstract: Estimating the size of automorphic L-functions on the critical line is a central problem in analytic number theory. An easy consequence of the standard analytic properties of the L-funct

From playlist Number Theory

Video thumbnail

Lecture 2 - Asymptotic Notation

This is Lecture 2 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture2.pdf

From playlist CSE373 - Analysis of Algorithms - 1997 SBU

Video thumbnail

Kehe Zhu: Products of Toeplitz operators on the Fock space

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Analysis and its Applications

Video thumbnail

Mod-02 Lec-09 Analysis Continued

Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in.

From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics

Video thumbnail

A polynomial lower bound for monotonicity testing...- Rocco Servedio

Rocco Servedio Columbia University March 31, 2014 We prove a ΊĖƒ (n1/5)Ί~(n1/5) lower bound on the query complexity of any non-adaptive two-sided error algorithm for testing whether an unknown n-variable Boolean function is monotone versus constant-far from monotone. This gives an exponenti

From playlist Mathematics

Video thumbnail

A nearly optimal lower bound on the approximate degree of AC00- Mark Bun

Computer Science/Discrete Mathematics Seminar I Topic: A nearly optimal lower bound on the approximate degree of AC00 Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker: Mark Bun Affiliation: Princeton University Date: October 23, 2017 For more videos, pleas

From playlist Mathematics

Video thumbnail

Stochastic Gradient Descent and Machine Learning (Lecture 2) by Praneeth Netrapalli

PROGRAM: BANGALORE SCHOOL ON STATISTICAL PHYSICS - XIII (HYBRID) ORGANIZERS: Abhishek Dhar (ICTS-TIFR, India) and Sanjib Sabhapandit (RRI, India) DATE & TIME: 11 July 2022 to 22 July 2022 VENUE: Madhava Lecture Hall and Online This school is the thirteenth in the series. The schoo

From playlist Bangalore School on Statistical Physics - XIII - 2022 (Live Streamed)

Video thumbnail

Definition of a Surjective Function and a Function that is NOT Surjective

We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht

From playlist Injective, Surjective, and Bijective Functions

Related pages

Sequence space | Nowhere continuous function | Support (mathematics) | Monotonic function | Liouville's theorem (complex analysis) | Continuous function | Entire function | Bounded operator | Rational number | Sequence | Local boundedness | Radian | Bounded set | Mathematics | Natural number | Function (mathematics) | Set (mathematics) | Real number | Pathological (mathematics) | Tangent (trigonometry) | Compact space | Complex number | Irrational number | Uniform boundedness