Functions and mappings | Types of functions | Mathematical relations | Basic concepts in set theory
In mathematics, a surjective function (also known as surjection, or onto function) is a function f that every element y can be mapped from element x so that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y. The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French word sur means over or above, and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain. Any function induces a surjection by restricting its codomain to the image of its domain. Every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily a surjection. The composition of surjective functions is always surjective. Any function can be decomposed into a surjection and an injection. (Wikipedia).
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
The Definition of a Surjective(Onto) Function and Explanation
The Definition of a Surjective(Onto) Function and Explanation
From playlist Functions, Sets, and Relations
Abstract Algebra | Surjective Functions
We give the definition of a surjective function, an outline for proving that a function is surjective, and some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
The Composition of Surjective(Onto) Functions is Surjective Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Composition of Surjective(Onto) Functions is Surjective Proof. I included some pictures in the proof with the hope that perhaps it makes more sense.
From playlist Proofs
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
Abstract Algebra | Injective Functions
We give the definition of an injective function, an outline of proving that a given function is injective, and a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Surjective, Injective, and Bijective Functions
This video introduces surjective, injective, and bijective functions.
From playlist Functions (Discrete Math)
3 Ways to Think About Injections and Surjections
Contact me for tutoring here: https://www.herndonmathservices.com/ In this video I explain a few different ways to think about injections and surjections. See the timeline for more info. Here are a few proofs that did not make it in the video: https://proofwiki.org/wiki/Injection_iff_Lef
From playlist Summer of Math Exposition Youtube Videos
Fundamentals of Mathematics - Lecture 24 (with C Vincent!): Functions! Injectivity, Surjectivity
course page - https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton, UVM
From playlist Fundamentals of Mathematics
Fundamentals of Mathematics - Lecture 28: Left and Right Inverses and the Axiom of Choice
Course Page: https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html videography - Eric Melton UVM
From playlist Fundamentals of Mathematics
INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS
We introduce the concept of injective functions, surjective functions, bijective functions, and inverse functions. #DiscreteMath #Mathematics #Functions Support me on Patreon: http://bit.ly/2EUdAl3 Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--P
From playlist Discrete Math 1
The basics of functions || Abstract Linear Algebra 1
⭐Highly Suggested Linear Algebra books⭐ Linear Algebra, an introduction to abstract mathematics: https://amzn.to/3rkp4Wc Linear Algebra Done Right: https://amzn.to/3rkp4Wc The Manga Guide to Linear Algebra: https://amzn.to/3HnS59o A First Course in Linear Algebra: http://linear.ups.edu/ Li
From playlist Abstract Linear Algebra
Fundamentals of Mathematics - Lecture 27: Composition of Functions and Left/Right Inverses
course page: https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html Videography - Eric Melton (UVM)
From playlist Fundamentals of Mathematics
Surjective (onto) and injective (one-to-one) functions | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/inverse-transformations/v/surjective-onto-and-injective-one-to-one-functions Introduction to surjective and injective functio
From playlist Matrix transformations | Linear Algebra | Khan Academy
How to Prove a Function is Not Surjective(Onto)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Prove a Function is Not Surjective(Onto)
From playlist Proofs
Determine if Various Functions are Surjective, Injective, and Bijective
This video explains how to determine if a function is surjective, injective, bijective or none of these.
From playlist Functions (Discrete Math)
1.11.4 Cantor's Theorem: Video
MIT 6.042J Mathematics for Computer Science, Spring 2015 View the complete course: http://ocw.mit.edu/6-042JS15 Instructor: Albert R. Meyer License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Spring 2015