How to Prove a Function is Injective(one-to-one) Using the Definition
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to prove a function is injective. Injective functions are also called one-to-one functions. This is a short video focusing on the proof.
From playlist Proofs
The Composition of Injective(one-to-one) Functions is Injective Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the composition of injective(one-to-one) functions is also injective(one-to-one)
From playlist Proofs
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
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
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
Bijective Functions Have a Two-Sided Inverse
A proof that bijections have two-sided inverses by considering the preimages of injective and surjective functions. Functions playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJG35bSmijiKFxerMar8jMCi Subscribe to see more new math videos! Music: C418 - Pr Department
From playlist Functions
Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one). Given two functions f : A to B and g: B to C, we prove that if the composition g o f: A to C is an injective function then f is also an injective function
From playlist Proofs
Proving a Function is One-to-One and Onto
This video gives an example of how to show that a function is both 1-1(injective) and onto(surjective). In other words we show that the function is a one-to-one correspondence(bijection). The example given involves a function which maps the set of all 2 x 2 matrices with real entries into
From playlist Functions, Sets, and Relations
The Contrapositive and Proof by Contrapositive
The contrapositive is a powerful tool that can be used to prove various mathematical statements. It is most useful when a direct proof is awkward or impossible, and - if it can be used - is often a much more elegant method that employing proof by contradiction. #proof #contrapositive #proo
From playlist Proofs and Explanations
Lecture 2: Cantor's Theory of Cardinality (Size)
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 What does it mean for one set to be bigger
From playlist MIT 18.100A Real Analysis, Fall 2020
What is infinity? Can there be different sizes of infinity? Surprisingly, the answer is yes. In fact, there are many different ways to make bigger infinite sets. In this video, a few different sets of infinities will be explored, including their surprising differences and even more surpris
From playlist Summer of Math Exposition 2 videos
How to Prove a Function is a Bijection and Find the Inverse
How to Prove a Function is a Bijection and Find the Inverse If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer There are several ways that you can
From playlist Math Proofs for Beginners
Cardinality -- Proof Writing 22
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From playlist Proof Writing
Countable Sets -- Proof Writing 23
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From playlist Proof Writing
Real Analysis Chapter 2: Cardinality and Cantor's Theorem
A day late, but no worse off! Today we cover the topic of Cardinality, the size of the set of Real Numbers, and my personal favorite, Cantor's Theorem! This lovely result forces us to conclude that there is an infinitely tall hierarchy of different sizes of infinity, whatever the hectogo
From playlist Real Analysis
Xavier Viennot: Heaps and lattice paths
CIRM HYBRID EVENT Recorded during the meeting "Lattice Paths, Combinatorics and Interactions" the June 25, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Combinatorics
Permutations of {1,2,...,n} -- Abstract Linear Algebra 2
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From playlist Abstract Linear Algebra
proving equal cardinality -- proof writing examples 22
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From playlist Proof Writing
Functions with a Two-Sided Inverse are Bijective
One way to prove that a function is bijective is to find a two-sided inverse function. In this video, we explain why having a two-sided inverse means that a function is a bijection! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
Fundamentals of Mathematics - Lecture 32.2 : Proof of the Pidgeonhole Principle
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics