-
What is Bijection? (Set Theory)
An explanation of Bijective functions in set theory.
This series covers the basics of set theory and higher order logic. In this month we are looking at the Operations and Relations of Sets. This month includes unions, intersections, differences, power sets, Cartesian products, functions, ordered pairs and more! We are also looking at the fifth and sixth axioms of a basic universe, following Neumann Berneays Gödel (NBG) set theory. In the next month we will look at Peano Arithmetic. (#SetTheory #Logic)
Sponsors: Joshua Furman, Joshua Opell, NBA_Ruby, Eugene SY, Antoinemp1, Antibody, Ismail Fagundes, Adrien Ecoffet, Tom Amedro, Christopher McGevna, Joao Sa, and Dennis Sexton. Thanks for your support!
Donate on Patreon: https://www.patreon.com/Carneades
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published: 26 Oct 2020
-
INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS
Looking for paid tutoring or online courses with practice exercises, text lectures, solutions, and exam practice? http://TrevTutor.com has you covered!
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
*--Playlists--*
Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz
Discrete Mathematics 2: https://www.youtube.com/playlist?list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
*--Recommended Textbooks--*
Discrete and Combinatorial Mathematics (Grimaldi): https://amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): https://am...
published: 19 May 2015
-
Counting with Bijections 1
Lesson 1/11/13 for Sage School Mathcounts tutoring.
published: 11 Jan 2013
-
Bijective Functions and Why They're Important | Bijections, Bijective Proof, Functions and Relations
What are bijective functions and why should we care about them? We'll be going over bijections, examples, proofs, and non-examples in today's video math lesson!
A bijection is a function that is both injective and surjective. We mention two very important things about bijections in the lesson. First, suppose f is a function from A to B and f is injective and surjective. Thus, f is bijective. Then, we can define an inverse function from B to A that takes the images of f and sends them back to their respective pre-images. This can only be done with a bijective function, which is very important!
However, there is a lot of possibility for nuance in the definition of inverse functions (we don't give a formal definition in this lesson), and while only a bijective function can have an inverse...
published: 20 Oct 2019
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Introduction to Bijection
published: 06 May 2019
-
Example: Making a Bijection
Justin discusses an example that asks us to find a domain, given a correspondence and codomain, that will yield a bijection.
published: 08 Jun 2020
-
Bijective Function (Bijection) | Discrete mathematics
👉Subscribe to our new channel:https://www.youtube.com/@varunainashots
►One to One Function (Injection):
https://youtu.be/z810qMsf5So
►ONTO Function(Surjection):
https://youtu.be/jqaNaJRrg3s
►Discrete Mathematics(Complete Playlist):
https://www.youtube.com/playlist?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3
Other subject-wise playlist Links:
--------------------------------------------------------------------------------------------------------------------------------------
►Design and Analysis of algorithms (DAA):
https://www.youtube.com/playlist?list=PLxCzCOWd7aiHcmS4i14bI0VrMbZTUvlTa
►Database Management System:
https://www.youtube.com/playlist?list=PLxCzCOWd7aiFAN6I8CuViBuCdJgiOkT2Y
► Software Engineering:
https://www.youtube.com/playlist?list=PLxCzCOWd7aiEed7SKZBnC6ypFDWYLRvB2
►Artific...
published: 21 May 2021
-
Bijective Function Problem 1 - Functions - Discrete Mathematics
Subject - Discrete Mathematics
Video Name - Bijective Function Problem 1
Chapter - Functions
Faculty - Prof. Farhan Meer
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published: 09 Apr 2022
-
3.3.3 Counting with Bijections: 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
published: 12 Sep 2016
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Bijection between (0,1) and (-inf, inf)
Which interval contains more real numbers: (0, 1) or (-inf, inf)?
Check out the previous video: N vs. Z: https://youtu.be/CuzEqMY9Ys0
Proving a function is a bijection: https://youtu.be/PCge0dU7Gbk
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math for fun
published: 12 Aug 2019
4:28
What is Bijection? (Set Theory)
An explanation of Bijective functions in set theory.
This series covers the basics of set theory and higher order logic. In this month we are looking at the O...
An explanation of Bijective functions in set theory.
This series covers the basics of set theory and higher order logic. In this month we are looking at the Operations and Relations of Sets. This month includes unions, intersections, differences, power sets, Cartesian products, functions, ordered pairs and more! We are also looking at the fifth and sixth axioms of a basic universe, following Neumann Berneays Gödel (NBG) set theory. In the next month we will look at Peano Arithmetic. (#SetTheory #Logic)
Sponsors: Joshua Furman, Joshua Opell, NBA_Ruby, Eugene SY, Antoinemp1, Antibody, Ismail Fagundes, Adrien Ecoffet, Tom Amedro, Christopher McGevna, Joao Sa, and Dennis Sexton. Thanks for your support!
Donate on Patreon: https://www.patreon.com/Carneades
Buy stuff with Zazzle: http://www.zazzle.com/carneades
Follow us on Twitter: @CarneadesCyrene https://twitter.com/CarneadesCyrene
Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!
https://wn.com/What_Is_Bijection_(Set_Theory)
An explanation of Bijective functions in set theory.
This series covers the basics of set theory and higher order logic. In this month we are looking at the Operations and Relations of Sets. This month includes unions, intersections, differences, power sets, Cartesian products, functions, ordered pairs and more! We are also looking at the fifth and sixth axioms of a basic universe, following Neumann Berneays Gödel (NBG) set theory. In the next month we will look at Peano Arithmetic. (#SetTheory #Logic)
Sponsors: Joshua Furman, Joshua Opell, NBA_Ruby, Eugene SY, Antoinemp1, Antibody, Ismail Fagundes, Adrien Ecoffet, Tom Amedro, Christopher McGevna, Joao Sa, and Dennis Sexton. Thanks for your support!
Donate on Patreon: https://www.patreon.com/Carneades
Buy stuff with Zazzle: http://www.zazzle.com/carneades
Follow us on Twitter: @CarneadesCyrene https://twitter.com/CarneadesCyrene
Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!
- published: 26 Oct 2020
- views: 6074
17:15
INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS
Looking for paid tutoring or online courses with practice exercises, text lectures, solutions, and exam practice? http://TrevTutor.com has you covered!
We intr...
Looking for paid tutoring or online courses with practice exercises, text lectures, solutions, and exam practice? http://TrevTutor.com has you covered!
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
*--Playlists--*
Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz
Discrete Mathematics 2: https://www.youtube.com/playlist?list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
*--Recommended Textbooks--*
Discrete and Combinatorial Mathematics (Grimaldi): https://amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): https://amzn.to/2Hh7H41
Discrete Mathematics and Its Applications (Rosen): https://amzn.to/3lUgrMI
Book of Proof (Hammack): https://amzn.to/35eEbVg
Like us on Facebook: http://on.fb.me/1vWwDRc
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
https://wn.com/Injective,_Surjective,_And_Bijective_Functions_Discrete_Mathematics
Looking for paid tutoring or online courses with practice exercises, text lectures, solutions, and exam practice? http://TrevTutor.com has you covered!
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
*--Playlists--*
Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz
Discrete Mathematics 2: https://www.youtube.com/playlist?list=PLDDGPdw7e6Aj0amDsYInT_8p6xTSTGEi2
*--Recommended Textbooks--*
Discrete and Combinatorial Mathematics (Grimaldi): https://amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): https://amzn.to/2Hh7H41
Discrete Mathematics and Its Applications (Rosen): https://amzn.to/3lUgrMI
Book of Proof (Hammack): https://amzn.to/35eEbVg
Like us on Facebook: http://on.fb.me/1vWwDRc
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.
- published: 19 May 2015
- views: 1024694
6:20
Counting with Bijections 1
Lesson 1/11/13 for Sage School Mathcounts tutoring.
Lesson 1/11/13 for Sage School Mathcounts tutoring.
https://wn.com/Counting_With_Bijections_1
Lesson 1/11/13 for Sage School Mathcounts tutoring.
- published: 11 Jan 2013
- views: 2521
10:10
Bijective Functions and Why They're Important | Bijections, Bijective Proof, Functions and Relations
What are bijective functions and why should we care about them? We'll be going over bijections, examples, proofs, and non-examples in today's video math lesson!...
What are bijective functions and why should we care about them? We'll be going over bijections, examples, proofs, and non-examples in today's video math lesson!
A bijection is a function that is both injective and surjective. We mention two very important things about bijections in the lesson. First, suppose f is a function from A to B and f is injective and surjective. Thus, f is bijective. Then, we can define an inverse function from B to A that takes the images of f and sends them back to their respective pre-images. This can only be done with a bijective function, which is very important!
However, there is a lot of possibility for nuance in the definition of inverse functions (we don't give a formal definition in this lesson), and while only a bijective function can have an inverse like we described, other types of functions can have other types of inverses that follow less strict definitions. This lesson is not meant to be an in-depth presentation of inverse functions, so I hope you'll look forward to learning more about them.
Here is a definition for you if you are interested: Let F be a function from A to B. Then a function, G, that maps B to A, is an inverse function of F if and only if g(f(a)) = a for all a in A and f(g(b)) = b for all b in B.
If you need a recap on injective and surjective functions, check out my lessons on them!
Injections: https://www.youtube.com/watch?v=GBUi70WCgEE
Surjections: https://www.youtube.com/watch?v=OZDFIDGcioA
SOLUTION TO PRACTICE PROBLEM:
We want to show that the integers (Z) have the same cardinality as the odd numbers (we'll call the set of odd numbers S). So we want to find a bijection from one to the other; Z to X or X to Z. A good place to start, as we did with the example in the video, is with the definition of an odd number. An odd number is a number equal to 2k + 1 for some integer k. So if we define a function f from Z to X as f(z) = 2z + 1, that should work out! We just need to prove it.
First, we prove f is injective. Take z, w in Z and suppose f(z) = f(w). Then 2z + 1 = 2w + 1. Thus, 2z = 2w and z = w. So f is injective.
Proving surjectivity is even easier. Take x in X. By definition of X, x is odd and therefore there exists an integer k such that 2k + 1 = x. Then, f(k) = 2k + 1 = x. Thus, f is surjective. Therefore, since f is injective and surjective, f is bijective so |Z| = |X|.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
********************************************************************
+WRATH OF MATH+
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https://wn.com/Bijective_Functions_And_Why_They're_Important_|_Bijections,_Bijective_Proof,_Functions_And_Relations
What are bijective functions and why should we care about them? We'll be going over bijections, examples, proofs, and non-examples in today's video math lesson!
A bijection is a function that is both injective and surjective. We mention two very important things about bijections in the lesson. First, suppose f is a function from A to B and f is injective and surjective. Thus, f is bijective. Then, we can define an inverse function from B to A that takes the images of f and sends them back to their respective pre-images. This can only be done with a bijective function, which is very important!
However, there is a lot of possibility for nuance in the definition of inverse functions (we don't give a formal definition in this lesson), and while only a bijective function can have an inverse like we described, other types of functions can have other types of inverses that follow less strict definitions. This lesson is not meant to be an in-depth presentation of inverse functions, so I hope you'll look forward to learning more about them.
Here is a definition for you if you are interested: Let F be a function from A to B. Then a function, G, that maps B to A, is an inverse function of F if and only if g(f(a)) = a for all a in A and f(g(b)) = b for all b in B.
If you need a recap on injective and surjective functions, check out my lessons on them!
Injections: https://www.youtube.com/watch?v=GBUi70WCgEE
Surjections: https://www.youtube.com/watch?v=OZDFIDGcioA
SOLUTION TO PRACTICE PROBLEM:
We want to show that the integers (Z) have the same cardinality as the odd numbers (we'll call the set of odd numbers S). So we want to find a bijection from one to the other; Z to X or X to Z. A good place to start, as we did with the example in the video, is with the definition of an odd number. An odd number is a number equal to 2k + 1 for some integer k. So if we define a function f from Z to X as f(z) = 2z + 1, that should work out! We just need to prove it.
First, we prove f is injective. Take z, w in Z and suppose f(z) = f(w). Then 2z + 1 = 2w + 1. Thus, 2z = 2w and z = w. So f is injective.
Proving surjectivity is even easier. Take x in X. By definition of X, x is odd and therefore there exists an integer k such that 2k + 1 = x. Then, f(k) = 2k + 1 = x. Thus, f is surjective. Therefore, since f is injective and surjective, f is bijective so |Z| = |X|.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: https://www.patreon.com/wrathofmathlessons
Follow Wrath of Math on...
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- published: 20 Oct 2019
- views: 17787
7:40
Example: Making a Bijection
Justin discusses an example that asks us to find a domain, given a correspondence and codomain, that will yield a bijection.
Justin discusses an example that asks us to find a domain, given a correspondence and codomain, that will yield a bijection.
https://wn.com/Example_Making_A_Bijection
Justin discusses an example that asks us to find a domain, given a correspondence and codomain, that will yield a bijection.
- published: 08 Jun 2020
- views: 5094
3:22
Bijective Function (Bijection) | Discrete mathematics
👉Subscribe to our new channel:https://www.youtube.com/@varunainashots
►One to One Function (Injection):
https://youtu.be/z810qMsf5So
►ONTO Function(Surjection)...
👉Subscribe to our new channel:https://www.youtube.com/@varunainashots
►One to One Function (Injection):
https://youtu.be/z810qMsf5So
►ONTO Function(Surjection):
https://youtu.be/jqaNaJRrg3s
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https://www.youtube.com/playlist?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3
Other subject-wise playlist Links:
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►Database Management System:
https://www.youtube.com/playlist?list=PLxCzCOWd7aiFAN6I8CuViBuCdJgiOkT2Y
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https://wn.com/Bijective_Function_(Bijection)_|_Discrete_Mathematics
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►One to One Function (Injection):
https://youtu.be/z810qMsf5So
►ONTO Function(Surjection):
https://youtu.be/jqaNaJRrg3s
►Discrete Mathematics(Complete Playlist):
https://www.youtube.com/playlist?list=PLxCzCOWd7aiH2wwES9vPWsEL6ipTaUSl3
Other subject-wise playlist Links:
--------------------------------------------------------------------------------------------------------------------------------------
►Design and Analysis of algorithms (DAA):
https://www.youtube.com/playlist?list=PLxCzCOWd7aiHcmS4i14bI0VrMbZTUvlTa
►Database Management System:
https://www.youtube.com/playlist?list=PLxCzCOWd7aiFAN6I8CuViBuCdJgiOkT2Y
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- published: 21 May 2021
- views: 190817
7:14
Bijective Function Problem 1 - Functions - Discrete Mathematics
Subject - Discrete Mathematics
Video Name - Bijective Function Problem 1
Chapter - Functions
Faculty - Prof. Farhan Meer
Upskill and get Placements with Eke...
Subject - Discrete Mathematics
Video Name - Bijective Function Problem 1
Chapter - Functions
Faculty - Prof. Farhan Meer
Upskill and get Placements with Ekeeda Career Tracks
Data Science - https://ekeeda.com/career-track/data-scientist
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#Functions #DiscreteMathematics
https://wn.com/Bijective_Function_Problem_1_Functions_Discrete_Mathematics
Subject - Discrete Mathematics
Video Name - Bijective Function Problem 1
Chapter - Functions
Faculty - Prof. Farhan Meer
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#Functions #DiscreteMathematics
- published: 09 Apr 2022
- views: 57573
11:43
3.3.3 Counting with Bijections: 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...
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
https://wn.com/3.3.3_Counting_With_Bijections_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
- published: 12 Sep 2016
- views: 16900
7:39
Bijection between (0,1) and (-inf, inf)
Which interval contains more real numbers: (0, 1) or (-inf, inf)?
Check out the previous video: N vs. Z: https://youtu.be/CuzEqMY9Ys0
Proving a function is a b...
Which interval contains more real numbers: (0, 1) or (-inf, inf)?
Check out the previous video: N vs. Z: https://youtu.be/CuzEqMY9Ys0
Proving a function is a bijection: https://youtu.be/PCge0dU7Gbk
T-shirts: https://teespring.com/stores/blackpenredpen
my site: https://blackpenredpen.com
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Patreon: https://www.patreon.com/blackpenredpen
Blue Microphone: https://amzn.to/2DAbHYL
black marker red marker: https://amzn.to/2UVLDCm
blackpenredpen,
math for fun
https://wn.com/Bijection_Between_(0,1)_And_(_Inf,_Inf)
Which interval contains more real numbers: (0, 1) or (-inf, inf)?
Check out the previous video: N vs. Z: https://youtu.be/CuzEqMY9Ys0
Proving a function is a bijection: https://youtu.be/PCge0dU7Gbk
T-shirts: https://teespring.com/stores/blackpenredpen
my site: https://blackpenredpen.com
twitter: https://twitter.com/blackpenredpen
Patreon: https://www.patreon.com/blackpenredpen
Blue Microphone: https://amzn.to/2DAbHYL
black marker red marker: https://amzn.to/2UVLDCm
blackpenredpen,
math for fun
- published: 12 Aug 2019
- views: 33305