INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS

  Рет қаралды 970,992

TrevTutor

TrevTutor

9 жыл бұрын

Looking for paid tutoring or online courses with practice exercises, text lectures, solutions, and exam practice? TrevTutor.com has you covered!
We introduce the concept of injective functions, surjective functions, bijective functions, and inverse functions.
#DiscreteMath #Mathematics #Functions
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-Playlists-
Discrete Mathematics 1: • Discrete Math (Sets, L...
Discrete Mathematics 2: • Discrete Math (Countin...
-Recommended Textbooks-
Discrete and Combinatorial Mathematics (Grimaldi): amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): amzn.to/2Hh7H41
Discrete Mathematics and Its Applications (Rosen): amzn.to/3lUgrMI
Book of Proof (Hammack): amzn.to/35eEbVg
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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.

Пікірлер: 324
@FMAPR
@FMAPR 8 жыл бұрын
I've got to say, you are far better than the professor I have for Discrete Math, it has everything to be quite the interesting, but some people just cannot teach. Anyway, thanks for the videos
@Trevtutor
@Trevtutor 8 жыл бұрын
+FMAPR I wish I could take his job :(
@dastanmambetaliev7947
@dastanmambetaliev7947 8 жыл бұрын
lol ))
@charlesperry6408
@charlesperry6408 7 жыл бұрын
Yes!
@jadbiz
@jadbiz 7 жыл бұрын
Totally agree! In youtube people make video because they like it, teacher teach only for money. That's why we found far better teacher on youtube than in our schools.
@Tee_eej
@Tee_eej 6 жыл бұрын
I disagree with the fact that you think teachers teach for money, but at any rate it is a really good video for DM.
@SgtMajorJay
@SgtMajorJay 4 жыл бұрын
Seriously... that's it?? Why was this to complicated when our professor taught it. Thank you so much!
@jackmenirons4989
@jackmenirons4989 3 жыл бұрын
My thoughts exactly. After struggling through bad lectures and cryptic textbooks these 5-10 minute videos make it as easy as addition and subtraction. No idea why this seems to be so hard to teach in most colleges.
@romaisha2198
@romaisha2198 7 ай бұрын
Hahahhaha could relate!
@Mike-lx9qn
@Mike-lx9qn 5 ай бұрын
Some truly can't teach jack* & shouldn't.
@parvezshahid8906
@parvezshahid8906 5 ай бұрын
Universities and professors make it sooo complicated, these concepts seem so abstract and just confusing.
@Abdushaye
@Abdushaye 2 ай бұрын
I don't even understand why university professors make it so complicated. Thanks to trev tutor he is my savior when exams come up.
@BangMaster96
@BangMaster96 7 жыл бұрын
Discrete Math is so fun, when i can understand it Thank you Sir, for helping me pass my exams
@michaelsun2901
@michaelsun2901 8 жыл бұрын
You are by far the best teacher of Discrete Math compared to any other youtube tutors as well as my Uni teacher
@amansinghbhadauria2818
@amansinghbhadauria2818 5 жыл бұрын
your university prof. wants to know your location.
@MDArif-xy5cc
@MDArif-xy5cc 4 жыл бұрын
@@amansinghbhadauria2818 haahhahaha
@SudeepBose-ct9kq
@SudeepBose-ct9kq 3 жыл бұрын
Watch organic chemistry tutor
@TheMrsteakman
@TheMrsteakman 4 жыл бұрын
Injective: 0:39 Surjective: 5:25 Bijective: 10:07
@aminamasoud3387
@aminamasoud3387 Ай бұрын
Life saver
@aminamasoud3387
@aminamasoud3387 Ай бұрын
Life saver
@aidahuseynova2639
@aidahuseynova2639 7 жыл бұрын
İ'm trying to learn sth from the professor at the uni but it's impossible,because he cannot explain it clearly.You're doing a great job and now i'm starting to learn from your videos and it's really awesome.İ've never got functions before better than now.Thank you so much,maybe we can improve ourselves because of the person like you.
@muhammadmansha4595
@muhammadmansha4595 6 жыл бұрын
then he should be Phd holder ..
@hessnej
@hessnej 5 жыл бұрын
I have watched most of your Discrete Math tutorials. They are easy to understand and well arranged. I like your tone of voice which in not monotonous for a tutor. So Thank you and I hope you would develop more contents in the other areas. you greatly helped me in my last DM test.
@TheFearlocator
@TheFearlocator 5 жыл бұрын
I'm so grateful for your existence in this world! You are best teacher of discrete math and you are saving my life!
@khSoraya01
@khSoraya01 3 жыл бұрын
Thank u so much ! I attended this cource twice with my teacher and I couldn't understand but I watched your video Once and I understand ..U just made things clear and easy going you deserve a big price!
@yvonneykke
@yvonneykke 2 жыл бұрын
Been struggling to understand this for a few weeks now, this one video I accidentally found just explains it all. Thank you!!
@ozzyfromspace
@ozzyfromspace 6 жыл бұрын
+TheTrevTutor your videos are setting me up for Group Theory and Manifolds...can't tell you how much I appreciate your lectures. Thank you!
@imansantamaria1055
@imansantamaria1055 8 жыл бұрын
Thank you my friend. Thanks to your channel, I've found the will to keep moving forward with my discrete math subject despite failing my first quiz. I hope I pass. Subbed.
@cxeenyi
@cxeenyi 4 жыл бұрын
I passed my math test all to you! Really really grateful for every single video you've done! 💟 credits to Trev for being very much helpful and kind to share these. Knowledge with us. 😭
@saisurendrapatthigulla4754
@saisurendrapatthigulla4754 Жыл бұрын
Only Passed?
@Panditatt
@Panditatt 4 жыл бұрын
I’m ready for my final tmm. You explained it in such a easier way, thank you 🙏🏼
@afaq-6753
@afaq-6753 2 жыл бұрын
How'd it go?
@RadRobbie
@RadRobbie 3 жыл бұрын
I feel like I'm ascending to another plane when I watch these videos, you explain the same stuff as my lecturer but so much clearer
@jiashangliu5243
@jiashangliu5243 Жыл бұрын
Thanks!! This is really way more understandable and intuitive than what my professor had taught in class🤩
@anilajanaki4609
@anilajanaki4609 7 жыл бұрын
you r a the best tutor i have ever seen in my life ,
@myatthuaung2570
@myatthuaung2570 8 жыл бұрын
The best video ever !! I am now crystal clear. Thanks.
@im-nazmul
@im-nazmul 4 жыл бұрын
I have to say this is the complete solution of the topic. I haven’t seen this kind of video before. Thank you so much 😊
@RyanTorrecampo
@RyanTorrecampo 5 жыл бұрын
I watched this video and went back to my professors lecture notes. The first time I went through the notes, I felt like I only truly understood 60% of the material. After watching the video, I feel like I can now teach the course.
@mustafakhanani1577
@mustafakhanani1577 2 жыл бұрын
I know that this video was made in 2015 and its 2021, which is also ending, but all thanks to you TrevTutor, I was able to complete my assignments on time and receive distinction on the paper! Keep up the great work!
@ansu7168
@ansu7168 Жыл бұрын
By the way Im watching this in 2022 .....its still far better than that of college professor and tons of videos available online just for wasting the time .
@aneetaiqbal9386
@aneetaiqbal9386 6 жыл бұрын
Tomorrow is my mid,and your videos are really gonna help me, your work should be appreciated teacher..thank u so much.
@brandonthompson9659
@brandonthompson9659 5 жыл бұрын
Thank you! May professor has a very strong accent that's hard to understand, this is helping tremendously.
@icy5982
@icy5982 3 жыл бұрын
I dont know why my lecturers are boring af but can listen to you for ages when you do your videos. They are actually engaging and not confusing
@kansterstrak
@kansterstrak 8 жыл бұрын
Thank you for all the videos, they're awesome!
@speclesic
@speclesic Жыл бұрын
i have to learn functions, uncountable vs countable sets, and relations in 2 days before my exam, wish me luck
@johnbraganza9316
@johnbraganza9316 6 жыл бұрын
Thank you so much my teacher is really bad and I was really stressing out about my homework. I scoured the internet for hours and you were by far the easiest to understand :)
@lizziethelemon
@lizziethelemon 2 жыл бұрын
I came here for Set Theory but I stayed for the soothing voice and personality and comprehension of course!!! Thank you soooooo much! You are an absolute|😇!| This is the first time I retained Set Theory and even answered the questions before you said them!
@ahmedbahaj8786
@ahmedbahaj8786 3 жыл бұрын
I just.. I wanna say.... I'm speechless, Man oh man I wish you a lifetime of happiness, you know I wish happiness rains on you to the level that you are struggling with swimming .
@natriac.6092
@natriac.6092 3 жыл бұрын
OMG THANK YOU! Now I truly understand this topic !!!
@brianmwasaru797
@brianmwasaru797 7 жыл бұрын
woooow! bro actually compared to how my lecturer teaches,i would say you are the best and i cant imagn how you've made this topic look so easy,,, clearly u deserve this profession,,,thank you so much kip up same spirit
@amonGustavo07
@amonGustavo07 2 жыл бұрын
Bro…. what, if only my professor was this good. Thank you. I finally understand and now I can move on to actually studying for my test.
@jacksonfraser6251
@jacksonfraser6251 8 жыл бұрын
Subscribed. Thanks for making such great quality videos. Really helping me with my Discrete Structures in Computing course
@creepercraft97
@creepercraft97 7 жыл бұрын
I love your writing ! Very well explained.
@sitembekilekhumalo8235
@sitembekilekhumalo8235 Жыл бұрын
wow this is the best .I now understand set theory.You are the best professor!
@mclovin510
@mclovin510 8 жыл бұрын
"x2 was just x1 in disguise". This sentence alone clarified everything to me. My private tutor couldn't explain it to me in an hour. I assumed that if we were to put different numbers like 1 and 2, the outcome will be different. so f(1) not equal to f(2). Now I understand that f(x2) can not be different, and that is essentially what we had to prove. Thank you very much.
@caseycarlyle5337
@caseycarlyle5337 3 жыл бұрын
I have an exam tomorrow, and this is really helping me. Thank you!!
@abdoennajah2702
@abdoennajah2702 3 жыл бұрын
What a great explanation, thanks a lot man ❤
@jonsilva3849
@jonsilva3849 7 жыл бұрын
You are doing a good thing, man. Thanks!
@jacquelinehernandez8453
@jacquelinehernandez8453 8 ай бұрын
i always look for these videos when i don't understand something in class. He does such a good job of explaining things . #trevtutorforprez
@beasaheric906
@beasaheric906 4 жыл бұрын
any time i watch ur vidoe i feel very satisfied with your explanations ....
@shirleywang789
@shirleywang789 6 жыл бұрын
amazing! much better than my professor who explained this for 2 hours but still confused me
@patrickmensah2338
@patrickmensah2338 5 жыл бұрын
very understanding video. Thank you so much!
@sahilm483
@sahilm483 5 жыл бұрын
you are an absolute god! You are better than my lecturer man!
@akankhachatterjee1505
@akankhachatterjee1505 6 жыл бұрын
Thamkw soo much.....my cocept is pretty clear now....d videos are very helpful.......thanx 4 it....
@DBuza
@DBuza 3 жыл бұрын
May God massively bless you sir.
@billson7583
@billson7583 2 жыл бұрын
U are such a good lecture..uv made me understand this concept,,thanks a great deal
@Hoacook
@Hoacook 4 жыл бұрын
Thank you! Love from Viet Nam. btw: good hand writting. I like it
@naziruadam3950
@naziruadam3950 7 жыл бұрын
Nice and easy to comprehend lecture. thanks
@abhaykr8489
@abhaykr8489 6 жыл бұрын
You rocked..cleared my biggest doubt..luv u
@jadekenzi
@jadekenzi 5 жыл бұрын
This is amazing, thank you so much!
@layloelmuratova2695
@layloelmuratova2695 2 жыл бұрын
I GOTTA SAY ....YOUR VIDEO LESSON WAS GREAT AND CLEARLY SO I LIKE IT.I'M GOING TO WAIT YOUR OTHER LESSONS.
@achadesmondachalefac4845
@achadesmondachalefac4845 2 ай бұрын
your are the Best teacher for this subject sir thanks Alot
@daverickdanquah7093
@daverickdanquah7093 Жыл бұрын
I am happy i understand this before my exams on discrete math
@neilkozlowski8023
@neilkozlowski8023 3 жыл бұрын
Hey, thank you. This is very helpful!
@pritamadey3029
@pritamadey3029 3 жыл бұрын
The best explanation ever.
@MelodiesAndRhythms
@MelodiesAndRhythms 2 жыл бұрын
This math is so cool when it’s explained well like this
@helloguy1179
@helloguy1179 2 жыл бұрын
Thanks very much. your explanation is so good
@growingupfuture4324
@growingupfuture4324 7 ай бұрын
Thank you for the worksheets and solutions.
@enganewguinea
@enganewguinea Ай бұрын
Bro you nailed it. Now I am satisfied
@ghm572
@ghm572 8 жыл бұрын
thanks alot sir you have just solved all my problems here
@user-cf6qd6wb2h
@user-cf6qd6wb2h Жыл бұрын
Thanks for the video sir. I found it's helpful...!!
@subhayansinha4417
@subhayansinha4417 3 жыл бұрын
This was helpful. Thank you sir.
@emilcarlsson2287
@emilcarlsson2287 8 жыл бұрын
really great video! 1000x thanks
@dankmillennialmeals1800
@dankmillennialmeals1800 5 жыл бұрын
Love it! Thank you.
@amanatazizkhan8765
@amanatazizkhan8765 3 жыл бұрын
Thanks a lot!!! Wish I had found you earlier
@saladprayer8239
@saladprayer8239 8 жыл бұрын
Thank you. Just thanks, man.
@justsomeguywith1rinnegan709
@justsomeguywith1rinnegan709 2 жыл бұрын
We love your work here in south Africa🇿🇦
@ruskodudesko9679
@ruskodudesko9679 7 жыл бұрын
bro you're a badass tutor I wish I was as good a tutor as you
@adamboyen4727
@adamboyen4727 3 жыл бұрын
Very helpful on my assignment to state that an equation is neither injective nor surjective, thank you
@mikailuharuna6093
@mikailuharuna6093 6 жыл бұрын
Why do they have to make everything so difficult. Thanks discrete maths for making my life easier.
@danielnwosu3971
@danielnwosu3971 Жыл бұрын
My professor has tons of practice questions and explanations and I still couldn't understand how he was doing the injective proofs. I wish he had just prefaced from the start, like you did, that he is using the contrapositive of the definition of injection. I have my finals tomorrow in an introductory discrete math course and you might have just saved my grades, ty.
@m.i_ggwp
@m.i_ggwp 7 жыл бұрын
this helped alot thanks man!!...
@lovisasjoberg7250
@lovisasjoberg7250 2 жыл бұрын
I am so happy I found these
@jatirijhatjhat
@jatirijhatjhat 2 жыл бұрын
thanks a mil! great explanation!
@0321890
@0321890 8 жыл бұрын
I was dreading to go through the book but then i recalled that there exist some guy called TheTrevTutor in the world. Thanks for saving my time through helpful videos. Keep Up.
@jiaaaverse._
@jiaaaverse._ Жыл бұрын
youre my lifesaverrr ❤️😭😭😭
@user-lt4zz8fb7w
@user-lt4zz8fb7w 7 ай бұрын
Ur really good keep up the good work my g
@abdulrahmanhusam6991
@abdulrahmanhusam6991 3 жыл бұрын
Thanks you are so good . God bless you.
@jessicajaja6132
@jessicajaja6132 4 жыл бұрын
I was honestly failing Discrete maths until I watched this video. Thank you
@jgalang1881
@jgalang1881 5 жыл бұрын
Thanks. very helpful.
@juliatodorova252
@juliatodorova252 6 жыл бұрын
Thank you so much!
@harshdesai4664
@harshdesai4664 7 жыл бұрын
Thanks for these videos, your channel deserves way more views and subs!
@ikeikeikeikeikeikeikeike
@ikeikeikeikeikeikeikeike 5 жыл бұрын
You are fantastic!
@pound9799
@pound9799 Жыл бұрын
bro posted the best math video 7 years ago and thought we wouldn't notice
@mlfm28
@mlfm28 8 жыл бұрын
Thanks!! big help :D
@bedresamarth
@bedresamarth 5 жыл бұрын
Good Job mate....Keep it up....nice video
@kobebeef2424
@kobebeef2424 6 жыл бұрын
All other discrete math videdos are trash.. these make sense!! Thank you!!
@nidaaa7714
@nidaaa7714 6 жыл бұрын
you are the best thank you
@netsanetmelese2640
@netsanetmelese2640 2 жыл бұрын
You are amazing !!!!!
@icee562
@icee562 4 жыл бұрын
Beautiful sir!
@themarinect
@themarinect 6 жыл бұрын
Can you make more example solving videos? That'd be awesome. I really appreciate it.
@bradtagegogona7076
@bradtagegogona7076 6 жыл бұрын
Thank yu Sir
@gospelmusic24
@gospelmusic24 7 жыл бұрын
THANK YOU VERY MUCH SIR, FOR TAKING YOUR PRECIOUS TIME TO PRESENT THIS TUTORIAL. PLEASE SIR, I AM NEW TO THIS KIND OF MATHS, HERE ARE SOME QUESTIONS, I NEED YOUR HELP ON THIS ONE... 1. (a) The universal set is {1, 2, . . . 10}. Let A = {1, 2, 3, 4, 6, 7}, B = {2, 3, 4, 5, 8} and C = {1, 3, 5, 6, 8, 9}. Find the elements of the following sets: (i) A∆B (ii) (A ∩ B) ′\C (b) Given the relation R such that R = {(m, n) ∈ R|m, n ∈ A, m2 − n ≥ 4} when A is the set {0, 1, 2, 3, 4}, (i) express the relation R as a set of ordered pairs. (ii) draw an arrow diagram to represent this relation. (iii) investigate whether the relation is symmetric, transitive and/or reflexive. (c) Determine if the following functions are one-to-one and/or onto and use these to determine whether the function is a bijection. Assume both functions are such where f : R → R. (i) f(x) = 6x − 9 (ii) f(x) = x 2 − 2x + 1
@abhi-nav22
@abhi-nav22 4 жыл бұрын
Your videos are great and easy to understand but if you post some exercises on the discription it will be more helpful. 👍
@komz_
@komz_ 8 жыл бұрын
THANKYOU!
@vidurahansageeth2766
@vidurahansageeth2766 2 жыл бұрын
Thank you so much❤
@arontesfay2520
@arontesfay2520 5 жыл бұрын
This material should go on Khan Academy since they don't have a discrete math course and these are excellent
@yasserzahran9921
@yasserzahran9921 Жыл бұрын
i shall say thank u for the explanation
@ManyStandAlone
@ManyStandAlone 6 жыл бұрын
Thank you, thank you thank you
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