INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS

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  • เผยแพร่เมื่อ 18 พ.ค. 2015
  • 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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    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.

ความคิดเห็น • 328

  • @SgtMajorJay
    @SgtMajorJay 4 ปีที่แล้ว +321

    Seriously... that's it?? Why was this to complicated when our professor taught it. Thank you so much!

    • @jackmenirons4989
      @jackmenirons4989 3 ปีที่แล้ว +42

      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 9 หลายเดือนก่อน +2

      Hahahhaha could relate!

    • @Sh4dowbanned
      @Sh4dowbanned 6 หลายเดือนก่อน +1

      Some truly can't teach jack* & shouldn't.

    • @parvezshahid8906
      @parvezshahid8906 6 หลายเดือนก่อน +2

      Universities and professors make it sooo complicated, these concepts seem so abstract and just confusing.

    • @Abdushaye
      @Abdushaye 3 หลายเดือนก่อน +1

      I don't even understand why university professors make it so complicated. Thanks to trev tutor he is my savior when exams come up.

  • @FMAPR
    @FMAPR 8 ปีที่แล้ว +653

    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 ปีที่แล้ว +130

      +FMAPR I wish I could take his job :(

    • @dastanmambetaliev7947
      @dastanmambetaliev7947 8 ปีที่แล้ว +5

      lol ))

    • @charlesperry6408
      @charlesperry6408 7 ปีที่แล้ว +4

      Yes!

    • @jadbiz
      @jadbiz 7 ปีที่แล้ว +30

      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 ปีที่แล้ว +8

      I disagree with the fact that you think teachers teach for money, but at any rate it is a really good video for DM.

  • @BangMaster96
    @BangMaster96 7 ปีที่แล้ว +106

    Discrete Math is so fun, when i can understand it
    Thank you Sir, for helping me pass my exams

  • @michaelsun2901
    @michaelsun2901 8 ปีที่แล้ว +141

    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 ปีที่แล้ว +4

      your university prof. wants to know your location.

    • @MDArif-xy5cc
      @MDArif-xy5cc 4 ปีที่แล้ว +1

      @@amansinghbhadauria2818 haahhahaha

    • @SudeepBose-ct9kq
      @SudeepBose-ct9kq 3 ปีที่แล้ว +5

      Watch organic chemistry tutor

  • @TheMrsteakman
    @TheMrsteakman 4 ปีที่แล้ว +147

    Injective: 0:39
    Surjective: 5:25
    Bijective: 10:07

  • @aidahuseynova2639
    @aidahuseynova2639 7 ปีที่แล้ว +96

    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.

  • @RadRobbie
    @RadRobbie 3 ปีที่แล้ว +17

    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

  • @speclesic
    @speclesic ปีที่แล้ว +5

    i have to learn functions, uncountable vs countable sets, and relations in 2 days before my exam, wish me luck

  • @ozzyfromspace
    @ozzyfromspace 6 ปีที่แล้ว +1

    +TheTrevTutor your videos are setting me up for Group Theory and Manifolds...can't tell you how much I appreciate your lectures. Thank you!

  • @kansterstrak
    @kansterstrak 9 ปีที่แล้ว +3

    Thank you for all the videos, they're awesome!

  • @hessnej
    @hessnej 5 ปีที่แล้ว +1

    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.

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    @TheFearlocator 5 ปีที่แล้ว +1

    I'm so grateful for your existence in this world! You are best teacher of discrete math and you are saving my life!

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    @myatthuaung2570 8 ปีที่แล้ว

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  • @jacksonfraser6251
    @jacksonfraser6251 8 ปีที่แล้ว

    Subscribed. Thanks for making such great quality videos. Really helping me with my Discrete Structures in Computing course

  • @yvonneykke
    @yvonneykke 2 ปีที่แล้ว +1

    Been struggling to understand this for a few weeks now, this one video I accidentally found just explains it all. Thank you!!

  • @Panditatt
    @Panditatt 4 ปีที่แล้ว +14

    I’m ready for my final tmm. You explained it in such a easier way, thank you 🙏🏼

    • @afaq-6753
      @afaq-6753 2 ปีที่แล้ว

      How'd it go?

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    @anilajanaki4609 7 ปีที่แล้ว +1

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  • @jiashangliu5243
    @jiashangliu5243 ปีที่แล้ว +5

    Thanks!! This is really way more understandable and intuitive than what my professor had taught in class🤩

  • @khSoraya01
    @khSoraya01 3 ปีที่แล้ว

    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!

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    @creepercraft97 7 ปีที่แล้ว

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    @jadekenzi 5 ปีที่แล้ว

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    @jonsilva3849 7 ปีที่แล้ว

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  • @RyanTorrecampo
    @RyanTorrecampo 5 ปีที่แล้ว +2

    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.

  • @imansantamaria1055
    @imansantamaria1055 8 ปีที่แล้ว +1

    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.

  • @patrickmensah2338
    @patrickmensah2338 5 ปีที่แล้ว

    very understanding video. Thank you so much!

  • @im-nazmul
    @im-nazmul 4 ปีที่แล้ว

    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 😊

  • @abdoennajah2702
    @abdoennajah2702 3 ปีที่แล้ว +2

    What a great explanation, thanks a lot man ❤

  • @natriac.6092
    @natriac.6092 3 ปีที่แล้ว +1

    OMG THANK YOU! Now I truly understand this topic !!!

  • @cxeenyi
    @cxeenyi 4 ปีที่แล้ว +5

    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. 😭

  • @Zavi0001
    @Zavi0001 6 ปีที่แล้ว +1

    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 ปีที่แล้ว +1

    Thank you! May professor has a very strong accent that's hard to understand, this is helping tremendously.

  • @billson7583
    @billson7583 2 ปีที่แล้ว

    U are such a good lecture..uv made me understand this concept,,thanks a great deal

  • @naziruadam3950
    @naziruadam3950 7 ปีที่แล้ว

    Nice and easy to comprehend lecture. thanks

  • @dankmillennialmeals1800
    @dankmillennialmeals1800 5 ปีที่แล้ว

    Love it! Thank you.

  • @neilkozlowski8023
    @neilkozlowski8023 3 ปีที่แล้ว

    Hey, thank you. This is very helpful!

  • @icy5982
    @icy5982 4 ปีที่แล้ว +2

    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

  • @lizziethelemon
    @lizziethelemon 2 ปีที่แล้ว +1

    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 ปีที่แล้ว +2

    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 .

  • @user-cf6qd6wb2h
    @user-cf6qd6wb2h ปีที่แล้ว

    Thanks for the video sir. I found it's helpful...!!

  • @johnbraganza9316
    @johnbraganza9316 6 ปีที่แล้ว

    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
    :)

  • @sitembekilekhumalo8235
    @sitembekilekhumalo8235 2 ปีที่แล้ว +1

    wow this is the best .I now understand set theory.You are the best professor!

  • @Hoacook
    @Hoacook 4 ปีที่แล้ว

    Thank you! Love from Viet Nam.
    btw: good hand writting. I like it

  • @emilcarlsson2287
    @emilcarlsson2287 8 ปีที่แล้ว

    really great video! 1000x thanks

  • @mclovin510
    @mclovin510 8 ปีที่แล้ว

    "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.

  • @mustafakhanani1577
    @mustafakhanani1577 2 ปีที่แล้ว +3

    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 ปีที่แล้ว

      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 .

  • @saladprayer8239
    @saladprayer8239 8 ปีที่แล้ว

    Thank you. Just thanks, man.

  • @DBuza
    @DBuza 3 ปีที่แล้ว +2

    May God massively bless you sir.

  • @abhaykr8489
    @abhaykr8489 6 ปีที่แล้ว

    You rocked..cleared my biggest doubt..luv u

  • @kachuolbuongjok
    @kachuolbuongjok 8 ปีที่แล้ว

    thanks alot sir you have just solved all my problems here

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    @beasaheric906 4 ปีที่แล้ว

    any time i watch ur vidoe i feel very satisfied with your explanations ....

  • @enganewguinea
    @enganewguinea 2 หลายเดือนก่อน +1

    Bro you nailed it. Now I am satisfied

  • @subhayansinha4417
    @subhayansinha4417 3 ปีที่แล้ว

    This was helpful. Thank you sir.

  • @jacquelinehernandez8453
    @jacquelinehernandez8453 10 หลายเดือนก่อน

    i always look for these videos when i don't understand something in class. He does such a good job of explaining things . #trevtutorforprez

  • @m.i_ggwp
    @m.i_ggwp 7 ปีที่แล้ว

    this helped alot thanks man!!...

  • @brianmwasaru797
    @brianmwasaru797 7 ปีที่แล้ว

    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

  • @growingupfuture4324
    @growingupfuture4324 9 หลายเดือนก่อน

    Thank you for the worksheets and solutions.

  • @achadesmondachalefac4845
    @achadesmondachalefac4845 4 หลายเดือนก่อน

    your are the Best teacher for this subject sir thanks Alot

  • @lovisasjoberg7250
    @lovisasjoberg7250 2 ปีที่แล้ว

    I am so happy I found these

  • @jatirijhatjhat
    @jatirijhatjhat 2 ปีที่แล้ว

    thanks a mil! great explanation!

  • @sahilm483
    @sahilm483 5 ปีที่แล้ว

    you are an absolute god! You are better than my lecturer man!

  • @caseycarlyle5337
    @caseycarlyle5337 3 ปีที่แล้ว

    I have an exam tomorrow, and this is really helping me. Thank you!!

  • @juliatodorova252
    @juliatodorova252 6 ปีที่แล้ว

    Thank you so much!

  • @abdulrahmanhusam6991
    @abdulrahmanhusam6991 3 ปีที่แล้ว

    Thanks you are so good . God bless you.

  • @parvezshahid8906
    @parvezshahid8906 6 หลายเดือนก่อน

    You made this sooooo much simpler to understand than my University Professor who gets paid $100K+ yet still can't explain a simple concept simply. Kudos to you sir 🫡

  • @MelodiesAndRhythms
    @MelodiesAndRhythms 2 ปีที่แล้ว

    This math is so cool when it’s explained well like this

  • @jgalang1881
    @jgalang1881 5 ปีที่แล้ว

    Thanks. very helpful.

  • @amonGustavo07
    @amonGustavo07 2 ปีที่แล้ว

    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.

  • @user-lt4zz8fb7w
    @user-lt4zz8fb7w 9 หลายเดือนก่อน +1

    Ur really good keep up the good work my g

  • @pritamadey3029
    @pritamadey3029 3 ปีที่แล้ว

    The best explanation ever.

  • @akankhachatterjee1505
    @akankhachatterjee1505 6 ปีที่แล้ว

    Thamkw soo much.....my cocept is pretty clear now....d videos are very helpful.......thanx 4 it....

  • @themarinect
    @themarinect 6 ปีที่แล้ว

    Can you make more example solving videos? That'd be awesome. I really appreciate it.

  • @helloguy1179
    @helloguy1179 2 ปีที่แล้ว

    Thanks very much. your explanation is so good

  • @danielnwosu3971
    @danielnwosu3971 ปีที่แล้ว

    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.

  • @mlfm28
    @mlfm28 8 ปีที่แล้ว

    Thanks!! big help :D

  • @daverickdanquah7093
    @daverickdanquah7093 2 ปีที่แล้ว

    I am happy i understand this before my exams on discrete math

  • @netsanetmelese2640
    @netsanetmelese2640 2 ปีที่แล้ว

    You are amazing !!!!!

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    @ikeikeikeikeikeikeikeike 5 ปีที่แล้ว

    You are fantastic!

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    @ruskodudesko9679 7 ปีที่แล้ว

    bro you're a badass tutor I wish I was as good a tutor as you

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    @justsomeguywith1rinnegan709 2 ปีที่แล้ว

    We love your work here in south Africa🇿🇦

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    @jiaaaverse._ ปีที่แล้ว

    youre my lifesaverrr ❤️😭😭😭

  • @vidurahansageeth2766
    @vidurahansageeth2766 2 ปีที่แล้ว +1

    Thank you so much❤

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    @amanatazizkhan8765 3 ปีที่แล้ว

    Thanks a lot!!! Wish I had found you earlier

  • @harshdesai4664
    @harshdesai4664 7 ปีที่แล้ว

    Thanks for these videos, your channel deserves way more views and subs!

  • @layloelmuratova2695
    @layloelmuratova2695 2 ปีที่แล้ว

    I GOTTA SAY ....YOUR VIDEO LESSON WAS GREAT AND CLEARLY SO I LIKE IT.I'M GOING TO WAIT YOUR OTHER LESSONS.

  • @bradtagegogona7076
    @bradtagegogona7076 7 ปีที่แล้ว +1

    Thank yu Sir

  • @bedresamarth
    @bedresamarth 5 ปีที่แล้ว

    Good Job mate....Keep it up....nice video

  • @shirleywang789
    @shirleywang789 6 ปีที่แล้ว

    amazing! much better than my professor who explained this for 2 hours but still confused me

  • @komz_
    @komz_ 8 ปีที่แล้ว

    THANKYOU!

  • @mikailuharuna6093
    @mikailuharuna6093 6 ปีที่แล้ว

    Why do they have to make everything so difficult.
    Thanks discrete maths for making my life easier.

  • @Auxytocin
    @Auxytocin 5 ปีที่แล้ว

    Is the process for proving injective and surjective the same for piecewise defined functions? Only you have to do a case for each piece?

  • @adamboyen4727
    @adamboyen4727 3 ปีที่แล้ว

    Very helpful on my assignment to state that an equation is neither injective nor surjective, thank you

  • @nidaaa7714
    @nidaaa7714 6 ปีที่แล้ว

    you are the best thank you

  • @floris8392
    @floris8392 ปีที่แล้ว

    thanks man!

  • @yasserzahran9921
    @yasserzahran9921 ปีที่แล้ว

    i shall say thank u for the explanation

  • @suguwus
    @suguwus ปีที่แล้ว

    tysm!!!

  • @ChaseFLable
    @ChaseFLable 6 ปีที่แล้ว +11

    Man, you know i'm really reaching to enjoy math when I laugh at 1:12 when he says it's just x1 in disguise. Why was that funny... idk...

    • @Trevtutor
      @Trevtutor  6 ปีที่แล้ว +16

      Everyone loves it when the killer is finally unmasked!

  • @markokoth5609
    @markokoth5609 6 ปีที่แล้ว

    Well explained

  • @nixonangatiaamukoya2616
    @nixonangatiaamukoya2616 7 ปีที่แล้ว +2

    nice tutorial,but could you please give solution to inverse of f(x)=5x+2?

  • @icee562
    @icee562 4 ปีที่แล้ว

    Beautiful sir!

  • @ManyStandAlone
    @ManyStandAlone 6 ปีที่แล้ว

    Thank you, thank you thank you