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INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS

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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.

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5 сен 2024

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Комментарии : 329

@SgtMajorJay 4 года назад

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

@jackmenirons4989 3 года назад

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 10 месяцев назад

Hahahhaha could relate!

@Sh4dowbanned 8 месяцев назад

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

@parvezshahid8906 8 месяцев назад

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

@Abdushaye 5 месяцев назад

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 8 лет назад

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 8 лет назад

+FMAPR I wish I could take his job :(

@dastanmambetaliev7947 8 лет назад

lol ))

@charlesperry6408 8 лет назад

Yes!

@jadbiz 7 лет назад

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 6 лет назад

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

@michaelsun2901 8 лет назад

You are by far the best teacher of Discrete Math compared to any other youtube tutors as well as my Uni teacher

@amansinghbhadauria2818 5 лет назад

your university prof. wants to know your location.

@MDArif-xy5cc 4 года назад

@@amansinghbhadauria2818 haahhahaha

@SudeepBose-ct9kq 3 года назад

Watch organic chemistry tutor

@BangMaster96 7 лет назад

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

@aidahuseynova2639 8 лет назад

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 6 лет назад

then he should be Phd holder ..

@TheMrsteakman 4 года назад

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

@aminamasoud3387 4 месяца назад

Life saver

@aminamasoud3387 4 месяца назад

Life saver

@RadRobbie 3 года назад

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 Год назад

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

@mustafakhanani1577 2 года назад

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 Год назад

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 .

@jamesbaldwin7169 2 года назад

f: R->Z given by f(x)=5x+2 is NOT surjective. It's clear just from looking at it that the range of f(x) is R, but the codomain of the function is Z, so it is not surjective. If, on the other hand, you're talking about the function f:R->Z given by f(y)=(y-2)/5, this again is not surjective by the same reasoning. For either of these functions to be surjective, you'd need f:Z->R

@realitymeetstheworld8217 17 дней назад

I was looking for this comment, Thank you Got confused there at 9:29

@enganewguinea 4 месяца назад

Bro you nailed it. Now I am satisfied

@RyanTorrecampo 5 лет назад

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.

@cxeenyi 4 года назад

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 Год назад

Only Passed?

@Panditatt 4 года назад

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

@afaq-6753 2 года назад

How'd it go?

@jiashangliu5243 Год назад

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

@icy5982 4 года назад

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 2 года назад

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 3 года назад

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 .

@TheFearlocator 5 лет назад

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

@Zavi0001 6 лет назад

Tomorrow is my mid,and your videos are really gonna help me, your work should be appreciated teacher..thank u so much.

@amonGustavo07 2 года назад

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.

@mclovin510 8 лет назад

"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.

@hessnej 5 лет назад

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.

@yvonneykke 3 года назад

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

@danielnwosu3971 Год назад

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.

@danieljulian4676 3 года назад

Really well done. I've seen some bad YT math videos, and good ones like yours help me both to develop my understanding of the topic you're explaining and also to see more quickly when I'm wasting my time with other vids. I can't articulate what that is, maybe someone will comment. Well-organized lecture, and not a lot of dead air and/or needless repetition. I think that's it. Thanks!

@brandonthompson9659 5 лет назад

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

@khSoraya01 3 года назад

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!

@jacquelinehernandez8453 11 месяцев назад

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

@anilajanaki4609 7 лет назад

you r a the best tutor i have ever seen in my life ,

@w3nhan_ 3 года назад

This man deserves a kiss from each one of us! TY!!

@Trevtutor 3 года назад

You're welcome

@w3nhan_ 3 года назад

@@Trevtutor oh wtf sorry I didn’t know u teach at SFU😳😳¿

@w3nhan_ 3 года назад

@@Trevtutor whatttt yo that’s so cool what courses do u teach?

@Trevtutor 3 года назад

LING courses. Get your B-Socs 😂🙃

@w3nhan_ 3 года назад

@@Trevtutor hahaha Aweh I’m in SIAT BSc, but I’ll try to take a LING course in the future as an elective

@sitembekilekhumalo8235 2 года назад

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

@layloelmuratova2695 3 года назад

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

@DBuza 3 года назад

May God massively bless you sir.

@imansantamaria1055 8 лет назад

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.

@caseycarlyle5337 3 года назад

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

@adamboyen4727 3 года назад

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

@daverickdanquah7093 2 года назад

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

@im-nazmul 4 года назад

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 😊

@parvezshahid8906 8 месяцев назад

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 🫡

@justsomeguywith1rinnegan709 2 года назад

We love your work here in south Africa🇿🇦

@achadesmondachalefac4845 5 месяцев назад

your are the Best teacher for this subject sir thanks Alot

@johnbraganza9316 6 лет назад

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 :)

@damianpatel2794 4 года назад

At around 9:45, you say that with a domain of real numbers and a codomain of integers, it is surjective; however, some domain values will not even have a mapping/value. Doesn't this mean that it no longer qualifies as a function?

@Bikash_The_1 Год назад

You can simply say co domain is subset of range.Or range(R)is bigger set than of co domain (Z).Hence That's not even a function.

@natriac.6092 3 года назад

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

@ozzyfromspace 6 лет назад

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

@supraocny 5 месяцев назад

Thank you, my learning material did not explain at all how to determine if a function is injective, surjective, or bijective.

@Trevtutor 5 месяцев назад

Glad it was helpful!

@mikailuharuna6093 6 лет назад

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

@gospelmusic24 8 лет назад

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

@ngndnd 2 года назад

i swear my professor skipped three whole sections. We had a test on sets last week and now we have one due next week on this thing and this is like your 54th video in the playlist

@ChaseFLable 7 лет назад

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 7 лет назад

Everyone loves it when the killer is finally unmasked!

@MelodiesAndRhythms 2 года назад

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

@harissid 8 лет назад

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.

@pound9799 Год назад

bro posted the best math video 7 years ago and thought we wouldn't notice

@arontesfay2520 5 лет назад

This material should go on Khan Academy since they don't have a discrete math course and these are excellent

@sahilm483 5 лет назад

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

@shirleywang789 6 лет назад

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

@lovisasjoberg7250 2 года назад

I am so happy I found these

@beasaheric906 4 года назад

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

@wolframhuttermann7519 2 месяца назад

Have you ever dealt with quasi-injective functions? This is a function f:A -> B where f(x)=b has at most finitely many solutions. Does it have any applications? Yes, it has. Consider a convergent real sequence a_n that converges against 0. Then a_n = a can have at most finitely many solutions if a /=0.

@kobebeef2424 6 лет назад

All other discrete math videdos are trash.. these make sense!! Thank you!!

@amanatazizkhan8765 3 года назад

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

@nixonangatiaamukoya2616 7 лет назад

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

@BoonkiCoC14 3 года назад

This video is great, however i just relazied something and would like to let everyone else know about it incase you are having a hard time understanding on how you can decide if something is surjective or not. You follow his steps, he explains perfectly on how you can determine if it's surjective or not. But you must pay attention to the range/domain, the domain/range decides whether the function is surjective or not. If the range is Z -> Z, then you can create a function (for example f(x)=x-4, the inverse is y+4 = x) which will give an output that ranges from all negative and positive values. If the inverse functions gives an output of a value that does not belong in the range/domain then it is not surjective. For instance if the function output all real numbers, or fractions then it is not surjective. I hope this helped, as this helped my stupid ass to understand lol.

@paddy2460 2 года назад

People are talking about uni while I’m learning this in secondary school

@abdoennajah2702 3 года назад

What a great explanation, thanks a lot man ❤

@Chrisymcmb 2 года назад

For the last example of the surjective proof for f(x)=5x+2, we wrote the function as y=5x+2, then rewrite the function in terms of x, so x=(y-2)/5. We lastly tried to prove if we mapped f:real->integers. This does work if we plug in for the function in terms of x, but if we plug in this mapping for the function in terms of y, then it is not possible. Should the mapping not work for the function in terms of a and y both when mapped f:real->integers ?

@Dubov1933 2 года назад

Man I can't wait to be done with this discrete math stuff.

@abhi-nav22 4 года назад

Your videos are great and easy to understand but if you post some exercises on the discription it will be more helpful. 👍

@myatthuaung2570 8 лет назад

The best video ever !! I am now crystal clear. Thanks.

@user-lt4zz8fb7w 10 месяцев назад

Ur really good keep up the good work my g

@pritamadey3029 4 года назад

The best explanation ever.

@abdulrahmanhusam6991 3 года назад

Thanks you are so good . God bless you.

@growingupfuture4324 10 месяцев назад

Thank you for the worksheets and solutions.

@fairlymoon448 7 лет назад

Okay, So if instead you were going from Z->R, in your example y-2/5= x how do you do that? I understand when its Z->Z or R->R, and R->Z makes sense because theres only a limited number of integers. but Z is everything except C numbers. so is it considered still onto? how would you do the math in the equation to prove it? [your vids rock even if i dont get everything]

@burmesehistorythiha 2 года назад

My professor is good at teaching too. But, he's just too slow. Your speed is just right for me!

@billson7583 2 года назад

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

@vidurahansageeth2766 2 года назад

Thank you so much❤

@brianmwasaru797 7 лет назад

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

@johnwick9329 3 года назад

I study maths in french its awful but fortunately you got my back 😉

@staratzenith9792 6 лет назад

Sir I have one question please make video on it as you have said we assumed x1=x2 then f(x1)=f(x2),,then in what case it will not satisfy the condition...I meant to say by this method how can we show a function is not injective

@reorange12 3 года назад

Trevor out here saving my uni career

@yasserzahran9921 Год назад

i shall say thank u for the explanation

@user-cf6qd6wb2h Год назад

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

@akankhachatterjee1505 7 лет назад

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

@jessicajaja6132 4 года назад

I was honestly failing Discrete maths until I watched this video. Thank you

@creepercraft97 7 лет назад

I love your writing ! Very well explained.

@kansterstrak 9 лет назад

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

@jiaaaverse._ Год назад

youre my lifesaverrr ❤️😭😭😭

@naziruadam3950 7 лет назад

Nice and easy to comprehend lecture. thanks

@helloguy1179 2 года назад

Thanks very much. your explanation is so good

@DarkCIoudStudios 6 лет назад

For 10:06 How can it be R -> Z? Most x's will not be able to be mapped so it cant be a function.

@nickgismo 5 лет назад

I know you asked this question a long time ago, but here is the answer. the function f:R->Z is a function. I will give an example: f:R->Z, where x maps to the lowest integer except if x is an integer. So this function will map any half open interval [x,x+1) to x itself. Meaning that the f(2.22245)=2 and f(10.999838)=10. This function is clearly not injective, since we have a continium of numbers that maps to a single point. But the function would actually be surjective, since we maps to all of Z. To give a better example, consider the function g:R->{1}. This function take any x in R, and maps it to the singleton {1}. We se agian that the function is not injective, but it is surjective. Functions defined like my to examples are still functions. An exercise for you to show would be: Let f:R->R be a function defined as f(x)=1. 1) Prove the function is not injective nor surjective. 2) Now define the function f:R->R\A with f(x)=1. Choose A such that f will be surjective. Hope this help.

@petruspetrusuom3342 5 лет назад

@@nickgismo Hello. Why did you assume that the function does that? As far as I see from what is written that there are no special requirements for what you just described. And for the question you asked: part (2) Should the answer be R- Complement 1? Or how do you mathematically write that ? Thanks!

@nickgismo 5 лет назад

@@petruspetrusuom3342 Whar do you mean with I assumed the function did that? I really cannot see what you meant with that question. For the second part, you are correct. We would write it as: R\{1}^C or R-{1}^C where C denote the compliment.

@ruskodudesko9679 8 лет назад

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

@jammesters03 5 лет назад

Great work sir! However, I think you misused R as Rational when it is Real Number . Q is denoted as Rational.

@adrianharo6586 5 лет назад

I think he assumed we knew Q is a subset of R

@emreturker4175 2 года назад

I gues 09:36 is not a function in the first place since there are some x's that cannot be mappen on to a value in our codomain. Say x=1.231 which is in our domain. However, when x takes that value, y happens to be a value that is not an integer, and I suppose that means what we have is not a function.