INJECTIVE, SURJECTIVE, and BIJECTIVE FUNCTIONS - DISCRETE MATHEMATICS

[@SgtMajorJay]

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

[@jackmenirons4989]

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]

Hahahhaha could relate!

[@parvezshahid8906]

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

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

[@mjusama369]

I thought my lecturer only does that 😂

[@FMAPR]

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]

+FMAPR I wish I could take his job :(

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lol ))

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Yes!

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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.

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

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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.

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then he should be Phd holder ..

[@BangMaster96]

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

[@michaelsun2901]

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

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your university prof. wants to know your location.

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[@SudeepBose-ct9kq]

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[@TheMrsteakman]

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

[@aminamasoud3387]

Life saver

[@aminamasoud3387]

Life saver

[@Horizon.6s]

Saved their life 2x

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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!

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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 .

[@lizziethelemon]

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!

[@speclesic]

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

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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]

"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.

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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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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.

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

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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. 😭

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Only Passed?

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How'd it go?

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

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

[@Trevtutor]

You're welcome

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LING courses. Get your B-Socs 😂🙃

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

[@danielnwosu3971]

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.

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

[@daverickdanquah7093]

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

[@adamboyen4727]

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

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

[@arontesfay2520]

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

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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 🫡

[@achadesmondachalefac4845]

your are the Best teacher for this subject sir thanks Alot

[@jamesbaldwin7169]

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]

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

[@umarfarook-ng7rs]

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[@gospelmusic24]

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

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[@BoonkiCoC14]

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.

[@supraocny]

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

[@Trevtutor]

Glad it was helpful!

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

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The best explanation ever.

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

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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

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

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

[@wolframhuttermann7519]

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.

[@nixonangatiaamukoya2616]

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

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

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Nice and easy to comprehend lecture. thanks

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[@emreturker4175]

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.

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

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Trevor out here saving my uni career

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

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Thank you so much❤

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[@damianpatel2794]

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]

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.

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thanks a mil! great explanation!

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

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[@Chrisymcmb]

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 ?

[@jammesters03]

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

[@adrianharo6586]

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