FUNCTIONS - DISCRETE MATHEMATICS

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We introduce functions. How to write them, the terminology, and how to compose them.
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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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28 дек 2014

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Комментарии : 159

@EpicGifted 8 лет назад

TrevTutor, I cannot explain how helpful these videos have been to my discrete math class. My professor is very old and vague but particular and makes us do hard proofs with little direction. The only reason I have an A is these videos, thank you so much.

@decaquits1035 6 лет назад

The Lord Alpha and Savior

@user-jajah585 Месяц назад

My comment is same as yours about my old professor😃👌

@mycul_ 2 года назад

The internet is such a beautiful place. Thank you for your participation to do something good in the world.

@sebamekdad6064 2 года назад

you're a lifesaver there are no words that can describe how thankful I am, I've been suffering from discrete mathematics since the beginning of the term you're a million times better than my professor, thank you so much

@radical_medusa5664 9 месяцев назад

Is anyone else watching this video the day before their test

@sharonosaze 3 месяца назад

Today is my test I hope I pass

@justiceboakye1740 3 месяца назад

today is my exam😅

@Usernameunknown23 2 месяца назад

Yep me

@exclar 2 месяца назад

*hour

@samykingislit5062 Месяц назад

More like 30mins before😭

@Trevtutor 9 лет назад

I made a mistake. 6:44 The range is the set of {x^2 | x is an integer}

@zaboomafia 7 лет назад

Annotation video overlay

@rajeshdansena 6 лет назад

I was about to ask you regarding that. Thanks :)

@hamzahtahir 6 лет назад

gandu

@decaquits1035 6 лет назад

true

@YashSharma-li8li 3 года назад

@@hamzahtahir xd

@dankdreamz 2 года назад

This would have helped me so much when I first started using functions back in my fundementals of college algebra course. Not enough teachers explain the abstract reasoning. I have found I do much better when I understand the whole concept and not just learning how to use it.

@fabianhaglund5792 6 лет назад

You explain discrete math superbly well, thank you!

@AlEx-ro7kd 4 года назад

got my uni exam in a week and am binge studying thank u for making this clear to understand

@makermark2159 5 лет назад

Hey Trev, did you ever make the video on proofs for relating to this topic? Thank you for the collection of fantastic videos.

@chrisp2639 Год назад

Your videos have helped me in my discrete math class so much. Thank you!

@huoenly 5 лет назад

without you i wouldn't of passed my uni exam thank you so so much lifesaver

@syed9576 3 года назад

Okay, I have never taken even trig, so how tf am I understanding this? Like just makes clear effin sense? Props to you my man.

@bugrahandurukan4665 6 лет назад

thanks to TrevTutor i never seen a teacher approach to math like this GG WP

@LisiQarkaxhija 7 лет назад

You're such a help! Thank you for making our life easier!!!

@josephkingyiu19 5 лет назад

I rarely, if ever comment on RU-vid. But for u sir, I am willing to make the exception! Thanks so much for the video. Liked and sub! U could explain this topic better than my Maths prof did in an hour of lecture. -NTU Student

@salmaK20012 9 месяцев назад

best explanation on the distinction between codomain and range!! You're amazing!!!

@marthaa.rangel25 7 лет назад

You are the best! Thanks for saving my grades!

@stephcurry7018 7 лет назад

same!

@toxicmystro1261 Год назад

Thanks for the delightful course, what a legend!

@Franco-Anglo 4 года назад

dude, the way you teach is awesome! Big thumbs up!

@AB-er8yx 7 лет назад

Thank you so much for the explanation of the composite functions! I think I finally understood what all those weird circles mean :D

@paigethompson1633 Год назад

Your videos have been so helpful! I wish you were my professor

@clambaek 7 лет назад

These videos are so helpful, thanks so much for making them! A question: in your first example, how do you decide what the codomain is? Is it based off the possible domain values? Like wouldn't all positive and negative integers also work for the codomain, or even all real numbers?

@Trevtutor 7 лет назад

Codomain is usually always specified. f:R->R, f:Z->Z, etc.

@MrWahsabii 6 лет назад

Do you have videos in your production queue for weighted discrete functions?

@yihanzhou8958 3 года назад

Before watching your video, i had no idea there's such clear way to understand functions

@seanc7472 4 года назад

thank a million. the videos you uploaded help me so so much !

@chinemelumj5349 Год назад

Thank you so much, I understand composite functions better now.

@gourav1163 2 года назад

Is there any necessary condition for a normal function, like every element of A must be mapped to An Element of B or anything like that?

@anime_edits823 3 года назад

That was a great explanation .(and your handwriting is amazing).

@organik05 7 лет назад

Probably wont get this but what about if you have something like X → A, how are you supposed to know what lines to draw where? That is the only part I am really lost on. How do you know to draw lines from the domains and co domains?

@lalaland31695 8 лет назад

Can you make a video about the growth of functions please? Thank you!

@lottakeller7352 8 лет назад

Could you please explain the identity function? My teacher expects us to already know it and I'm very confused. Thank you for the helpful video!

@conradpretorius_remaxjac 2 года назад

This is the problem I find with most maths teachers: they assume your knowledge and cannot explain maths. One needs someone like Trev to explain apples to apples.

@YO-in2ij 4 года назад

God bless you, man.

@nurzihanreya9023 3 года назад

I love this guy!

@meiqihe3708 Год назад

Thank you so much! You saved my life

@metehanyldz6919 6 лет назад

thanks trev or whatever your name. you are the best

@youngee9403 6 лет назад

This is so helpful especially when you can't really understand your professors thick accent... and tangent cs points.

@obertbrainMthimunye 8 лет назад

thank you prof nice video

@urvijain6605 2 года назад

what will be the signature of square of number for total function for real numbers ?

@mousaM469 9 лет назад

Thanks man this vid is very helpful

@zim249 8 лет назад

Awesome video!!

@D.2023 6 лет назад

13:57 "So, that was a quick and DIRTY introduction to functions..." Lol. So this is what a dirty math talk looks like? ahahah. Anyways, good explanation! As always. Thanks!

@karlzechmeister2147 2 года назад

Perfect explanation

@catsonair9432 2 года назад

what then is the difference between a function and a relation if they both map a set to another set?

@BangMaster96 7 лет назад

Thank you so much Sir

@Ravel1299 9 лет назад

Sooo super helpful!

@louoquen5623 4 года назад

@ 8:32 why is f(3) = 1 if it's not in that set?

@daverickdanquah7093 Год назад

what application did you use, to create the video, i want to help some people with my teaching skills also

@jeremiahnji6 7 лет назад

Beautiful!

@samiryounes4624 2 года назад

thank you till now dear

@dennis2571 6 лет назад

many thanks!!

@alhasanvlogs7572 4 года назад

I understand whenever I watch your videos but the I have a lot of difficulties in solving problems from the book or the tutorials

@niki5223 3 года назад

Very easily explained

@brod515 5 лет назад

So what decides that the range is all positive integers; why is the range not determined to be all x^2 where root x is an integers?

@masisimathias6164 Год назад

May God bless you for the nice videos

@caE8 9 лет назад

In regards to composite functions, what if a mapping from X to V(in your example) keeps some elements that is lost otherwise when mapping through f, g, h and j? I can't see why k would be the composite of those functions in that case.

@Trevtutor 9 лет назад

TheModernDante This would not happen. If y=f(x) and z=g(y), then g(f(x))=g(y)=z. So, if we let h(x)=g(f(x)), then h(x)=z as well. This is just the definition of functions and how we compose them.

@caE8 9 лет назад

TheTrevTutor I see. I just had conflicting ideas on how a mapping in this case would work. Thank you for your answer.

@SMARTPALASH 8 лет назад

excellent boss.

@nivekzurc 8 лет назад

i like big pictures and the barney style

@JM-ll2vv 2 года назад

You explain things so clearly, thanks!

@sonalchaudhary6957 4 года назад

Answered all my questions

@SuperSayiyajin 6 лет назад

Thanks a lot....

@pureawesomeness2382 7 лет назад

Thank you Trev? is that your name?:) you are mega helplful..!!

@robbieparekowhai-gudex2871 6 лет назад

You are a talent

@jbillz615 2 года назад

So in the example f(x) -> x^2, you say that the codomain is is positive integers, but the range is perfect squares. It seems that you chose your codomain rather arbitrarily. The fact that all the outcomes are positive is first of all, not true (0 can be an outcome), and second of all, a random characteristic that you chose to classify as the codomain. You could have also said that the codomain is all positive non-prime numbers, or all perfect squares (which would be the range). Why was positive integers the codomain? could we have labeled a different codomain? Thanks.

@user-nw2bc3en8o 4 года назад

Thanks a lot

@user-en2xe9sd8k Год назад

I'm stumped. Is the Codomain all that we define it to be? In 5:10 you reasoned that the function maps every integer to a positive integer, but outlined how the positive integer 3 will never be mapped. Hence you defined the Range seperate from the Codomain. But why could'nt we define the Codomain to be equal to the Range? Or why could'nt the Codomain simply be the set of all positive integers AND countries? Or better simply the Universal Set? Or is the Codomain simply what seems to be the set thats being mapped on? Could someone elucidate things for me?

@lanehensley9948 5 лет назад

wouldn't the range for f(x) = x^2 be {x^2 | sqrt(x^2) is an integer} rather than {x^2 | sqrt(x) is an integer}? Thanks so much for these tutorials btw. I can already tell the rest of theses tutorials are going to be extremely helpful.

@vichufeb16 Год назад

I have the same doubt! Or would it rather be sqrt (y)?

@matthewkurowski4568 9 месяцев назад

The range is the set of {x^2 | x is an integer}

@jaysmith4302 8 лет назад

If an element y is in the codomain but not in the range of f, then how is that element to be distinguished from the rest of the universe which is also not in the range of f? That is, what feature, apart from membership in the range of f, makes that element qualified to be in the codomain of f? Maybe an example would help.

@Trevtutor 8 лет назад

I'm not entirely sure what you're asking. Usually the universe of the domain is something like the set of all integers, rationals, complex numbers, vectors in a field, polynomials, etc. If y is in the codomain and not the range, then it just means that y has that same fundamental description (integer, or rational, or real, or complex, or polynomial), but just doesn't get mapped to by f on some element in the domain.

@Prepaidgeecko 6 лет назад

Dude I love you

@farrenmojela 3 года назад

Can someone suggest where I can start with discrete maths? I'm so lost! How do I learn the theorems?

@nickgismo 3 года назад

Here is a list of how i learned it back in my bach. 1) Basic Set theory. 2) The Euclidean algorithm and the arithmetic fundamental theorem. 3) Logic. (for example logical statements, quantifier, etc.) 4) Proofs. (How to prove direct, proof b contradiction, proof by contraposition, If and only if.) 5) Mathemathical induction. 6) Relations. 7) Maps and functions. 8) Combinatorics. 9) Permutation. 10) Basic Graph theory. (What is a path, Euler path, hamilton path, etc.) 11) Basic Order theory. (Parially ordered set, Well-ordered sets. The well ordering theorem, etc) Notice: you can skip since you also learn about this in topology. 12) Basic group theory 13) Basic ring theory That's about it for a mathematical pure education. But beware that different universities have different math you have to go through. So always be aware of what is required of the course. Hope this help. BSc at Copenhagen University.

@harleendiaries 5 лет назад

You are an angel ♥

@lovfall642 2 года назад

You are my dad, thank you for videos

@EDROCKSWOO 6 лет назад

is codomain the same as target space?

@Trevtutor 6 лет назад

Yes. Had to google that since I don't think I've ever heard that term before.

@senzmaki4890 2 года назад

thanks bruv

@tehreemamjad 4 года назад

Big fan 🙈

@EpicYobis 6 лет назад

Thanks

@imamhosain4991 4 года назад

Thanks sir!😊

@virtuosic4883 2 года назад

You're welcome, darling. (Sorry for my bad English).

@kawasakigf 7 лет назад

Have you ever watched the RU-vid channel Casually Explained? You sound a lot like him haha anyways thanks for the help!

@utopeandrishorts6853 3 года назад

Was thinking the exact same thing when watching this video

@HDitzzDH 4 года назад

13:10 You missed a bracket at the end :)

@laurenblake4138 Год назад

free education rocks!

@chronoskaos3987 6 лет назад

For the first example; the codomain includes zero and you've said the codomain is all positive integers. Zero isn't positive. The codomain would be the non-negative integers.

@chunhaobeh6569 5 лет назад

how about square root 3?

@dennisfranco2843 5 лет назад

not an integer

@-a5624 5 лет назад

I thought zero is neither positive nor negative, why can you say it's positive here? (the eg at 7:00)

@michaelkievits7073 6 лет назад

proof video please !

@akbarabbaskadaya8295 7 лет назад

what is one to one function and onto function?

@sorrenjao3014 7 лет назад

one to one is injective onto is surjective.

@davidzinder677 3 года назад

How is 0 an element in Z+ ?

@anikchau4052 8 месяцев назад

my glorious king

@jumbintoaffiliateprogram8412 2 года назад

Nice

@ericlin8331 4 года назад

Why can't x be sqrt of 3 to get the 3?

@WillRyan514 5 лет назад

"Zed" *Canada intensifies*

@EmmanuellaUdofia 4 года назад

Hunthard Britain Intensifies

@triton62674 4 года назад

*English intensifies*

@OnePiece-fy2kt 4 года назад

old but gold. Tip: watch at 1.75 or 1.5 speed.

@leostojkovski939 4 года назад

6:46 voice has left the chat

@bitflipped5337 3 года назад

and now I owe you 2hours of my life

@cashbuyer4221 Месяц назад

lol, everything was smooth sailing until 13:20.. where the hell did Z And W and v come from???

@samarrana1262 2 года назад

Can I clear my discrete mathematics by watching this vid it’s finals in uni and I haven’t studied full semester it’s day after tomorrow my exam

@richardforman2562 3 года назад

I do not believe 0 is a positive integer, so the example is not technically correct, but practically it is great.

@mohammed7140 6 лет назад

💙

@hggfi 6 лет назад

Is there a convention in discrete math saying that you should call everything "this guy" Because my professor does it as well XD

@Trevtutor 6 лет назад

Yep. It's part of our training. In Scotland they have to call them "wee little ones".

@DakshGargas 7 лет назад

Are you using Light pen?

@Trevtutor 7 лет назад

Yeah. I don't think my writing would be legible with a mouse.

@DakshGargas 7 лет назад

Was double checking, coz I've seen many people with good handwriting, mousewriting I must say Anyway, good video... Thanks

@gordonchan4801 2 года назад

5:36 should be Z^+_0

@Pages_Perfected 4 года назад

day 2 of 3 {studying for final}

@shaunwhyte6686 6 лет назад

can a function be something like a + 2b = 1

@Trevtutor 6 лет назад

That's an equation. You could have a function like f(a,b) = a + 2b - 1. Or you could have a function like f(b) = 1 - 2b, if you write a as a function of b.