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.
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
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.
I had my second lecture of Analysis I today. The professor just copies the book and writes it down with no further explanation. She expects us, who all come from high school, to understand all the terms immediately. Thank you for this video!
I rarely, if ever comment on UA-cam. 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
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?
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!
bro- how are you gonna explain to me 8 pages of notes from my discretemath class- mind you thats 5 diffrent lectures- in like the first 20 seconds of your video(actually in this whole 15 min video)!!!! thank you
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?
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.
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.
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.
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.
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?
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.
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.
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.
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.
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.
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.
The Lord Alpha and Savior
My comment is same as yours about my old professor😃👌
The internet is such a beautiful place. Thank you for your participation to do something good in the world.
I made a mistake. 6:44 The range is the set of {x^2 | x is an integer}
Annotation video overlay
I was about to ask you regarding that. Thanks :)
gandu
true
@@hamzahtahir xd
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
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.
You explain discrete math superbly well, thank you!
got my uni exam in a week and am binge studying thank u for making this clear to understand
I had my second lecture of Analysis I today. The professor just copies the book and writes it down with no further explanation. She expects us, who all come from high school, to understand all the terms immediately. Thank you for this video!
without you i wouldn't of passed my uni exam thank you so so much lifesaver
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.
I rarely, if ever comment on UA-cam. 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
Is anyone else watching this video the day before their test
Today is my test
I hope I pass
today is my exam😅
Yep me
*hour
More like 30mins before😭
best explanation on the distinction between codomain and range!! You're amazing!!!
You are the best! Thanks for saving my grades!
same!
Thanks for the delightful course, what a legend!
dude, the way you teach is awesome! Big thumbs up!
Thank you so much, I understand composite functions better now.
Your videos have been so helpful! I wish you were my professor
Your videos have helped me in my discrete math class so much. Thank you!
Before watching your video, i had no idea there's such clear way to understand functions
thanks to TrevTutor i never seen a teacher approach to math like this GG WP
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?
Codomain is usually always specified. f:R->R, f:Z->Z, etc.
Thank you so much! You saved my life
Thank you so much for the explanation of the composite functions! I think I finally understood what all those weird circles mean :D
You're such a help! Thank you for making our life easier!!!
That was a great explanation .(and your handwriting is amazing).
This is so helpful especially when you can't really understand your professors thick accent... and tangent cs points.
You are my dad, thank you for videos
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!
thank a million. the videos you uploaded help me so so much !
God bless you, man.
thank you till now dear
May God bless you for the nice videos
bro I accidentally fell asleep while watching this video. woke up after I spilled my tea on me and whole fucking bed
thanks trev or whatever your name. you are the best
Hey Trev, did you ever make the video on proofs for relating to this topic? Thank you for the collection of fantastic videos.
I love this guy!
bro- how are you gonna explain to me 8 pages of notes from my discretemath class- mind you thats 5 diffrent lectures- in like the first 20 seconds of your video(actually in this whole 15 min video)!!!! thank you
Perfect explanation
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?
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!
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.
Answered all my questions
You explain things so clearly, thanks!
Very easily explained
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?
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.
I have the same doubt! Or would it rather be sqrt (y)?
The range is the set of {x^2 | x is an integer}
thank you prof
nice video
Thanks man this vid is very helpful
I understand whenever I watch your videos but the I have a lot of difficulties in solving problems from the book or the tutorials
@ 8:32 why is f(3) = 1 if it's not in that set?
old but gold. Tip: watch at 1.75 or 1.5 speed.
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.
how about square root 3?
not an integer
free education rocks!
Awesome video!!
Have you ever watched the UA-cam channel Casually Explained? You sound a lot like him haha anyways thanks for the help!
Was thinking the exact same thing when watching this video
i like big pictures and the barney style
I thought zero is neither positive nor negative, why can you say it's positive here? (the eg at 7:00)
Thank you so much Sir
Big fan 🙈
You are a talent
Sooo super helpful!
10 minutes before the test, guys wish me luck (I'm cooked)
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.
Do you have videos in your production queue for weighted discrete functions?
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?
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?
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.
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.
TheTrevTutor I see. I just had conflicting ideas on how a mapping in this case would work. Thank you for your answer.
13:10 You missed a bracket at the end :)
Thank you Trev? is that your name?:) you are mega helplful..!!
Thanks sir!😊
You're welcome, darling. (Sorry for my bad English).
"Zed"
*Canada intensifies*
Hunthard Britain Intensifies
*English intensifies*
Dude I love you
what application did you use, to create the video, i want to help some people with my teaching skills also
excellent boss.
You are an angel ♥
what will be the signature of square of number for total function for real numbers ?
my glorious king
what then is the difference between a function and a relation if they both map a set to another set?
many thanks!!
Can you make a video about the growth of functions please? Thank you!
I have Test tomorrow ......
Anyone from 2019?!?!?!?
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.
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.
Thanks a lot....
and now I owe you 2hours of my life
Beautiful!
5:36 should be Z^+_0
Thanks a lot
Can someone suggest where I can start with discrete maths? I'm so lost! How do I learn the theorems?
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.
lol, everything was smooth sailing until 13:20.. where the hell did Z And W and v come from???
BTW I'm watching this during covid 19 pandemic
I do not believe 0 is a positive integer, so the example is not technically correct, but practically it is great.
missed a parentheses at 13:09
is codomain the same as target space?
Yes. Had to google that since I don't think I've ever heard that term before.
what is one to one function and onto function?
one to one is injective
onto is surjective.
Are you using Light pen?
Yeah. I don't think my writing would be legible with a mouse.
Was double checking, coz I've seen many people with good handwriting, mousewriting I must say
Anyway, good video... Thanks
How is 0 an element in Z+ ?
proof video please !
Thanks
thanks bruv
not sure why we introduce the idea of a co-domain. The range does everything we need.
Because a function won’t have an inverse if the range isn’t the same as the codomain.