You're an extremely skilled instructor. Thank you. I just transferred into the computer engineering program at the University of Michigan from an out-of-state community college. The EECS department advisor said I would be crushed in Discrete Math this fall. He doesn't know my work ethic lol. I'm watching this entire video course before the start of classes in hopes of getting a leg up and proving him wrong. I'll give an update this winter when I get my final grade.
I'm in love with this course so far. Thank you so much. All of my lecturers were sort of dancing around all the ideas and were explaining them using analogies "to not scare anyone with math", but I missed the straightforward and clear ways in which maths appears when you actually use maths to describe it and it helped me connect all the dots!
Commenting just to potentially increase your videos being recommended to someone =) I prefer your approach from a problem/example to formalism, instead of the converse.
thank you for such a great course,you're a source of inspiration for me and so many people who want to do something great in the math field. i am watching thoses video and i'll finish other courses that you made in youtube,again... thank you very much!
Thank you so much for such amazing intutive understanding of discrete mathematics i really could not understand and apply discrete mathematics on my own but your video series is making it more easy and fun!!!
This might be a dumb question but i'll ask it anyway. So long as the function is giving only one output when given an input , does it matter if two separate inputs give the same output? I assume this would be yes cause assuming -x and x give the same y output. Eg : (-2,4) (2,4)
I have a question. How important is it that each and every element must have an output? Let us take the "function" y = 1/(1-x). Then is it incorrect to call this a function because this has no output when x = 1? Every other point on the real number line has an output/image. Can't we just call it a function and it is just undefined at x = 1?
Really good videos dude. Regarding the first property of the functions 1) for every elemento x... could we say that if (x,y)€F then (x,y)€AxB? (sorry but I didn't find other symbol to use in behalf of the belonging better than the euro symbol)
Doesn't is say if (x,y) are in the set F and if (x,z) are in the set F, then y = z? How is that true or how does it relate to the vertical line test? My understanding is that y cannot equal z, otherwise it's not a function. I might be misreading something...
If I have a function F such that F(x)=sqrt(x) now for every possible perfect square there would be two outputs. How can I represent the vertical line test?
And just another question. Wouldn't it be necessary to show the first property for every function by, I don't know, maybe induction, or any other mean? Or is it enough to grasp it intuitively? Cheers
Any serious academic lecture that includes the phrase, "There can be only one.", should be closely examined for covert evil villianism. - Rule #1, "Good Guy Rulebook For Dummies", Superhero Press, 37,929 ACE.
You're an extremely skilled instructor. Thank you. I just transferred into the computer engineering program at the University of Michigan from an out-of-state community college. The EECS department advisor said I would be crushed in Discrete Math this fall. He doesn't know my work ethic lol. I'm watching this entire video course before the start of classes in hopes of getting a leg up and proving him wrong. I'll give an update this winter when I get my final grade.
doing the exact same thing right now! heard a lot of things about discrete math being difficult so am watching this before taking it this fall.
hey man let us know how it goes! I'm also thinking of transferring to a more stem-based major haha
I'm in love with this course so far. Thank you so much. All of my lecturers were sort of dancing around all the ideas and were explaining them using analogies "to not scare anyone with math", but I missed the straightforward and clear ways in which maths appears when you actually use maths to describe it and it helped me connect all the dots!
wow what a greatest explanation sir we Indians are really missing Math teachers like you
Commenting just to potentially increase your videos being recommended to someone =) I prefer your approach from a problem/example to formalism, instead of the converse.
This video commentary is a reliable set of textbook facts.
thank you for such a great course,you're a source of inspiration for me and so many people who want to do something great in the math field.
i am watching thoses video and i'll finish other courses that you made in youtube,again... thank you very much!
Thank you so much for such amazing intutive understanding of discrete mathematics i really could not understand and apply discrete mathematics on my own but your video series is making it more easy and fun!!!
Good video! Found this after quite some time searching and explains it the way it should be done! Suggesting it to my students!
I am in short of words to appraise you just wanna say I love you❤ for explaining in such a amazing way
Very nice explanation of the vertical line test.
This might be a dumb question but i'll ask it anyway. So long as the function is giving only one output when given an input , does it matter if two separate inputs give the same output? I assume this would be yes cause assuming -x and x give the same y output. Eg : (-2,4) (2,4)
This help A LOT! Thank you!
Glad it helped!
Thank you very much I finally understood this definition 👍🏽
Super awesome explanation!!
Great sir I find it very easy now
@ProfBazett - Is this another way of saying F is onto and one-to-one?
Does the second law (that for checking vertcal line test) concerns the transitive property?
Great lesson, tks a lot
I have a question. How important is it that each and every element must have an output? Let us take the "function" y = 1/(1-x). Then is it incorrect to call this a function because this has no output when x = 1? Every other point on the real number line has an output/image. Can't we just call it a function and it is just undefined at x = 1?
It is not a function on all of R. But it is a function on a subset of R
What would be the formal definition of a function f(x, g(x)) ?
Really good videos dude. Regarding the first property of the functions 1) for every elemento x... could we say that if (x,y)€F then (x,y)€AxB? (sorry but I didn't find other symbol to use in behalf of the belonging better than the euro symbol)
I think this inference is true, but the converse is not. I think F is a subset of A*B.
Thanks
Doesn't is say if (x,y) are in the set F and if (x,z) are in the set F, then y = z? How is that true or how does it relate to the vertical line test? My understanding is that y cannot equal z, otherwise it's not a function. I might be misreading something...
How do you get words on your glass screen such that you can underline them? I thought they were edited in post.
Isn’t it cool? Basically the same trick as a weather person, I see the output on a screen in front so I know where to touch or write
@@DrTrefor Ah, that makes sense
@@DrTrefor Honestly thats very very smart.
If I have a function F such that F(x)=sqrt(x) now for every possible perfect square there would be two outputs. How can I represent the vertical line test?
what if the output of the function is non existant such as x=0 at (1/x)?
Is f(x) =sqrt(x) a function? For 4 there is 2 possible outputs ±2
No four only has one output, 2. What you mean is X=y^2 is not a function because it become y= +-sqrt(x).
And just another question. Wouldn't it be necessary to show the first property for every function by, I don't know, maybe induction, or any other mean? Or is it enough to grasp it intuitively? Cheers
You don't need to prove it because it's a definition. If you let x=8, you don't need to prove that, because you're defining it to be 8.
👏👏👏👏
Any serious academic lecture that includes the phrase, "There can be only one.", should be closely examined for covert evil villianism. - Rule #1, "Good Guy Rulebook For Dummies", Superhero Press, 37,929 ACE.
He didnt go into one to one and etc sad😢
thanks