For anyone watching; a term that can be used to describe a function that is both injective(one to one) and surjective(onto) is referred to as BIJECTIVE
dumb f**king textbooks twists the words and sentences so hard that sometimes it is so hard to learn the material (especially theorems and definitions). Thank you Sal for making these videos.
You sir are responsible for my A+, I got yesterday! It was the only concept that wasn't clear even though my Teacher asked me about _"Do I make myself clear,"_ but I'm a shy kind so I affirmed and never got the actual concept!
Amazing. I was sick during the explanation of this at my school and altough english is not my main tongue, this thing made it clear to me. Thanks A LOT.
you're just an excellent techar, why can we have a teacher like you? I was in the lecture room for 2 hrs trying to understand, but I learnt it here in 10 mins, amazing!!!
Thank you so much!!!!!!!!!!!!!!!!! I never actually understood the concept to this day. I read all the definitions at least hundred of times and still didn't get it. Watched your video for 10 minutes and finally undersood something that I didn't get in years and years of math! Really,THANK YOU SO MUCH!!
Wow, this explanation was so clear, much better than my prof. just talking to himself on the board. You are indeed a true saint, making knowledge accessible to everybody.
Since it wasn't mentioned: the very last arrangement described, the one whereby the mapping is classified as _both_ surjective and injective, is called *_bijective_* .
I have a simpler way of putting it: -T: V->W is a linear tranformation: If T(v1)=T(v2) implies v1=v2, for any v1, v2 in V. Then T is said to be a 1 to 1 linear transformation -T:V->W is a linear transformation: If Range(T)=W Then T is onto W. For real tho, thanks for the explanation
In my book that I'm studying it says that an injective function is a function where for ever y belongs to Y, there's *EXACTLY* 1 x such that f(x) = y, meaning that you can't leave any member of y to be not mapped to, there must be exactly 1 x that is mapped to every member of y.
+Raidom I think that is the combination of surjective and injective which is bijective (not sure if this is the correct term in English for it) but it's basically what your textbook describes as injective.
Expected to know this from college algebra for calc I , was way better than my calc professors explination ( did it in five min and didn't help at all)
You forgot to add that if a function is both onto and one-to-one it's called a bijection aka one-to-one correspondence. But other than that this video is awesome tnx
Hey, I hope you're fine. I want to ask you, When they ask us to prove if the function is surjective or injection, how are we going to prove it? Well in the surjective I can say that the range equals the codomain, but what about the injective?????
A general function requires that each x in the domain can map to at most 1 element in the codomain. That is, the vertical line test. However an INJECTIVE function requires that for some x in the domain and some y in the codomain, if f(x) = f(y) then x must equal y. That is, every y value in the codomain can only be mapped onto by at most one x in the domain (horizontal line test). I’m 7 months late but hope that made sense.
I would Yes because 0 is not in the domain of f. Function is not defined at 0 in your example. Because 0 is not in the domain of such f, every element that IS in the domain gets mapped to the range at most once, and therefore the function is injective.
For anyone watching; a term that can be used to describe a function that is both injective(one to one) and surjective(onto) is referred to as BIJECTIVE
You don't say
THANK YOU!
THANKS
I think you meant BISEXUAL
It is also referred to as faithful mapping 😜
this 10 min video > 2 hour lecture
thank you Sal
i know right...
The irony.
Oh
It's been ten years did you finish school?
My teacher made this way harder than it actually is. Thank you!
dumb f**king textbooks twists the words and sentences so hard that sometimes it is so hard to learn the material (especially theorems and definitions). Thank you Sal for making these videos.
Welcome to the world of gate keeping!
rewatch it in a few minutes. should be available in hi-def then
Hi Sal
@@kewrie1630 lmao
You sir are responsible for my A+, I got yesterday!
It was the only concept that wasn't clear even though my Teacher asked me about _"Do I make myself clear,"_ but I'm a shy kind so I affirmed and never got the actual concept!
A minute of silence for that guy who never gets mapped to
syad lyfe
His name is Ryan Sale
That guy is an element of (Codomain)-(Range)
@@saurabhk3464 sepling wrong🤣🤣
@@aryansingh01 "sepling"
Sal is one of the greatest humans who have ever lived and breathed.
Agreed
Including grant
@@anshkharbanda2598 i love grant
bread
Salman*
This lesson is very well explained. Bravo. I couldn't understand the subject reading the textbook but now I can.
This was uploaded when i wasn't even born now its here saving me in my exams.Sal saving generations
Amazing. I was sick during the explanation of this at my school and altough english is not my main tongue, this thing made it clear to me. Thanks A LOT.
Where are you in life right now after 13 years?
How's life after 14 years?
Stop scrolling down go back to studying
im looking for help down here...
I feel attacked.
*sigh* you know me so well
hahaha
Sorry mom
you're just an excellent techar, why can we have a teacher like you? I was in the lecture room for 2 hrs trying to understand, but I learnt it here in 10 mins, amazing!!!
Hey
What are you doing now
Thank you so much!!!!!!!!!!!!!!!!! I never actually understood the concept to this day. I read all the definitions at least hundred of times and still didn't get it. Watched your video for 10 minutes and finally undersood something that I didn't get in years and years of math! Really,THANK YOU SO MUCH!!
Wow, this explanation was so clear, much better than my prof. just talking to himself on the board. You are indeed a true saint, making knowledge accessible to everybody.
Your videos are the best! I wish you could be my personal tutor, I would understand everything so much better!
Same here
hey .. now what r u doing ?
you still have your password?
from morocco i want to thak you for this clear explanation :))
THANK YOU .. JUST SAVED MY LIFE
I swear, if it weren't for Khan, I would not have passed Calculus and now I owe him my Discrete grade too.
Thank you so much you explained this perfectly, unlike my teacher at school who intended us to immediately understand the whole lesson in one class
You are the god of teaching math
You might be the reason I pass Discrete math, I thank you time and time again for all your videos to reference.
Since it wasn't mentioned: the very last arrangement described, the one whereby the mapping is classified as _both_ surjective and injective, is called *_bijective_* .
I have a simpler way of putting it:
-T: V->W is a linear tranformation: If T(v1)=T(v2) implies v1=v2, for any v1, v2 in V. Then T is said to be a 1 to 1 linear transformation
-T:V->W is a linear transformation: If Range(T)=W Then T is onto W.
For real tho, thanks for the explanation
Thanks Salman Khan, you taught me this very good. May Allah reward you here and in the hereafter.
Understood everything! But if you would graph it I would understand it even more! Thank you very much for help sir!
He is saving lives bro...thanks a lot
this was uploaded when i was 4 yrs old, but it is helping me now in 12th
i'm taking online discrete math course rn due to covid, prof posted lecture, but couldn't understand any. Thank you for posting videos abt this.
this is still helping after 12 years wowwy
It's unbelievable that we have this for free
In my book that I'm studying it says that an injective function is a function where for ever y belongs to Y, there's *EXACTLY* 1 x such that f(x) = y, meaning that you can't leave any member of y to be not mapped to, there must be exactly 1 x that is mapped to every member of y.
In my textbook, an injective function is a function where every y belongs to Y at MOST one. Hence, Khan Academy is right.
Yeah, he is right, my teacher said that the book wasn't accurate.
+Raidom I think that is the combination of surjective and injective which is bijective (not sure if this is the correct term in English for it) but it's basically what your textbook describes as injective.
Thank you for this lesson :)..
it`s very clear and helpful
Me watching it like 13 years after its upload woah 😂
Me 15years😂
Expected to know this from college algebra for calc I , was way better than my calc professors explination ( did it in five min and didn't help at all)
Thanks will have our long exam in set theory tomorrow.
Dang, you wrapped it pretty nicely. You even answer things I didnt know were my blind spots. I
Im from iraq and you learn me very smart thank you man you are clever 🌹❤️🌹
Man, I wish my math profs would be as descriptive as you are.
quick info: a function which is both injective and surjective is called a bijective function
You forgot to add that if a function is both onto and one-to-one it's called a bijection aka one-to-one correspondence.
But other than that this video is awesome tnx
Hey, I hope you're fine.
I want to ask you,
When they ask us to prove if the function is surjective or injection, how are we going to prove it?
Well in the surjective I can say that the range equals the codomain, but what about the injective?????
this guy is a hero!
you are.
what they call, a genius.
Atlast somebody made me understood it . It was confusing before , now it's all clear . Thanx
Thank u sir! Well explained ❤️
thanks had a test coming needed a refresh
midterms tomorrow thanks for this ^^
Watching Khan's videos are like eating raspberry pie or like listening poetry.
Gosh thx Khan academy! Amazing and easy way of explaining just what I needed to get back on track
will u plz tell me how can two differnt values of x give same answer in a function? i mean how can 4 and 5 both map to D
The only YT channel where 10 minutes = 2 hours
In terms of studying
Woah it's 11 years now!!
Explained very clearly
Dude your videos are like the best that i'm subscribed to, Thank you very much for everything you're doing for us.
Thank you 👏
Life saver! Thank you so much!
lmao, it took my prof to explain it in a matter of months, you did it in 9 minutes. With 10 times more clarity!
Josh Barber is that true
@khanacademy thanks for that, it looks fantastic now
My God it's very helpful ..... I couldn't get it in two days lectures 👍🏼 ... Thank you
+kareshma wali tru
thank you so much. My professor explained it in a completely confusing way.
How is life after 12 years?!
hi, you are brilliant, will you make a video on how to prove 1 to 1 and onto? :)
KHAN YOU ARE THE GOAT!
👁️👄👁️
teach at my school, it;s time for my pre cal teacher to retire
I already have one who should be retired
Khan with the SLAM DUNK once again
Got it ! Thanks.
way better than my professor at imperial college
It was very helpful
Thank you!
on point and short. Loved it!
Thank youuuuuu my I undrestand now
will u plz tell me how can two differnt values of x give same answer in a function? i mean how can 4 and 5 both map to D
@@belogical2396 imagine the graph is horisontal at y= 2 ... now x=5 and x=4 will give u both 2 EZ
you have my thanks as well, this video definitely helped me
Amazing explanation thank you.
What type of software are you using?
but i must say you gave us a clear picture of the subject chosen. I will definately download it
did you know the name of the software? if you did please tell me
you are great only 9 min I'm understand
thanks a lot for this!!
Best concise videos!!!
So basically, onto function has all its codomain "busy" in simple words. Every element of codomain has an element corresponding to it in domain.
and it's the basic condition required for the inverse of a function
You spend 3:40 just to say surjective means that every possible output of an algebraic expression must have at least one input.
I was today years ild when i found out that khan academy was not INDIAN teaching source. I really thought it to be an INDIAN source
yes because each y can be mapped by at least one x from X
khan, im feeling guilty that im wathcing such a good vid(which will help me at my math's test) and that it is for free:P
Smart. Thank u so much.
I'm from Ethiopia it's wow you are clever
It takes some thinking, but I do understand. For now. Thank you so much! :)
Thank you sir ,, you saved my life :)
Can you please tell me what software you're using for your digital pen? Are you writing on a tablet?
@Melgazar9 "one to one" means something different than a "one-to-one correspondence", i.e. bijection
Great person.
I thought Injective (ie not Surjective) meant that Y can't have many X. From what I know, what you are describing at 3:55 is a general function.
A general function requires that each x in the domain can map to at most 1 element in the codomain. That is, the vertical line test. However an INJECTIVE function requires that for some x in the domain and some y in the codomain, if f(x) = f(y) then x must equal y. That is, every y value in the codomain can only be mapped onto by at most one x in the domain (horizontal line test). I’m 7 months late but hope that made sense.
Great video and teacher
Bruhhhh ur so good
Thank You very much !
This is so good.
why does sal have such a beautiful voice
Great teacher
I would Yes because 0 is not in the domain of f. Function is not defined at 0 in your example. Because 0 is not in the domain of such f, every element that IS in the domain gets mapped to the range at most once, and therefore the function is injective.
Thank you so much!
tksmmmm, i appreciate that
Are u sure that if f is injective, then it is one to one? I think it is only one to one (bijective) if both cases satisfy (injective and surjective).
complete ncert exercise solution videos gave please
Thanks bro!