Surjective (onto) and Injective (one-to-one) functions

[meltz4ya]

omg .. you jus answered all my ''jectives'' question.. thanks alot...

[oijabez]

thanks man! now i really understand!! this is like a light in the middle of darkness!



[kev121314]

hi, you are brilliant, will you make a video on how to prove 1 to 1 and onto? :)

[zh1412]

Thanks man:)

[Melgazar9]

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).

[lizjakubowski]

@Melgazar9 "one to one" means something different than a "one-to-one correspondence", i.e. bijection

[PineNutButter]

Smart. Thank u so much.

[ejneboon]

Thank you for the tutorial. I understand this functions now even though english is not my first language. I couldn't understand this from the books that were written in my main language.

[UchiihaSasuke]

you are.

what they call, a genius.

[zawmer]

great video.. helped me a lot :)

[lihuo]

prove that there exists a one-to-one and onto function from 2^n to R..wish you can prove this one for me or any one of u ...thank you

[ScreamTheLoraxDid]

My teacher doesn't explain anything! Thank you thank you thank you i was literally willing to give up until i watched this video!

[XzNightWalkeRzX]

I wish you were my lecturer for maths! This really helped, thanks a lot :)

[bdragonst]

Thank you very much! In my class, professor make it look like those are very hard things, I did not understand his lecture on this section lol.. This video was very easy to understand :)

[paine536]

Thank u soo much :) I understood that a lot more than how they explained it in my class :P

[99madboy]

thank uuuuuu i love uuuuuu ...actually u helped me alot ..^_^ cheers

[15april94]

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

[Kingweb08]

You do not sound at all what you look like btw, which is not a bad thing, but good videos I basically teach myself now

[exemsexis]

Great tutorial, finally I got it !

[kannugmail]

so in the last part its onto and one to one! so its bijective right??

[brianyu0717]

@kannugmail Yes

[brianyu0717]

@kannugmail Yes it is bijective

[musichl]

im watching this, and i get what an onto function IS, but i dont understand how youd see if a function is onto on a graph. any help? like with a 1-1 function it has to pass the vertical and horizontal line test, what do you do with an onto function?

[wingz23oladapo]

Have you got any videos proving injectivity, subjectivity or bijectivity

[gtabro1337]

you have my thanks as well, this video definitely helped me

[peppercorns207]

Anybody else think it looks like a penis at 3:20 ?

[Polopalapop]

Say 1 is mapped to A, 2 to B, 3 to C and finally 4 to D. If 5 is an element of X and is not mapped to anything at all, is the function still injective? Do X elements always have to be mapped to something?

[mihurcina]

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.

[thanatos454]

You could have taken the opportunity to point out Bijection here but no big deal really. Great stuff!

[bboyjernej]

Thank you for this lesson :)..

it`s very clear and helpful 

[rockis18]

way better than my professor at imperial college

[jenish4]

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!!!

[bingarad]

Thank you so much.... I wish that you are

instead of my prof.....

THANK YOU SO MUCH

[Inspector93]

Very nice vid, thank you.

[IamBored529]

Great vid

Great handwriting

[jazzguitar2010]

Can you please tell me what software you're using for your digital pen? Are you writing on a tablet?

[SammerX]

I think that Sal uses a wacom intuous tablet. For this sort of thing the bamboo works just as well... You could really use most any paint software, I have done my homework like this using Sketchbook pro

[Hashbrowniepie]

thank you so much. My professor explained it in a completely confusing way.

[ganondufus]

Bijection!

[benfaysal23]

Dude your videos are like the best that i'm subscribed to, Thank you very much for everything you're doing for us.

[thepoet82]

Very nice, but I can't watch this in high definition.

Not being able to really makes the handwriting hard to read!

[khanacademy]

rewatch it in a few minutes. should be available in hi-def then

[thepoet82]

Ah, there it is! :-)