[Discrete Mathematics] Surjective Functions Examples

In these video we look at onto functions and do a counting problem.

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[brod]

@ 3:29 I think you should have gone with the approach of simply specifying that choosing 4 from 6 is actually just 6 * 5 * 4 * 3 which is choosing out of 6 then being left with five and choosing out of 5 e.t.c... That's where the choosing formula comes from anyway. adding the 4! make it seems like we are doing a extra procedure that we don't necessarily have to do.

[Zheliya]

wait wait wait, where did the 2! come from? from the last example
and thank you so much for these tutorials!!!!

[jimhorng]

The 2.ii how many are injective, can we just treat it as P(6, 4)? Since X has 4 unique slots that will be filled by 6 Ys non-repetitively ?

[nichellefayebalani]

Can anyone please explain where the 2 come from?

[saadafm]

weird thing is my textbook says that f(x) = x^3 is NOT

[yaluman.]

Can we answer onto fun using horizontal line test like one to one

[BeastyBlaka]

how would you prove f(x)=x ^ 3 is injective? I end up with x^3=y which is logically incorrect

[hamade]

How would you check the amount of surjective functions if IAI = IBI? Say A = {1, 2, 3, 4, 5, 6, 7, 8}? Thank you!

[parkermilligan]

How about this problem.

Prove or disprove: If f: A-->B and g: B-->C are functions, and g is surjective, then g o f is surjective.

[potato]

Wait, at the end why is it 6!/2! and not 6!/4! ?

[ZigaZagu]

Let I=[0, 1] and J=[0, 2]
Show that |I| = |J|

[johnyjoek]

I wish I had found your video series earlier. The professor I got rushes everything, skims over explanations and has a very strong foreign accent which causes a lot of the class to question what he said.

Like the Axiom of Choice he pronounces Axomchoi! His TAs only make it worse by also having a strong foreign accent and being quick to rush things.

So far, you've cleared up a lot of the questions I had from early on in the quarter. Only disliked because at 4:08 you rushed to explain this last bit:4!(6&4)

I am unfamiliar with that method you used. We never went over this.