/sci/ - Science & Math

>>6235686
im not trying to fuck with anyone, i'm having a bit of trouble proving functions are surjective

>>6235689

>>6235690
look i get that you're mad smart and all of math and physics comes easily to you and your IQ is unmeasurable
so can you help me prove this or not

>>6235684
>onto
I refuse to participate in any mathematics with such revoltingly poorly-chosen terms.

Just work from the definition, it's not hard at all.

Fix some b in the codomain and from that construct an a in the domain that maps to it.

functions are onto if every value of the domain has an image in the codomain

>>6235712
>>6235715
so i get the basic idea
but the domain is N x N and the codomain is just N and that's what i'm having trouble with

>>6235694
You should at least have given us the function.

>>6235723
What's the function? You'll have f(x)=(y1,y2), where you picked an arbitrary (y1,y2) in the codomain.

>>6235727
well i just wanted a hint instead of the answer but i guess i'll say the function
f: (N U {0}) x N -> (N - {1})
f(x,y) = x + 2y

>>6235729
Well clearly all even numbers are obtainable through setting x = 0. Can you obtain the odd ones in a similar way?

>>6235723
Depends on the function. Sometimes u can just ignore one of the numbers in the ordered pair and treat it as a function from N to N.

The important thing is for all elements of the codomain you have to find ANY element in the domain that maps to it

>>6235737
so if x = 0, i can get all even numbers
if x = 1, i can get all odd numbers except 1, but 1 is not in the codomain. so it's instantly onto?

>>6235743
>so it's instantly onto?
You just shown that its onto.

>>6235745
awesome, thanks a ton

>>6235700
inorite, why do people even say onto when surjective makes so much sense, especially given injective and bijective.

>>6235748
sorry about it, that's just the way it's been presented during my class

>>6235750
they are being autistic, don't worry.

>>6235684
Just make sure that's it's not unto, which is pretty easy to prove.