Function One to one / onto

Question

which one is correct?

Answer 1

i)False

Counter Example:->

functions f: N->N  (N is infinite set)

f(x) = x * 2
      Every distinct element of x has a different value of (x*2), thus
      the function is one-to-one.  On the other hand, some values in the
      range of the function (namely the odd numbers) are not under the image
      under f of any element in N.  Thus the function is not onto.

ii)True 

Take any example if it is one-to-one on finite set A to itself then it must be onto.

i.e. A={1,2,3} and f(x)=x

then it is one-to-one on finite set A to itself then it must be onto also.

http://math.stackexchange.com/questions/366146/a-one-to-one-function-from-a-finite-set-to-itself-is-onto-how-to-prove-by-indu

https://www.physicsforums.com/threads/how-to-prove-a-one-to-one-function-a-a-is-also-a-onto-function.135795/