Queston is :
Give an example Of afunction From N to N that
1. One to one but not onto.
2.onto but not one to one .
3.Both onto and one to one (but not the identity func.)
4.Nither one to one nor onto .
Hey I know this one:
one to one is an injective function, onto is a surjective function.
So let's see the first problem:
$\displaystyle f: N \rightarrow N$, so we need a function that does not repeat itself, $\displaystyle f(a) = f(a')$ so $\displaystyle a = a'$. $\displaystyle f(x) = 1 / (x - 1) $ would be sufficient.
As that function does not repeat itself and it has no value for $\displaystyle x = 1$.