3. Give an example of a function
(a) f : Z → N that is both 1-1 and onto.
(b) f : N → Z that is both 1-1 and onto

Isn't impossible to do both? I mean if you draw a venn diagram, one can see that one set is bigger than the other ( therefore not allowing it to be "onto") and at the same time the inverse wouldn't allow a one - to - one relationship. Any help on what I'm doing wrong?

Question

3. Give an example of a function
(a) f : Z → N that is both 1-1 and onto.
(b) f : N → Z that is both 1-1 and onto

Isn't impossible to do both? I mean if you draw a venn diagram, one can see that one set is bigger than the other ( therefore not allowing it to be "onto")  and at the same time the inverse wouldn't allow a one - to - one relationship. Any help on what I'm doing wrong?