# Thread: injection, surjection and bijection questions

1. ## injection, surjection and bijection questions

f, g : N -> N (Natural Numbers including zero)

f is injective but not surjective
g is surjective but not injective

1) Is it possible for (f composit g) to be a bijection?
2) Is it possible for (g composit f) to be a bijection?
3) Would the answers 1) and 2) be different if the natural numbers did not include zero?

2. Originally Posted by pseudonym
f, g : N -> N (Natural Numbers including zero)
f is injective but not surjective
g is surjective but not injective
1) Is it possible for (f composit g) to be a bijection?
2) Is it possible for (g composit f) to be a bijection?
3) Would the answers 1) and 2) be different if the natural numbers did not include zero?