# Thread: does f(x) = x^2 map Z onto Z?

1. ## does f(x) = x^2 map Z onto Z?

I do this:
f(x) = x^2
y = x^2
x = y^2
root(x) = y Since for some y in Z there is not an x in Z, this function does not map Z onto Z.

Am I thinking about this right? I am guessing no because isn't there some theorem that states that the set of natural numbers and the set of its squares are bijective? Doesn't this say that maps N to N? No real difference between N and Z. I need some clarification here. Thanks.

2. Is there any $t \in \mathbb{Z}$ such that $t^2=-5~?$

3. I clarified the range to be the set of squares. Thanks for the assistance Plato.

4. Originally Posted by pberardi
I clarified the range to be the set of squares.