I am solving some infimum/supremum problems, and my book has different answers for some of the problems.

Let $A = \{ x \in \Bbb N | x^2 < 5\}$ find sup A and inf A, their answer is sup A = $\sqrt5$, inf A = $-\sqrt5$.

I think this is wrong, since A is a finite set, its clear sup A = 2 and inf A = 0, am i missing something?

Another one, $A = \{x^2+x |x \in (-1, 1)\}$ they say sup A = 1 and inf A = 0, i think sup A = 2 and inf A = 0, again am i wrong?