I'm reading Sheldon Ross and he gives two proofs of the same result: that given some assumptions, $N(t)$ has a Poisson distribution with mean $\lambda t$. The first proof is in chapter 4 and introduces the pmf of the Poisson and the second proof comes many pages later in chapter 9 and talks about the Poisson Process.
My specific question
In the screenshot below, the blue box says $P(N(h) = 0) = 1 - \lambda h - o(h)$ whereas the red box says $P(N(h) = 0) = 1 - \lambda h + o(h)$. Can you help explain why are they different?
In both proofs, the $o(h)$ part eventually goes to zero so the sign doesn't seem that important. But I am trying to build okay understanding.
I am just learning about little o notation, but I don't think $o(h) = - o(h)$ because all probabilities have to be between $0$ and $1$ and $P(N(h) \ge 2) = o(h)$. From reading related posts I know $o(h)$'s can be different functions and all be called $o(h)$ (which is confusing for a noob like me) but I don't think the signs can be flipped as arbitrarily.