Laplace Transform of e^{-at}

Question

I have some trouble understanding the Laplace Transform of $x(t) = e^{-at}u(t)$, where $u(t)$ is the Heaviside step function. When calculating the integral, we get to a point where $$ X(s) = \int_{0}^{\infty} e^{-(a+s)t} \,dt = \lim_{T \to \infty} \frac{-1}{a + s} \left[e^{-(a + s)T} - 1\right]$$ Here we say that the Laplace Transfrom exists for $$-(a+s) < 0 \Rightarrow s > -a$$ a is a constant which can either a real or a complex number. s is a complex number for sure. How can we compare these 2? If a is real, how can we say that $$ complex > real$$ Because technically that is what we are implying when we say s > -a. Same goes for complex numbers. How can we say $$complex1 > complex2$$ Am I missing something?