In my notes I have a definition for $o(\Delta)$ which states that if a function $f$ is $o(\Delta)$ then as $\Delta$ approaches zero, $f(\Delta)/\Delta = 0$.
Then the notation gets used in equations such as this:
$P({N(t+\Delta) - N(t) = 1}) = \lambda*\Delta + o(\Delta),$
where $P$ stands for probability and $N(t)$ is a number of events that has occurred up to time $t$ (Poisson process of parameter $\lambda$)
Can someone please explain what the significance of this function is, and how it is getting used in that equation as a variable, when the definition states that it simply describes a function?