The first part of this has nothing to do with my question. It was just something I was scribbling:
Let's say I have a population that's growing. If p is my population:
$\frac{p'(t+1)}{p'(t)} >1$
If I want to check the rate as the difference approaches 0, then
$\lim_{i\to0} \frac{p'(t+i)}{p'(t)} = 1$
Well this is explicitly saying that the first function is absolutely greater than 1. But, if you add even the most tiny of values to t, then the limit is definitely equal to 1.
There's no question here, but I just thought it was interesting to see the necessity of a change of a symbol, by adding an infinitesimal. I don't know if that makes sense, I just thought it was interesting.
I better add a question just to make this post legit. Is math love? or how about: Is the level of emigration in a country proportional to the size of the population?