I didn't know where else to ask this, so here goes... (caveat: I've been away from math for awhile)
I'm trying to "say" symbolically that continued positive infinitesimal changes eventually (not at infinity, just over some finite but unspecified period of time) create an observable positive change...
Help?
I was thinking something using Leibniz's dx notation of derivative to represent the small changes, and the upper case delta to show the observable change...
$$ \Delta X = \int_\text{initial value of $t$}^\text{final value of $t$} X'(t)\,dt = \int_\text{initial}^\text{final} \frac{dX}{dt}\,dt = \int_\text{initial}^\text{final} dX. $$ Maybe the simplest way is this: $$ \Delta X = \int_\text{initial}^\text{final} \, dX. $$ The sum of the inifinitely many infinitely small changes in $X$ is the total change in $X$.