Capacitors charge/discharge continuously/smoothly on an 'ascentotic curve'...
which never actually peaks!! I don't care how long it has been charging, or what
'curve' you draw, it is ALWAYS still charging, but by lesser & lesser & lesser amounts.
There are no 'STEPS'. Just a continuous analog reductive progression. But there's a problem.
Consider a ball thrown perfectly vertical, which eventually comes down again. OK...
Did it ever STOP at the top?? NO!! It passed ZERO 'speed' for ZERO time!!So it never stopped.
I know where I'm going here mathematically... but do you ??
That's only on paper. In the real world, at some moment the last electron will take its seat on the capacitor plates (or will leave the capacitor if we are discharging) and that's it. The process stops, because we can not have a charge smaller than an electron.
As a thumb rule for the real world:
- infinite and zero does not exist,
- forever and nothingness does not exist,
- everything comes in "lumps",
- at some point those "lumps" can not be divided into even smaller lumps,
- there are small and apparently random fluctuations in everything, a background noise that is all over the place, and it seems to be coming out of nowhere, and it can not be dialed down to zero, to me that's the most intriguing feature of this Universe: the noise and it's randomness. (not talking here about the microwave background radiation, but about any kind of random fluctuations, either at a quantum or at a macroscopic level)
With enough randomness, I think a whole Universe can be built: the equivalence between mass and energy is already known, there is also an equivalence between energy and information, therefore it should be possible to generate matter out of information. We might still need two essential ingredients, space and time. If you ask me, matter emanates space (similar with a light source that emanates light), and that will also fix the need for black matter and black energy problem, but that's way out of mainstream physics. The only ingredient left to get is time, and if we buy the idea of spacetime as a continuous, than we can get the time for free, time will be generated by mass, too, together with space.
In conclusion, from randomness alone, we can get some unintended structure here and there, or else said information, and from information we can get energy, then matter, then space and time, and if we wait long enough, we get dinosaurs, and monkeys, and us.
Now, where from is all this randomness coming, I don't know...