/sci/ - Science & Math

Here is one that bugs me:

Let's say there is an object and some force f1 pulling it to a surface with FRICTION (like a massive rock and gravity).

Let's now say a force f2 acts on that object perpendicular to f1 (like a human pushing that rock). That force f2 does not manage to move the object visibly for a human eye.

Question:

1. Does it mean only because it doesn't move visibly, that it doesn't move at all? (I know this sounds silly)
2. If force f2 doesn't move the object, would it move the object given an infinite amount of time?

Or in other words: Is there a certain threshold which you need to pass to get things REALLY moving, OR, is this transition smooth and you get as much movement as much force you put it, regardless of the temporal distribution of the force.

>my sides when an upper year engineering undergrad can't demonstrate that the sum of two continuous functions is continuous
>my sides when a physics major treats dy/dx as a fraction without understanding the difference between real numbers and the extended real numbers
>my sides when they think they know anything about math