17 hours ago, TheBritishVillain said:
-Only 1cm away from the edge. Ok, move it closer.
-Now only 1mm for the edge. Closer.
-100 Micrometres? Closer.
Then onto Nanometres and picometres etc. Let's say it's only 1 picometre from the edge. Without changing the unit of choice, we can still get smaller. 0.1 picometre, 0.01, 0.001, 0.0001... You get the idea.
What you've just discovered is called a "supertask".
A super task is essentially a countably infinite sequence of "tasks" that seems like it should work. The commonly cited case of your example is called "Zenos runner" In which Zeno of Elea argues that motion is actually impossible by showing that a runner who moves half the distance to the finish line every "step" will never reach the finish line.
Michael from VSauce does a way better job explaining super tasks than I will ever be able to:
Edit:: I feel like I should mention that all super tasks are trivially paradoxes, since the definition of a "super task" is "some infinite series of operations that can be completed in finite time". For that statement to work, you would have to be able to complete tasks in "instantaneous time" or, in an equivalent sense, "The function V(t) that describes the velocity of task completion would approach infinity".