Heap of Sand

You take your truck to the beach and bring home a heap of sand that you pile on your front lawn.

That night an ant walks by and takes one of the grains home with him.

Do you still have a heap of sand? I would say, "yes". It's only one grain out of billions. You dropped more than that on the way home from the beach.

The next night, the ant returns and takes another grain from your lawn. Do you still have a heap? Sure you do. What's one grain compared to the whole pile.

It is apparent that this can't keep going forever. There is a finite number of grains in the pile. However, at what point do you not have a heap? (And what would you have if, at that point, the ant took a grain from the pile?).

I would say you only have a heap if the ants decide they should just move where it is rather than move it.
Just trying to be funny, but I get your point. It's not decided by math, but by a common definition.

Quote: Ayecarumba

You take your truck to the beach and bring home a heap of sand that you pile on your front lawn.

Why do I do this? Do I value sand? Wish to obscure my lawn from view? How is it that I am so watchful of the sand that I notice an ant? Why do ant's remove grains of sand, they normally do not eat sand or value it so much that they carry it away. At what point do I get even with the ants? At what point do I return the sand to the beach?

Your question reminds me of this one:

If it takes 4 workers 2 hours to dig 2 holes, and
it takes 2 workers 2 hours to dig 1 hole,
how long does it take 2 workers to dig half a hole?