On accuracy and perfection

Mathematics is all about absolutes and perfection; the real world is not. Mathematicians, physicists, engineers, and others recognize that their equations are estimates--not exact models--of the way the world works. The equations can be absolutely accurate, but never perfect.

Some riddles:

Q: What's the difference between "theory" and "practice"?

A: In theory, there is no difference.

Q: (Zeno's Paradox): A boy and a girl meet and instantly fall in love. As they approach each other, they must travel half the distance that separates them. Then they must travel half the remaining distance, and so on, halving the remaining distance, which gets smaller and smaller but can never reach zero. How close can they get?

A: Close enough for all practical purposes.

A single grain of sand does not constitute a "pile" of sand. Nor do two grains, nor three. But a handful of sand poured onto a table is clearly a pile. So logically, mathematically, there must be some number N such that N grains of sand are not a pile, but N+1 grains are. What is N?