Will the apple never end when your cutting it?

Yes it will because eventually it'll get down to the atomic level and when you split the final atom of the apple there is no more apple BUT before that you'll have to consider the question of when it ceases to be an "apple" that you are cutting up and that is a philosophical one. Personally I'd consider it not to be an apple any more once you get beyond the gross physical appearance of being one rather than when it gets too tiny to be visible to the human eye i.e. too small to cut by hand.