Consider the following. Before you stands a heap of sand. You have just returned home from the beach, and while there, you grabbed a bunch of sand, placed it in a jar, took it home, and dumped it onto the floor. These individual grains of sand are collectively a heap . We can both agree to this as “heap” is a rather vague description for a mound or pile of a particular substance. Now, there are probably hundreds upon hundreds of grains of sand in this heap. Let’s suppose there are exactly 10,000 grains. If we take exactly one grain of sand out of the heap, we would then have 9,999 grains of sand, and we would both still agree that 9,999 grains of sand is a heap. Likewise, if we remove another grain of sand, we are left with 9,998 grains, and it would still be a heap. Removing one grain of sand is so trivial a difference that it does not change whether the remaining grains are a heap. You might already see a potential problem with this argument. If we accept the premise that removing o...
