so the paradox goes like this. if n grains of sand is a heap, then n-1 grains of sand is a heap. with the justification being that you can't destroy a heap by removing a single grain of sand. is it just me or does this sound like bullcrap, as this would imply 0 grains is a heap and in turn -1 grains of sand is a heap doesn't this seem like we either have to accept that a heap is defined by that statement, or take it as a theorem of a heap hich can easily be shown to be false. I spent part of a Q&A session with a lecturer trying to convince him that there is no paradox here, and he did not budge. Any thoughts?