In his situation, I'd probably read 'any' in the second sense simply because as a non-mathematician I can imagine the second sense being a practical test: (I give you a number, you show me that the difference between A and B is smaller, we reach a conclusion) whereas the first seems esoteric (you test every conceivable small number...)

On the other hand, the first reading is so blatantly wrong, the commenter really should have stepped back and thought 'could this sentence be saying something that wasn't obviously incorrect?' Principle of charity and all that.