And if educators profess division by zero as an appropriate mathematical practice, we should not be surprised to see this error persist among students just as some authors themselves learned this abysmal practice from their own teachers. These occurrences are a painful, vivid demonstration of a widespread misconception. The notion of zero we have was introduced in the Middle Ages by Arabian scholars as a superior mathematical construction compared with the then prevalent Roman numerals, which do not contain the notion of zero. The scribe asked what to write and was instructed to draw an empty hole, thus introducing the present notation for zero. It may be considered frivolous hyperbole to suggest that the demise of the Roman Empire was due to the absence of zero in their number system, but one can only ponder the fate of our civilization given the difficulty our culture seems to have with the presence of zero in our number system.
Natural numbers are real numbers.
The negative sign is an extension of the number system used to indicate directionality. Sacrilegious as it may sound on first impression, the notation of zero is at heart nothing more than a directional separator. This is not a simple calculation exercise. Rather it reaches to the nature of the underlying physical reality. This writer advised that following his argument one could also demonstrate that one is equal to minus one.