Hey Safwan,

I studied some interesting topics recently and while exploring set theory and the history of it, I realized the answer is to be found here.

When Cantor postulated set theory, the problem with it was pointed out by Bertrand Russel that there is a problem with sets referencing themselves (using the barber analogy). And so the revised set theory (by sir Mellow et all) excluded sets that reference themselves. (Like the set containing all sets and the collection of sets not containing themselves). Nice.

But the empty set.... is a self reference too for it can only reference itself for there is nothing in it, so nothing else to reference. When we speak about this set we speak about the set itself for it holds nothing. So here is the paradox: It is a set containing nothing are therefor it must contain itself because it is nothing... but then it contains something....which is ...nothing...etc.

So the empty set is not a set to begin with, according the revised set theory for no set that references itself is a valid set.

And so zero is ultimately a self reference because it cannot reference anything else, no value, no quantity because zero is... well zero.

To state there are 0 cows in a field is as silly as pointless, just as silly as stating there are 0 Ferrari 's there. It explains why dividing by zero is nonsense. Zero is a concept and not a number and is self referencing by nature. A (true) number is always a reference to something, some value, some quantity. Zero is not.

The use of 0 in a decimal system relies on convention, in the same way bits in boolean Algebra have a specific value based on their position and is therefor very different from the meaning of 'zero'.