>>13675416Ok I will try to explain my way of intuitively understanding divisibility.
Say we have a stick of length , stick of type 1, and a couple of sticks of length , sticks of type 2.
Dividing the number by means getting some sticks of type 2 and fitting them so they form a long stick of length . Lets say you used sticks but now if you add one more you will obtain a stick with length bigger than so we stop considering getting more sticks. In that way if we join all sticks of type 2 they have a length of and of course the stick of type 1 is bigger by units ( might be 0).
In that way we write . It can be proven that for all sticks (meaning any length) there exist exactly 1 pair of numbers and such that we can replicate our situation.
Now consider a stick of length 0. and a stick of length . If we put another stick we overflow so we stop. Obviously we are left of with a stick of length 0 and we are not off by a any unit (0 remainder). In other words our definition of division with sticks works even for the case of . (btw stick of length zero can be interpreted as a non-existent stick)
I am sure you will deny that what I am saying makes any sense but I don't care I have nothing better to do.
