Hello, there's something i've been wondering about through these days. Why does zero share the same properties as any other number? Like
n( n+1) = n^2 + n
n( x+y) = nx + ny
why are those properties valid even for zero? I now this might seem stupid, but it has been messing with my mind. I know that if i do all the calculations it will say so, i just can't find a theoretical explanation for it. Can someone help me plz?