I dont know if this is the right place to place this question. The other day i started thinking a lot about this, and it just won't get out of my mind. Why does zero has the properties of any other number? Maybe the question should be, "why shouldn't it?"
1+1+1 = 3x1
n x n = n^2
n( n+1)= n^2 + n
why can N be replaced by 0 and all properties still hold?
why does 3*0 = 0, and 0*0*0=0^3 and still its the same as 0?
why does zero has properties like N x 0 =0 for any N
i can't even explain my question in good terms, its just a brainwashing of non-intuition on my mind, which i cannot get rid of, and its destroying my intuitions. Can someone help me believing again that 0 is a number like any other??
Thanks in advance