Why minus into minus is plus.

someone asked me why minus into minus is plus. Here is my answer:

1 is mathematically not correct. It should either be -1 or +1. When we write 1 it actually means +1.

1-1 means actually (+1) + (-1)

(-1)*(1-1)
= (-1)*[(+1)+(-1)]
= (-1)*(+1)+(-1)(-1)
= (-1)+(+1)
= -1+1 = 0

This means if (-1)*(-1) is not +1, then we can not prove the above. This is logic.

Now let me explain you the philosophy.

+(-1)

Suppose:
+ = same direction as sign
- = opposite direction sign

+(-1) = same direction to - so answer is -1

-(-1) = oppsite direction to - so the answer is +1