No, it doesn't mean that 0= 1. It simply means that the additive inverse of 0 is 0 and the additive inverse of 1 is 1. From the rules 0+ 0= 0, 1+ 0= 1, and 0+ 1= 1 you have that 0 is the additive identity: it added to any other member of the set is that member. 1 is NOT the additive identity because 1+ 1= 0, not 1.

1 is, of course, the multiplicative identity.