This is actually wrong. You can have an equivalence relation where 0 is equivalent to 1. Furthermore, in the Trivial Ring (that is, the ring algebra of a single element) the multiplicative identity (written as 1) and the and the additive identity (written as 0) are the same element, and thus in the context of the trivial ring 0=1. Isn’t that fascinating?
This is actually wrong. You can have an equivalence relation where 0 is equivalent to 1. Furthermore, in the Trivial Ring (that is, the ring algebra of a single element) the multiplicative identity (written as 1) and the and the additive identity (written as 0) are the same element, and thus in the context of the trivial ring 0=1. Isn’t that fascinating?