It's even worse than that. Because integers a and b are congruent modulo n iff n | a - b, and 1 divides every integer, the integers modulo 1 has only 1 element

It's even worse than that. Because integers a and b are congruent modulo n iff n | a - b, and 1 divides every integer, the integers modulo 1 has only 1 element. This gives you the somewhat pathological object called the zero ring: https://en.wikipedia.org/wiki/Zero_ring https://en.wikipedia.org/wiki/Zero_ring