### Worthless math insight of the day

Apr. 3rd, 2012 06:01 pm**winterkoninkje**

The integers mod 3 are better thought of as `{-1, 0, 1}`

rather than the traditional `{0,1,2}`

. This makes it clear that the two non-zero elements are additive inverses of one another. And it also makes it clear that multiplication of non-zero elements just returns an "is same/different" judgment, which comes for free from our usual arithmetic: `(-1)*(-1) = 1 = 1*1`

and `(-1)*1 = -1 = 1*(-1)`

.