TITLE: In mod3, is 3 greater than, or less than 1?
QUESTION [14 upvotes]: In modular arithmetic (say mod3), is the largest number (3) greater than or less than the smallest number?
Because, intuitively, it would be greater, but 3+1=1 in mod3 which would suggest that it is smaller.

REPLY [2 votes]: My interpretation of modular arithmetic was that you reduce everything to the group {0, 1, 2}, which would mean that 3 would be equivalent to 0. Therefore the question "is 3 greater than 1 (mod3)" doesn't make sense, since 3 isn't on your number line; the question would simply be "is 0 greater than 1", to which the answer is no.
EDIT: Sorry I didn't see; this is basically what iadvd said, but less thorough.