Question

In a finite group z/3z,
why -1̅ = 2̅ ?

Answer 1

Z/3Z is the group addition modulo 3

Answer 2

which is the set of equivalence classes {0* , 1* , 2*} (i cant draw bars over numbers)

Answer 3

so you can think of this as a clock

Answer 4

Does it work like standard algebra?
I know that 2̅+1̅=0, so i subtract -1̅ from both sides and end up with 2̅=-1̅?

Answer 5

What about \[1^{-1}\]

Answer 6

lets define movements as clockwise. so 1* + 1* = 2*

Answer 7

1^-1 + ? = 0 on this clock

Answer 8

1?

Answer 9

define -1 as going counterclockwise 120 degrees. 1+ as a clockwise rotation 120 degrees

Answer 10

so start from zero

Answer 11

-1 is counterclockwise 120 degrees, where do you end up?