The Levi-Civita symbol is, in programming lingo, a function that takes three arguments: epsilon(i,j,k) where i, j and k are integers that label the coordinate axes. Let 0 stand for the x axis, 1 for the y and 2 for the z. Then epsilon(0,1,2) equals 1. If we swap the values of any two arguments, we flip the sign: e.g., epsilon(1,0,2) evaluates to -1. Now, swap again: epsilon(1,2,0) must change sign again, so it evaluates to 1. But the sequence 1,2,0 is just the original sequence 0,1,2 read cyclically from a different starting point. In this way, we can work out what the value of the epsilon function is for any input. When the inputs are all different, the output is either 1 or -1, depending on whether the input sequence is “in order” or “in reverse order”. Write the numbers 0, 1 and 2 around a circle. Read clockwise, and you get one output; read counterclockwise, and you get the other. If two inputs are the same, then epsilon must evaluate to zero, because, for example, epsilon(0,0,1) with the first two inputs swapped is epsilon(0,0,1) again, meaning that the output must be minus itself.