II. There is a tensor (

) skew-symmetrical with respect to all pairs of indices, whose rank is equal to the number of dimensions,

, and whose components are equal to +1 or -1 according as

is an even or odd permutation of 1 2 3....

The proof follows with the aid of the theorem proved above

These few simple theorems form the apparatus from the theory of invariants for building the equations of pre-relativity physics and the theory of special relativity.