Since a finite number of particles is only susceptible of finite transpositions, it must happen (he says), in an eternal duration that every possible order or position will be tried an infinite number of times, and hence this world is to be regarded (as the Stoics maintained) as an exact reproduction of previous worlds.
Let k such transpositions be necessary; then the expression X(kal aa2 N a 3.
A and 13 are transposed, and it is clear that the number of transpositions necessary to convert the permutation say...v of the second suffixes to the natural order is changed by unity.
Now a11A11= alla22a33...ann, wherein all is not to be changed, but the second suffixes in the product a 22 a 33 ...a nn assume all permutations, the number of transpositions necessary determining the sign to be affixed to the member.
These transpositions are purely arithmetical.
How would you define transpositions? Add your definition here.