with multiplication +, zero element +∞, and unit element 0.[3]

If a ring is finite and every nonzero element is cancellative, then by an application of the pigeonhole principle, every nonzero element of the ring is invertible, and division by any nonzero element is possible.

The function matrix (FM) is changed such that each one of the columns has at least two non-zero elements (-1, 1) and at least one zero element (0).

Summation of an empty sequence (a sequence with zero element) results, by convention, in 0.

? denotes repetition of the previous item zero or one time.

? denotes repetition of the previous item zero or one time.

Repeats the preceding character zero or one times.

So, the first element 5, has index zero and represents the 6th (element zero is the first) snapshot contained in the iSnapTab, the second element 7 represents the 8th element of iSnapTab and so on.