An array is built starting with an empty array, and then a sequence of insertions: insert $a_1$ at index $z_1=1$ insert $a_2$ at index $z_2$ insert $a_3$ at index $z_3$ ... and so on. When we insert element $a_i$ and index $z_i$ the result is that $a_i$ is now at index $z_i$, whereas everyth...

I understand the terms automata or automaton to mean "self operating machine". I can't think of any such "machine" besides maybe (if it is even a machine and even exits) cyclic universe of a big-bang--big-crunch phenomena; either in sequence ("finite automata"), or in eternal occurrence ("infini...