An algorithm has finite length, but an infinite sequence of algorithms need not. For algorithm A to actually carry out "if the input has size n where N_i <= n

An algorithm has finite length, but an infinite sequence of algorithms need not. For algorithm A to actually carry out "if the input has size n where N_i <= n < N_{i+1}, perform A_i", it needs to be able to generate the code for each of the infinite number of A_i's.