An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an "arbitrary" "input" integer or integers that, in theory, can be arbitrarily large. For example, an algorithm can be an algebraic equation such as "y = m + n" (i.e., two arbitrary "input variables" "m" and "n" that produce an output "y"), but various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example):