Algorithm
The word 'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to "algorismus". Al-Khwārizmī (, , c. 780–850) was a Persian mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad, whose name means 'the native of Khwarezm', a region that was part of Greater Iran and is now in Uzbekistan.
Algorithm
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. Thus an algorithm can be an algebraic equation such as "y = m + n" – 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):