If the algorithms are intended to be processed by a machine then they are known as computer programmers. Otherwise they are mathematicians.
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A function can map for sets with infinite elements. Recursive variables, being 'algorithms of algorithms', are restricted to finite elements.
Introduction to Algorithms was created in 1990.
Translating algorithms (such that a machine can understand them) is known as programming.
'ASM' is sort for Assembly, it has nothing to do with sorting algorithms.