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.
'ASM' is sort for Assembly, it has nothing to do with sorting algorithms.
Translating algorithms (such that a machine can understand them) is known as programming.