ELEMENTARY

The term elementary was originally introduced by László Kalmár in the context of computability theory. He defined the class of elementary recursive functions as a subset of the primitive recursive functions — specifically, those that can be computed using a limited set of operations such as composition, bounded sums, and bounded products. These functions grow no faster than a fixed-height tower of exponentiation. Not all primitive recursive functions are elementary; for example, tetration grows too rapidly to be included in the elementary class. The elementary recursive functions correspond to the class of the Grzegorczyk hierarchy.