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Calculus. In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point.
Abacus. An abacus ( pl.: abaci or abacuses ), also called a counting frame, is a hand -operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Arabic numeral system. [1] An abacus consists of a two-dimensional array of slidable beads (or similar objects).
Tetration is also defined recursively as. allowing for attempts to extend tetration to non-natural numbers such as real and complex numbers . The two inverses of tetration are called super-root and super-logarithm, analogous to the nth root and the logarithmic functions. None of the three functions are elementary .
A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator and the digital computer .
Digital root. The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.
Definitions. The super-logarithm, written is defined implicitly by. This definition implies that the super-logarithm can only have integer outputs, and that it is only defined for inputs of the form and so on. In order to extend the domain of the super-logarithm from this sparse set to the real numbers, several approaches have been pursued.
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