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In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. The exponential of a variable x {\displaystyle x} is denoted exp x {\displaystyle \exp x} or e x {\displaystyle e^{x}} , with the two notations used interchangeably.
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
Exponentiation for a natural power is defined as iterated multiplication, which Knuth denoted by a single up-arrow: a ↑ b = H 3 ( a , b ) = a b = a × a × ⋯ × a ⏟ b copies of a {\displaystyle {\begin{matrix}a\uparrow b=H_{3}(a,b)=a^{b}=&\underbrace {a\times a\times \dots \times a} \\&b{\mbox{ copies of }}a\end{matrix}}}
The term hyperpower [4] is a natural combination of hyper and power, which aptly describes tetration. The problem lies in the meaning of hyper with respect to the hyperoperation sequence. When considering hyperoperations, the term hyper refers to all ranks, and the term super refers to rank 4, or tetration.
Visualization of powers of two from 1 to 1024 (2 0 to 2 10) as base-2 Dienes blocks. A power of two is a number of the form 2 n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. In the fast-growing hierarchy, 2 n is exactly equal to ().