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Powers of 2 appear in set theory, since a set with n members has a power set, the set of all of its subsets, which has 2 n members. Integer powers of 2 are important in computer science. The positive integer powers 2 n give the number of possible values for an n-bit integer binary number; for example, a byte may take 2 8 = 256 different values.
Knuth's up-arrow notation. In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [ 1] In his 1947 paper, [ 2] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation ...
Working to the left, use the next a to the left, as the base b, and evaluate the new b^c. 'Descend down the tower' in turn, with the new value for c on the next downward step. Owing in part to some shared terminology and similar notational symbolism , tetration is often confused with closely related functions and expressions.
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent . Powers of two with non-negative exponents are integers: 20 = 1, 21 = 2, and 2n is two multiplied by itself n times. [ 1][ 2] The first ten powers of 2 for non-negative values of n are:
In arithmetic and algebra, the fifth power or sursolid[ 1] of a number n is the result of multiplying five instances of n together: n5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube . The sequence of fifth powers of integers is:
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
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 ...
Exponentiation is when a number b, the base, is raised to a certain power y, the exponent, to give a value x; this is denoted =. For example, raising 2 to the power of 3 gives 8: = The logarithm of base b is the inverse operation, that provides the output y from the input x.