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By comparison, powers of two with negative exponents are fractions: for positive integer n, 2 −n is one half multiplied by itself n times. Thus the first few negative powers of 2 are 1 / 2 , 1 / 4 , 1 / 8 , 1 / 16 , etc. Sometimes these are called inverse powers of two because each is the multiplicative inverse of ...
The first negative powers of 2 have special names: is a half; is a quarter. 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 prefixes of the metric system, such as kilo and milli, represent multiplication by positive or negative powers of ten. In information technology it is common to use binary prefixes, which are based on powers of two. Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognised by ...
The reciprocals of the non-negative integer powers of 2 sum to 2 . This is a particular case of the sum of the reciprocals of any geometric series where the first term and the common ratio are positive integers. If the first term is a and the common ratio is r then the sum is r / a (r − 1) .
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite. [1] [2] The impolite numbers are exactly the powers of two, and the polite numbers are the natural numbers that are not powers of two.
The only known almost perfect numbers are powers of 2 with non-negative exponents (sequence A000079 in the OEIS). Therefore the only known odd almost perfect number is 2 0 = 1, and the only known even almost perfect numbers are those of the form 2 k for some positive integer k; however, it has not been shown that all almost perfect numbers are ...
(Reuters) -U.S. President Donald Trump on Saturday ordered 25% tariffs on Canadian and Mexican imports and 10% on goods from China starting on Tuesday to address a national emergency over fentanyl ...
If n is a power of an odd prime number the formula for the totient says its totient can be a power of two only if n is a first power and n − 1 is a power of 2. The primes that are one more than a power of 2 are called Fermat primes, and only five are known: 3, 5, 17, 257, and 65537. Fermat and Gauss knew of these. Nobody has been able to ...