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Gross domestic product (GDP) is the market value of all final goods and services from a nation in a given year. [2] Countries are sorted by nominal GDP estimates from financial and statistical institutions, which are calculated at market or government official exchange rates.
This illustrates the relationship a + b a = a b = φ. In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if.
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.
- History
- Main Classification
- Subclasses of The Integers
- Subclasses of The Complex Numbers
- Extensions of The Concept
- References
- External Links
First use of numbers
Bones and other artifacts have been discovered with marks cut into them that many believe are tally marks.These tally marks may have been used for counting elapsed time, such as numbers of days, lunar cycles or keeping records of quantities, such as of animals. A tallying system has no concept of place value (as in modern decimalnotation), which limits its representation of large numbers. Nonetheless, tallying systems are considered the first kind of abstract numeral system. The first known s...
Numerals
Numbers should be distinguished from numerals, the symbols used to represent numbers. The Egyptians invented the first ciphered numeral system, and the Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets. Roman numerals, a system that used combinations of letters from the Roman alphabet, remained dominant in Europe until the spread of the superior Hindu–Arabic numeral system around the late 14th century, and the Hindu–Arabic numeral system remains the most common...
Zero
The first known documented use of zero dates to AD 628, and appeared in the Brāhmasphuṭasiddhānta, the main work of the Indian mathematician Brahmagupta. He treated 0 as a number and discussed operations involving it, including division. By this time (the 7th century) the concept had clearly reached Cambodia as Khmer numerals, and documentation shows the idea later spreading to China and the Islamic world. Brahmagupta's Brāhmasphuṭasiddhānta is the first book that mentions zero as a number, h...
Numbers can be classified into sets, called number sets or number systems, such as the natural numbers and the real numbers. The main number systems are as follows: Each of these number systems is a subsetof the next one. So, for example, a rational number is also a real number, and every real number is also a complex number. This can be expressed ...
Even and odd numbers
An even number is an integer that is "evenly divisible" by two, that is divisible by two without remainder; an odd number is an integer that is not even. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) Any odd number n may be constructed by the formula n = 2k + 1, for a suitable integer k. Starting with k = 0, the first non-negative odd numbers are {1, 3, 5, 7, ...}. Any even number m has the form m = 2k where k is again an integer. Similarly, the fi...
Prime numbers
A prime number, often shortened to just prime, is an integer greater than 1 that is not the product of two smaller positive integers. The first few prime numbers are 2, 3, 5, 7, and 11. There is no such simple formula as for odd and even numbers to generate the prime numbers. The primes have been widely studied for more than 2000 years and have led to many questions, only some of which have been answered. The study of these questions belongs to number theory. Goldbach's conjectureis an exampl...
Other classes of integers
Many subsets of the natural numbers have been the subject of specific studies and have been named, often after the first mathematician that has studied them. Example of such sets of integers are Fibonacci numbers and perfect numbers. For more examples, see Integer sequence.
Algebraic, irrational and transcendental numbers
Algebraic numbers are those that are a solution to a polynomial equation with integer coefficients. Real numbers that are not rational numbers are called irrational numbers. Complex numbers which are not algebraic are called transcendental numbers. The algebraic numbers that are solutions of a monic polynomial equation with integer coefficients are called algebraic integers.
Constructible numbers
Motivated by the classical problems of constructions with straightedge and compass, the constructible numbersare those complex numbers whose real and imaginary parts can be constructed using straightedge and compass, starting from a given segment of unit length, in a finite number of steps.
Computable numbers
A computable number, also known as recursive number, is a real number such that there exists an algorithm which, given a positive number n as input, produces the first n digits of the computable number's decimal representation. Equivalent definitions can be given using μ-recursive functions, Turing machines or λ-calculus. The computable numbers are stable for all usual arithmetic operations, including the computation of the roots of a polynomial, and thus form a real closed field that contain...
p-adic numbers
The p-adic numbers may have infinitely long expansions to the left of the decimal point, in the same way that real numbers may have infinitely long expansions to the right. The number system that results depends on what base is used for the digits: any base is possible, but a prime number base provides the best mathematical properties. The set of the p-adic numbers contains the rational numbers, but is not contained in the complex numbers. The elements of an algebraic function field over a fi...
Hypercomplex numbers
Some number systems that are not included in the complex numbers may be constructed from the real numbers in a way that generalize the construction of the complex numbers. They are sometimes called hypercomplex numbers. They include the quaternions H, introduced by Sir William Rowan Hamilton, in which multiplication is not commutative, the octonions, in which multiplication is not associative in addition to not being commutative, and the sedenions, in which multiplication is not alternative,...
Transfinite numbers
For dealing with infinite sets, the natural numbers have been generalized to the ordinal numbers and to the cardinal numbers. The former gives the ordering of the set, while the latter gives its size. For finite sets, both ordinal and cardinal numbers are identified with the natural numbers. In the infinite case, many ordinal numbers correspond to the same cardinal number.
Tobias Dantzig, Number, the language of science; a critical survey written for the cultured non-mathematician, New York, The Macmillan Company, 1930.[ISBN missing]Erich Friedman, What's special about this number? Archived 2018-02-23 at the Wayback MachineSteven Galovich, Introduction to Mathematical Structures, Harcourt Brace Javanovich, 1989, ISBN 0-15-543468-3.Paul Halmos, Naive Set Theory, Springer, 1974, ISBN 0-387-90092-6.Nechaev, V.I. (2001) [1994]. "Number". Encyclopedia of Mathematics. EMS Press.Tallant, Jonathan. "Do Numbers Exist". Numberphile. Brady Haran. Archived from the original on 8 March 2016. Retrieved 6 April 2013.In Our Time: Negative Numbers. BBC Radio 4. 9 March 2006. Archived from the originalon 31 May 2022.Robin Wilson (7 November 2007). "4000 Years of Numbers". Gresham College. Archivedfrom the original on 8 April 2022.The United States of America ( USA or U.S.A. ), commonly known as the United States ( US or U.S.) or America, is a country primarily located in North America. It is a federation of 50 states, which also includes its federal capital district of Washington, D.C., and 326 Indian reservations.
BRICS is an intergovernmental organization comprising Brazil, Russia, India, China, South Africa, Iran, Egypt, Ethiopia, and the United Arab Emirates. Originally identified to highlight investment opportunities, [1] the grouping evolved into an actual geopolitical bloc, with their governments meeting annually at formal summits and ...
In telecommunications, 5G is the fifth-generation technology standard for cellular networks, which cellular phone companies began deploying worldwide in 2019, and is the successor to 4G technology that provides connectivity to most current mobile phones.
