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The term arithmetic has its root in the Latin term arithmetica which derives from the Ancient Greek words ἀριθμός (arithmos), meaning ' number ', and ἀριθμητική τέχνη (arithmetike tekhne), meaning ' the art of counting '. [3] There are disagreements about its precise definition.
In applied fields the word "tight" is often used with the same meaning. [2] smooth Smoothness is a concept which mathematics has endowed with many meanings, from simple differentiability to infinite differentiability to analyticity, and still others which are more complicated. Each such usage attempts to invoke the physically intuitive notion ...
In Disquisitiones Arithmeticae (1801) Gauss proved the unique factorization theorem and used it to prove the law of quadratic reciprocity. In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the ...
A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science. Some just say, "mathematics is what mathematicians do". [166] [167] A common approach is to define mathematics by its object of study. [168] [169] [170 ...
Most contemporary reference works define mathematics by summarizing its main topics and methods: The abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra. [16] Oxford English Dictionary ...
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.
Arithmetica is the earliest extant work present that solve arithmetic problems by algebra. Diophantus however did not invent the method of algebra, which existed before him. [ 8 ] Algebra was practiced and diffused orally by practitioners, with Diophantus picking up technique to solve problems in arithmetic.
The two most widely used arithmetic symbols are addition and subtraction, + and −. The plus sign was used starting around 1351 by Nicole Oresme [47] and publicized in his work Algorismus proportionum (1360). [48] It is thought to be an abbreviation for "et", meaning "and" in Latin, in much the same way the ampersand sign also