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History Of Computing
The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or without the aid of tables. Concrete devices Digital computing is intimately tied to the representation of number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...s. But long before abstractions like ''the number'' arose, there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as: *''Bijection, One-to-one correspondence'', a rule to counting, count ''how many'' items, e.g. on a tally stick, eventually abstracted into ''numbers''. *''Comparison to a standard'', a method for assuming ''reproducibility'' in a measure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Computing Hardware
The history of computing hardware spans the developments from early devices used for simple calculations to today's complex computers, encompassing advancements in both analog and digital technology. The first aids to computation were purely mechanical devices which required the operator to set up the initial values of an elementary arithmetic operation, then manipulate the device to obtain the result. In later stages, computing devices began representing numbers in continuous forms, such as by distance along a scale, rotation of a shaft, or a specific voltage level. Numbers could also be represented in the form of digits, automatically manipulated by a mechanism. Although this approach generally required more complex mechanisms, it greatly increased the precision of results. The development of transistor technology, followed by the invention of integrated circuit chips, led to revolutionary breakthroughs. Transistor-based computers and, later, integrated circuit-based computers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numeral (linguistics)
In linguistics, a numeral in the broadest sense is a word or phrase that describes a numerical quantity. Some theories of grammar use the word "numeral" to refer to cardinal numbers that act as a determiner that specify the quantity of a noun, for example the "two" in "two hats". Some theories of grammar do not include determiners as a part of speech and consider "two" in this example to be an adjective. Some theories consider "numeral" to be a synonym for "number" and assign all numbers (including ordinal numbers like "first") to a part of speech called "numerals". Numerals in the broad sense can also be analyzed as a noun ("three is a small number"), as a pronoun ("the two went to town"), or for a small number of words as an adverb ("I rode the slide twice"). Numerals can express relationships like quantity (cardinal numbers), sequence (ordinal numbers), frequency (once, twice), and part (fraction). Identifying numerals Numerals may be attributive, as in ''two dogs'', or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Root
In mathematics, a square root of a number is a number such that y^2 = x; in other words, a number whose ''square'' (the result of multiplying the number by itself, or y \cdot y) is . For example, 4 and −4 are square roots of 16 because 4^2 = (-4)^2 = 16. Every nonnegative real number has a unique nonnegative square root, called the ''principal square root'' or simply ''the square root'' (with a definite article, see below), which is denoted by \sqrt, where the symbol "\sqrt" is called the '' radical sign'' or ''radix''. For example, to express the fact that the principal square root of 9 is 3, we write \sqrt = 3. The term (or number) whose square root is being considered is known as the ''radicand''. The radicand is the number or expression underneath the radical sign, in this case, 9. For non-negative , the principal square root can also be written in exponent notation, as x^. Every positive number has two square roots: \sqrt (which is positive) and -\sqrt (which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Function
In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called the Domain of a function, domain of the function and the set is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. History of the function concept, Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable function, differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Expression
In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers, variables, operations, and functions. Other symbols include punctuation marks and brackets, used for grouping where there is not a well-defined order of operations. Expressions are commonly distinguished from '' formulas'': expressions are a kind of mathematical object, whereas formulas are statements ''about'' mathematical objects. This is analogous to natural language, where a noun phrase refers to an object, and a whole sentence refers to a fact. For example, 8x-5 is an expression, while the inequality 8x-5 \geq 3 is a formula. To ''evaluate'' an expression means to find a numerical value equivalent to the expression. Expressions can be ''evaluated'' or ''simplified'' by replacing operations that appear in them with their result. For example, the expression 8\times 2-5 simplifies to 16-5, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paper
Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, Textile, rags, poaceae, grasses, Feces#Other uses, herbivore dung, or other vegetable sources in water. Once the water is drained through a fine mesh leaving the fibre evenly distributed on the surface, it can be pressed and dried. The papermaking process developed in east Asia, probably China, at least as early as 105 Common Era, CE, by the Han Dynasty, Han court eunuch Cai Lun, although the earliest archaeological fragments of paper derive from the 2nd century BCE in China. Although paper was originally made in single sheets by hand, today it is mass-produced on large machines—some making reels 10 metres wide, running at 2,000 metres per minute and up to 600,000 tonnes a year. It is a versatile material with many uses, including printing, painting, graphics, signage, design, packaging, decorating, writing, and Housekeeping, cleaning. It may also be used a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Europe
Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south, and Asia to the east. Europe shares the landmass of Eurasia with Asia, and of Afro-Eurasia with both Africa and Asia. Europe is commonly considered to be Boundaries between the continents#Asia and Europe, separated from Asia by the Drainage divide, watershed of the Ural Mountains, the Ural (river), Ural River, the Caspian Sea, the Greater Caucasus, the Black Sea, and the waterway of the Bosporus, Bosporus Strait. "Europe" (pp. 68–69); "Asia" (pp. 90–91): "A commonly accepted division between Asia and Europe ... is formed by the Ural Mountains, Ural River, Caspian Sea, Caucasus Mountains, and the Black Sea with its outlets, the Bosporus and Dardanelles." Europe covers approx. , or 2% of Earth#Surface, Earth's surface (6.8% of Earth's land area), making it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindu–Arabic Numeral System
The Hindu–Arabic numeral system (also known as the Indo-Arabic numeral system, Hindu numeral system, and Arabic numeral system) is a positional notation, positional Decimal, base-ten numeral system for representing integers; its extension to non-integers is the decimal, decimal numeral system, which is presently the most common numeral system. The system was invented between the 1st and 4th centuries by Indian mathematics, Indian mathematicians. By the 9th century, the system was adopted by Arabic mathematics, Arabic mathematicians who extended it to include fraction (mathematics), fractions. It became more widely known through the writings in Arabic of the Persian mathematician Al-Khwārizmī (''On the Calculation with Hindu Numerals'', ) and Arab mathematician Al-Kindi (''On the Use of the Hindu Numerals'', ). The system had spread to medieval Europe by the High Middle Ages, notably following Fibonacci's 13th century ''Liber Abaci''; until the evolution of the printing pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Notation
Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any radix, base of the Hindu–Arabic numeral system (or decimal, decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred (however, the values may be modified when combined). In modern positional systems, such as the decimal, decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string. The Babylonian Numerals, Babylonian numeral system, base 60, was the first positional sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Algorithm
In mathematics, the Euclidean algorithm,Some widely used textbooks, such as I. N. Herstein's ''Topics in Algebra'' and Serge Lang's ''Algebra'', use the term "Euclidean algorithm" to refer to Euclidean division or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his ''Elements'' (). It is an example of an ''algorithm'', a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is a deductive reasoning, deductive Argument-deduction-proof distinctions, argument for a Proposition, mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty, to be distinguished from empirical evidence, empirical arguments or non-exhaustive inductive reasoning that establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theorem
In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ''corollary'' for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formal system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
