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Symbolic Language (mathematics)
In mathematics, a symbolic language is a language that uses characters or symbols to represent concepts, such as mathematical operations, expressions, and statements, and the entities or operands on which the operations are performed. See also *Formal language *Language of mathematics *Glossary of mathematical symbols *Mathematical Alphanumeric Symbols *Mathematical notation *Notation system *Symbolic language (other) A symbolic language is a method of communication that uses characters or images to represent concepts. Symbolic language may refer to: * Symbolic language (art) * Symbolic language (engineering) * Symbolic language (literature) * Symbolic lan ... References External links Mathematical Symbols Mathematical notation {{Math-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Character (computing)
In computing and telecommunications, a character is the internal representation of a character (symbol) used within a computer or system. Examples of characters include letters, numerical digits, punctuation marks (such as "." or "-"), and whitespace. The concept also includes control characters, which do not correspond to visible symbols but rather to instructions to format or process the text. Examples of control characters include carriage return and tab as well as other instructions to printers or other devices that display or otherwise process text. Characters are typically combined into '' strings''. Historically, the term ''character'' was used to denote a specific number of contiguous bits. While a character is most commonly assumed to refer to 8 bits (one byte) today, other options like the 6-bit character code were once popular, and the 5-bit Baudot code has been used in the past as well. The term has even been applied to 4 bits with only 16 possible valu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symbols
A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise different concepts and experiences. All communication is achieved through the use of symbols: for example, a red octagon is a common symbol for " STOP"; on maps, blue lines often represent rivers; and a red rose often symbolizes love and compassion. Numerals are symbols for numbers; letters of an alphabet may be symbols for certain phonemes; and personal names are symbols representing individuals. The academic study of symbols is called semiotics. In the arts, symbolism is the use of a concrete element to represent a more abstract idea. In cartography, an organized collection of symbols forms a legend for a map. Etymology The word ''symbol'' derives from the late Middle French masculine noun , which appeared around 1380 in a theological sense sign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operation (mathematics)
In mathematics, an operation is a function from a set to itself. For example, an operation on real numbers will take in real numbers and return a real number. An operation can take zero or more input values (also called "'' operands''" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant. The mixed product is an example of an operation of arity 3, also called ternary operation. Generally, the arity is taken to be finite. However, infinitary operations are sometimes considered, in which case the "usual" operations of finite arity are called finitary operations. A partial operation is defined similarly to an operatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expression (mathematics)
In mathematics, an expression is a written arrangement of symbol (mathematics), symbols following the context-dependent, syntax (logic), syntactic conventions of mathematical notation. Symbols can denote numbers, variable (mathematics), variables, operation (mathematics), operations, and function (mathematics), functions. Other symbols include punctuation marks and bracket (mathematics), brackets, used for Symbols of grouping, grouping where there is not a well-defined order of operations. Expressions are commonly distinguished from ''mathematical formula, 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 (linguistics), sentence refers to a fact. For example, 8x-5 is an expression, while the Inequality (mathematics), inequality 8x-5 \geq 3 is a formula. To ''evaluate'' an expression means to find a numeric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositions
A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky is blue" expresses the proposition that the sky is blue. Unlike sentences, propositions are not linguistic expressions, so the English sentence "Snow is white" and the German "Schnee ist weiß" denote the same proposition. Propositions also serve as the objects of belief and other propositional attitudes, such as when someone believes that the sky is blue. Formally, propositions are often modeled as functions which map a possible world to a truth value. For instance, the proposition that the sky is blue can be modeled as a function which would return the truth value T if given the actual world as input, but would return F if given some alternate world where the sky is green. However, a number of alternative formalizations have been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operands
In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Unknown operands in equalities of expressions can be found by equation solving. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above example, '+' is the symbol for the operation called addition. The operand '3' is one of the inputs (quantities) followed by the addition operator, and the operand '6' is the other input necessary for the operation. The result of the operation is 9. (The number '9' is also called the sum of the augend 3 and the addend 6.) An operand, then, is also referred to as "one of the inputs (quantities) for an operation". Notation Expressions as operands Operands may be nested, and may consist of expressions also made up of operators with operands. :(3 + 5) \times 2 In the above expression '(3 + 5)' is the first operand for the multiplication operator and '2' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called ''well-formed words''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar. In computer science, formal languages are used, among others, as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages, in which the words of the language represent concepts that are associated with meanings or semantics. In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Language Of Mathematics
The language of mathematics or mathematical language is an extension of the natural language (for example English language, English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proof (mathematics), proofs, logical deductions, etc.) with concision, precision and unambiguity. Features The main features of the mathematical language are the following. * Use of common words with a derived meaning, generally more specific and more precise. For example, "or (logic), or" means "one, the other or both", while, in common language, "both" is sometimes included and sometimes not. Also, a "line (mathematics), line" is straight and has zero width. * Use of common words with a meaning that is completely different from their common meaning. For example, a mathematical ring (mathematics), ring is not related to any other meaning of "ring". Real numbers and imaginary numbers are two sorts of numbers, none being more real or more imaginary than the ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Mathematical Symbols
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 or a mathematical expression. More formally, a ''mathematical symbol'' is any grapheme used in mathematical formulas and expressions. As formulas and expressions are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics. The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other types of mathematical object. As the number of these types has increased ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Alphanumeric Symbols
Mathematical Alphanumeric Symbols is a Unicode block comprising styled forms of Latin alphabet, Latin and Greek alphabet, Greek letters and decimal numerical digit, digits that enable mathematicians to denote different notions with different letter styles. The letters in various fonts often have specific, fixed meanings in particular areas of mathematics. By providing uniformity over numerous mathematical articles and books, these conventions help to read mathematical formulas. These also may be used to differentiate between concepts that share a letter in a single problem. Unicode now includes many such symbols (in the range U+1D400–U+1D7FF). The rationale behind this is that it enables design and usage of special mathematical characters (typeface, fonts) that include all necessary properties to differentiate from other alphanumerics, e.g. in mathematics an italic type, italic letter "𝐴" can have a different meaning from a roman type, roman letter "A". Unicode or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Notation
Mathematical notation consists of using glossary of mathematical symbols, symbols for representing operation (mathematics), operations, unspecified numbers, relation (mathematics), relations, and any other mathematical objects and assembling them into expression (mathematics), expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and property (philosophy), properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula E=mc^2 is the quantitative representation in mathematical notation of mass–energy equivalence. Mathematical notation was first introduced by François Viète at the end of the 16th century and largely expanded during the 17th and 18th centuries by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler. Symbols and typeface The use of many symbols is the basis of mathematical notation. They play a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
