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0-ary Function
In logic, mathematics, and computer science, arity () is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and philosophy, arity may also be called adicity and degree. In linguistics, it is usually named valency. Examples In general, functions or operators with a given arity follow the naming conventions of ''n''-based numeral systems, such as binary and hexadecimal. A Latin prefix is combined with the -ary suffix. For example: * A nullary function takes no arguments. ** Example: f()=2 * A unary function takes one argument. ** Example: f(x)=2x * A binary function takes two arguments. ** Example: f(x,y)=2xy * A ternary function takes three arguments. ** Example: f(x,y,z)=2xyz * An ''n''-ary function takes ''n'' arguments. ** Example: f(x_1, x_2, \ldots, x_n)=2\prod_^n x_i Nullary A constant can be treated as the output of an operation of arity 0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acidity
An acid is a molecule or ion capable of either donating a proton (i.e. hydrogen cation, H+), known as a Brønsted–Lowry acid, or forming a covalent bond with an electron pair, known as a Lewis acid. The first category of acids are the proton donors, or Brønsted–Lowry acids. In the special case of aqueous solutions, proton donors form the hydronium ion H3O+ and are known as Arrhenius acids. Brønsted and Lowry generalized the Arrhenius theory to include non-aqueous solvents. A Brønsted–Lowry or Arrhenius acid usually contains a hydrogen atom bonded to a chemical structure that is still energetically favorable after loss of H+. Aqueous Arrhenius acids have characteristic properties that provide a practical description of an acid. Acids form aqueous solutions with a sour taste, can turn blue litmus red, and react with bases and certain metals (like calcium) to form salts. The word ''acid'' is derived from the Latin , meaning 'sour'. An aqueous solution of an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Operation
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, a binary operation on a set is a binary function that maps every pair of elements of the set to an element of the set. Examples include the familiar arithmetic operations like addition, subtraction, multiplication, set operations like union, complement, intersection. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. A binary function that involves several sets is sometimes also called a ''binary operation''. For example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Binary operations are the keystone of most structures that are studied in algebra, in parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ceiling Function
In mathematics, the floor function is the function that takes as input a real number , and gives as output the greatest integer less than or equal to , denoted or . Similarly, the ceiling function maps to the least integer greater than or equal to , denoted or . For example, for floor: , , and for ceiling: , and . The floor of is also called the integral part, integer part, greatest integer, or entier of , and was historically denoted (among other notations). However, the same term, ''integer part'', is also used for truncation towards zero, which differs from the floor function for negative numbers. For an integer , . Although and produce graphs that appear exactly alike, they are not the same when the value of is an exact integer. For example, when , . However, if , then , while . Notation The ''integral part'' or ''integer part'' of a number ( in the original) was first defined in 1798 by Adrien-Marie Legendre in his proof of the Legendre's formula. Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a rational number, fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the Function (mathematics), function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an Involution (mathematics), involution). Multiplying by a number is the same as Division (mathematics), dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Successor Function
In mathematics, the successor function or successor operation sends a natural number to the next one. The successor function is denoted by ''S'', so ''S''(''n'') = ''n'' +1. For example, ''S''(1) = 2 and ''S''(2) = 3. The successor function is one of the basic components used to build a primitive recursive function. Successor operations are also known as zeration in the context of a zeroth hyperoperation: H0(''a'', ''b'') = 1 + ''b''. In this context, the extension of zeration is addition, which is defined as repeated succession. Overview The successor function is part of the formal language used to state the Peano axioms, which formalise the structure of the natural numbers. In this formalisation, the successor function is a primitive operation on the natural numbers, in terms of which the standard natural numbers and addition are defined. For example, 1 is defined to be ''S''(0), and addition on natural numbers is defined recursively by: : This can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced'' '' – like the letter c'') is a general-purpose programming language. It was created in the 1970s by Dennis Ritchie and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted Central processing unit, CPUs. It has found lasting use in operating systems code (especially in Kernel (operating system), kernels), device drivers, and protocol stacks, but its use in application software has been decreasing. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the most widely used programming langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary Minus
In mathematics, the additive inverse of an element , denoted , is the element that when added to , yields the additive identity, 0 (zero). In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero element. In elementary mathematics, the additive inverse is often referred to as the opposite number, or its negative. The unary operation of arithmetic negation is closely related to ''subtraction'' and is important in solving algebraic equations. Not all sets where addition is defined have an additive inverse, such as the natural numbers. Common examples When working with integers, rational numbers, real numbers, and complex numbers, the additive inverse of any number can be found by multiplying it by −1. The concept can also be extended to algebraic expressions, which is often used when balancing equations. Relation to subtraction The additive inverse is closely related to subtraction, which can be viewed as an addition using th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary Operator
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to ''binary operations'', which use two operands. An example is any function , where is a set; the function is a unary operation on . Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial ), functional notation (e.g. or ), and superscripts (e.g. transpose ). Other notations exist as well, for example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent of the argument. Examples Absolute value Obtaining the absolute value of a number is a unary operation. This function is defined as , n, = \begin n, & \mbox n\geq0 \\ -n, & \mbox n<0 \end where is the absolute value of . Negation |
Global Variable
In computer programming, a global variable is a variable with global scope, meaning that it is visible (hence accessible) throughout the program, unless shadowed. The set of all global variables is known as the ''global environment'' or ''global state.'' In compiled languages, global variables are generally static variables, whose extent (lifetime) is the entire runtime of the program, though in interpreted languages (including command-line interpreters), global variables are generally dynamically allocated when declared, since they are not known ahead of time. In some languages, all variables are global, or global by default, while in most modern languages variables have limited scope, generally lexical scope, though global variables are often available by declaring a variable at the top level of the program. In other languages, however, global variables do not exist; these are generally modular programming languages that enforce a module structure, or class-based object-or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Side Effect (computer Science)
In computer science, an operation, function or expression is said to have a side effect if it has any observable effect other than its primary effect of reading the value of its arguments and returning a value to the invoker of the operation. Example side effects include modifying a non-local variable, a static local variable or a mutable argument passed by reference; raising errors or exceptions; performing I/O; or calling other functions with side-effects. In the presence of side effects, a program's behaviour may depend on history; that is, the order of evaluation matters. Understanding and debugging a function with side effects requires knowledge about the context and its possible histories. Side effects play an important role in the design and analysis of programming languages. The degree to which side effects are used depends on the programming paradigm. For example, imperative programming is commonly used to produce side effects, to update a system's state. By contrast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
