DefinitionA definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
Lexical definitionThe lexical definition of a term, also known as the dictionary definition, is the definition closely matching the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictionary. A lexical definition is usually the type expected from a request for definition, and it is generally expected that such a definition will be stated as simply as possible in order to convey information to the widest audience.
PolynomialIn mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1. Polynomials appear in many areas of mathematics and science.
Circular definitionA circular definition is a type of definition that uses the term(s) being defined as part of the description or assumes that the term(s) being described are already known. There are several kinds of circular definition, and several ways of characterising the term: pragmatic, lexicographic and linguistic. Circular definitions are related to Circular reasoning in that they both involve a self-referential approach. Circular definitions may be unhelpful if the audience must either already know the meaning of the key term, or if the term to be defined is used in the definition itself.
Definition of planetThe definition of planet has changed several times since the word was coined by the ancient Greeks. Greek astronomers employed the term ἀστέρες πλανῆται (), 'wandering stars', for star-like objects which apparently moved over the sky. Over the millennia, the term has included a variety of different celestial bodies, from the Sun and the Moon to satellites and asteroids. In modern astronomy, there are two primary conceptions of a 'planet'.
Greatest common divisorIn mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, . In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), etc.
Integer factorizationIn number theory, integer factorization is the decomposition, when possible, of a positive integer into a product of smaller integers. If the factors are further restricted to be prime numbers, the process is called prime factorization, and includes the test whether the given integer is prime (in this case, one has a "product" of a single factor). When the numbers are sufficiently large, no efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist.
Geophysical definition of planetThe International Union of Geological Sciences (IUGS) is the internationally recognized body charged with fostering agreement on nomenclature and classification across geoscientific disciplines. However, they have yet to create a formal definition of the term planet. As a result, there are various geophysical definitions in use among professional geophysicists, planetary scientists, and other professionals in the geosciences. Many professionals opt to use one of several of these geophysical definitions instead of the definition voted on by the International Astronomical Union.
ProtestA protest (also called a demonstration, remonstration or remonstrance) is a public expression of objection, disapproval or dissent towards an idea or action, typically a political one. Protests can be thought of as acts of cooperation in which numerous people cooperate by attending, and share the potential costs and risks of doing so. Protests can take many different forms, from individual statements to mass political demonstrations.
Nth rootIn mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as , where x is the radicand and n is the index (also sometimes called the degree). This is pronounced as "the nth root of x". The definition then of an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: A root of degree 2 is called a square root (usually written without the n as just ) and a root of degree 3, a cube root (written ).
22 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method.
1 + 2 + 3 + 4 + ⋯The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ⋯ is a divergent series. The nth partial sum of the series is the triangular number which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum. Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting results.
