SequenceIn mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position.
Cauchy productIn mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin-Louis Cauchy. The Cauchy product may apply to infinite series or power series. When people apply it to finite sequences or finite series, that can be seen merely as a particular case of a product of series with a finite number of non-zero coefficients (see discrete convolution). Convergence issues are discussed in the next section.
Mon peopleThe Mon (ဂကူမန်;(Thai Mon=ဂကူမည်); မွန်လူမျိုး, mʊ̀ɰ̃ lù mjó; มอญ, mɔ̄ːn ) are an ethnic group who inhabit Lower Myanmar's Mon State, Kayin State, Kayah State, Tanintharyi Region, Bago Region, the Irrawaddy Delta, and several areas in Thailand (mostly in Pathum Thani province, Phra Pradaeng and Nong Ya Plong). The native language is Mon, which belongs to the Monic branch of the Austroasiatic language family and shares a common origin with the Nyah Kur language, which is spoken by the people of the same name that live in Northeastern Thailand.
Austroasiatic languagesThe Austroasiatic languages ˌɒstroʊ.eɪʒiˈætɪk,_ˌɔː- , are a large language family in Mainland Southeast Asia, South Asia and East Asia. These languages are scattered throughout parts of Thailand, Laos, India, Myanmar, Malaysia, Bangladesh, Nepal, and southern China. Austroasiatic constitute the majority languages of Vietnam and Cambodia. There are around 117 million speakers of Austroasiatic languages, of which more than two-thirds are Vietnamese speakers. Of these languages, only Vietnamese, Khmer, and Mon have a long-established recorded history.
Interval (mathematics)In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers , the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).
ExistenceExistence is the ability of an entity to interact with reality. In philosophy, it refers to the ontological property of being. The term existence comes from Old French existence, from Medieval Latin existentia/exsistentia, from Latin existere, to come forth, be manifest, ex + sistere, to stand. Materialism holds that the only things that exist are matter and energy, that all things are composed of material, that all actions require energy, and that all phenomena (including consciousness) are the result of the interaction of matter.
Existence of GodThe existence of God (or more generally, the existence of deities) is a subject of debate in theology, philosophy of religion and popular culture. A wide variety of arguments for and against the existence of God or deities can be categorized as logical, empirical, metaphysical, subjective or scientific. In philosophical terms, the question of the existence of God or deities involves the disciplines of epistemology (the nature and scope of knowledge) and ontology (study of the nature of being or existence) and the theory of value (since some definitions of God include "perfection").
Fixed point (mathematics)hatnote|1=Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where math|1=f(x) = 0. In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically for functions, a fixed point is an element that is mapped to itself by the function. Formally, c is a fixed point of a function f if c belongs to both the domain and the codomain of f, and f(c) = c.
Fixed-point iterationIn numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.
