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infinite subset

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  • Infinite set — In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are: * the set of all integers, {..., 1, 0, 1, 2, ...}, is a countably infinite set; and * the set of all real numbers… …   Wikipedia

  • Subset — In mathematics, especially in set theory, a set A is a subset of a set B if A is contained inside B . Notice that A and B may coincide. The relationship of one set being a subset of another is called inclusion.DefinitionsIf A and B are sets and… …   Wikipedia

  • Infinite broom — In topology, the infinite broom is a subset of the Euclidean plane that is used as an example distinguishing various notions of connectedness. The closed infinite broom is the closure of the infinite broom, and is also referred to as the broom… …   Wikipedia

  • Infinite-dimensional holomorphy — In mathematics, infinite dimensional holomorphy is a branch of functional analysis. It is concerned with generalizations of the concept of holomorphic function to functions defined and taking values in complex Banach spaces (or Fréchet spaces… …   Wikipedia

  • infinite — infinitely, adv. infiniteness, n. /in feuh nit/, adj. 1. immeasurably great: an infinite capacity for forgiveness. 2. indefinitely or exceedingly great: infinite sums of money. 3. unlimited or unmeasurable in extent of space, duration of time,… …   Universalium

  • Infinite descending chain — Given a set S with a partial order le;, an infinite descending chain is a chain V , that is, a subset of S upon which le; defines a total order, such that V has no least element, that is, an element m such that for all elements n in V it holds… …   Wikipedia

  • infinite — in•fi•nite [[t]ˈɪn fə nɪt[/t]] adj. 1) immeasurably great: infinite patience[/ex] 2) indefinitely or exceedingly great: infinite sums of money[/ex] 3) unbounded or unlimited; boundless; endless 4) math. Math. a) math. not finite b) math. (of a… …   From formal English to slang

  • Dedekind-infinite set — In mathematics, a set A is Dedekind infinite if some proper subset B of A is equinumerous to A. Explicitly, this means that there is a bijective function from A onto some proper subset B of A. A set is Dedekind finite if it is not Dedekind… …   Wikipedia

  • There is no infinite-dimensional Lebesgue measure — In mathematics, it is a theorem that there is no analogue of Lebesgue measure on an infinite dimensional space. This fact forces mathematicians studying measure theory on infinite dimensional spaces to use other kinds of measures: often, the… …   Wikipedia

  • Fixed point theorems in infinite-dimensional spaces — In mathematics, a number of fixed point theorems in infinite dimensional spaces generalise the Brouwer fixed point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first… …   Wikipedia

  • Fixed-point theorems in infinite-dimensional spaces — In mathematics, a number of fixed point theorems in infinite dimensional spaces generalise the Brouwer fixed point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first… …   Wikipedia

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