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the least upper bound of a sequence

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  • Least upper bound axiom — The least upper bound axiom, also abbreviated as the LUB axiom, is an axiom of real analysis stating that if a nonempty subset of the real numbers has an upper bound, then it has a least upper bound. It is an axiom in the sense that it cannot be… …   Wikipedia

  • Least-upper-bound property — In mathematics, the least upper bound property is a fundamental property of the real numbers and certain other ordered sets. The property states that any non empty set of real numbers that has an upper bound necessarily has a least upper bound… …   Wikipedia

  • Denotational semantics of the Actor model — The denotational semantics of the Actor model is the subject of denotational domain theory for Actors. The historical development of this subject is recounted in [Hewitt 2008b]. Contents 1 Actor fixed point semantics 2 Compositionality in… …   Wikipedia

  • Completeness of the real numbers — Intuitively, completeness implies that there are not any “gaps” (in Dedekind s terminology) or “missing points” in the real number line. This contrasts with the rational numbers, whose corresponding number line has a “gap” at each irrational… …   Wikipedia

  • Construction of the real numbers — In mathematics, there are several ways of defining the real number system as an ordered field. The synthetic approach gives a list of axioms for the real numbers as a complete ordered field. Under the usual axioms of set theory, one can show that …   Wikipedia

  • Logic and the philosophy of mathematics in the nineteenth century — John Stillwell INTRODUCTION In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the… …   History of philosophy

  • Cauchy sequence — In mathematics, a Cauchy sequence, named after Augustin Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. To be more precise, by dropping enough (but still only a finite number of) terms from… …   Wikipedia

  • The Animatrix — DVD Cover Directed by Wachowski brothers Koji Morimoto Shinichiro Watanabe Mahiro Maeda Peter Chung Andy Jones Yoshiaki Kawaji …   Wikipedia

  • The World Ends with You — Left to right, Joshua, Neku, Beat (above), Shiki, and Rhyme Developer(s) Square Enix Jupiter …   Wikipedia

  • Exact sciences (The) in Hellenistic times: texts and issues — The exact sciences in Hellenistic times: Texts and issues1 Alan C.Bowen Modern scholars often rely on the history of Greco Latin science2 as a backdrop and support for interpreting past philosophical thought. Their warrant is the practice… …   History of philosophy

  • Geology of the Grand Canyon area — The geology of the Grand Canyon area exposes one of the most complete sequences of rock anywhere, representing a period of nearly 2 billion years of the Earth s history in that part of North America. The major sedimentary rock layers exposed in… …   Wikipedia

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