axiom of nested intervals

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• 0.999... — In mathematics, the repeating decimal 0.999... (which may also be written as 0.9, , 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0 …   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

• Cardinal number — This article describes cardinal numbers in mathematics. For cardinals in linguistics, see Names of numbers in English. In mathematics, cardinal numbers, or cardinals for short, are generalized numbers used to measure the cardinality (size) of… …   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

• 0,9 periódico — En matemáticas, 0,999... es el número decimal periódico que se demuestra denota[1] al número 1. En otras palabras, los símbolos 0,999... y 1 son dos representaciones distintas del mismo número real. Las demostraciones matemáticas de esta igualdad …   Wikipedia Español

• Reverse mathematics — is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. The method can briefly be described as going backwards from the theorems to the axioms. This contrasts with the ordinary… …   Wikipedia

• Ordered pair — In mathematics, an ordered pair (a, b) is a pair of mathematical objects. In the ordered pair (a, b), the object a is called the first entry, and the object b the second entry of the pair. Alternatively, the objects are called the first and… …   Wikipedia

• Laws of Form — (hereinafter LoF ) is a book by G. Spencer Brown, published in 1969, that straddles the boundary between mathematics and of philosophy. LoF describes three distinct logical systems: * The primary arithmetic (described in Chapter 4), whose models… …   Wikipedia