Non-Archimedean time

Non-Archimedean time

A non-Archimedean time theory of time is any theory that holds that there exist instants infinitely in the future or infinitely in the past. It is so called because, if the instants of such time are assigned numbers, the set of such numbers must be non-Archimedean.

Non-Archimedean future time would entail the existence of a future moment T, such that for any finite duration y there exists a moment Now + y but less than T. Note that if such a future moment T existed, there would exist an infinity of moments such that for all finite moments y' , T − y' would be after every moment Now + y where y is a finite duration. Likewise, one may conceive of a non-archimedean past.

One may distinguish singularly, multiply and infinitely non-Archimedean times. In a singularly non-archimedean time, we can choose (albeit arbitrarily) a single moment T infinitely in the future (and/or the past, mutatis mutandis), such that every other moment infinitely in the future (past) is finitely in the future or past of T. In a multiply non-Archimedean time, there exists a finite set of moments S (where the cardinality of S is greater than two) such that each member of S, T, is infinitely in the future or past of every other element of S, and there exists an infinity of moments finitely in the future of T, and every instant that is not an element of S is finitely in the future or past of one element of S, and infinitely in the future or past of every other element of S. Finally, for an infinitely non-archimedean time there is no such finite set S, but there is an infinite set S, mutatis mutandis.


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Non-archimedean time — A non Archimedean time theory of time is any theory that holds that there exist instants infinitely in the future or infinitely in the past. It is so called because, if the instants of such time are assigned numbers, the set of such numbers must… …   Wikipedia

  • Non-Archimedean — In mathematics and physics, non Archimedean refers to something without the Archimedean property. This includes: Ultrametric space notably, p adic numbers Non Archimedean ordered field, namely: Levi Civita field Hyperreal numbers Surreal numbers… …   Wikipedia

  • 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

  • Surreal number — In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share… …   Wikipedia

  • Transfer principle — In mathematics, the transfer principle is a concept in Abraham Robinson s non standard analysis of the hyperreal numbers. It states that any sentence expressible in a certain formal language that is true of real numbers is also true of hyperreal… …   Wikipedia

  • Euclidean geometry — A Greek mathematician performing a geometric construction with a compass, from The School of Athens by Raphael. Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his… …   Wikipedia

  • Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …   Wikipedia

  • P-adic quantum mechanics — One may compute the energy levels for a potential well like this one.[note 1] P adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics. It is the application of p adic analysis to quantum… …   Wikipedia

  • metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… …   Universalium

  • Friedwardt Winterberg — Infobox Scientist name = Friedwardt Winterberg image width = 200px caption = Friedwart Winterberg birth date = birth date|1929|06|12 birth place = Berlin, Germany residence = Germany, United States citizenship = American, previously German… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”