翻訳と辞書 Words near each other ・ Choice of Arms ・ Choice of code name Geronimo ・ Choice of Colors ・ Choice of law ・ Choice of law clause ・ Choice of Russia ・ Choice of techniques ・ Choice of the People ・ Choice of the Year Ukraine ・ Choice of Weapon ・ Choice on Termination of Pregnancy Act, 1996 ・ Choice Paradise ・ Choice Picks ・ Choice Provisions ・ Choice School ・ Choice sequence ・ Choice set ・ Choice theory ・ Choice TV ・ Choice USA ・ Choice-supportive bias ・ Choice37 ・ Choiceland ・ Choiceless awareness ・ ChoiceOdds ・ ChoicePoint ・ ChoiceQuote Insurance Services ・ Choices (album) ・ Choices (Billy Yates song) ・ Choices (Buffy the Vampire Slayer) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Choice sequence ： ウィキペディア英語版 Choice sequence In intuitionistic mathematics, a choice sequence is a constructive formulation of a sequence. Since the Intuitionistic school of mathematics, as formulated by L. E. J. Brouwer, rejects the idea of a completed infinity, in order to use a sequence (which is, in classical mathematics, an infinite object), we must have a formulation of a finite, constructible object that can serve the same purpose as a sequence. Thus, Brouwer formulated the choice sequence, which is given as a construction, rather than an abstract, infinite object. ==Lawlike and lawless sequences== A distinction is made between ''lawless'' and ''lawlike'' sequences. A ''lawlike'' sequence is one that can be described completely — it is a completed construction, that can be fully described. For example, the natural numbers $\backslash mathbb\; N$ can be thought of as a lawlike sequence: the sequence can be fully constructively described by the unique element 0 and a successor function. Given this formulation, we know that the $i$th element in the sequence of natural numbers will be the number $i-1$. Similarly, a function $f\; :\; \backslash mathbb\; N\; \backslash mapsto\; \backslash mathbb\; N$ mapping from the natural numbers into the natural numbers effectively determines the value for any argument it takes, and thus describes a lawlike sequence. A ''lawless'' (also, ''free'') sequence, on the other hand, is one that is not predetermined. It is to be thought of as a procedure for generating values for the arguments 0, 1, 2, .... That is, a lawless sequence $\backslash alpha$ is a procedure for generating $\backslash alpha\_0$, $\backslash alpha\_1$, ... (the elements of the sequence $\backslash alpha$) such that: *At any given moment of construction of the sequence $\backslash alpha$, only an initial segment of the sequence is known, and no restrictions are placed on the future values of $\backslash alpha$; and *One may specify, in advance, an initial segment $\backslash langle\; \backslash alpha\_0,\; \backslash alpha\_1,\; \backslash ldots,\; \backslash alpha\_k\; \backslash rangle$ of $\backslash alpha$. Note that the first point above is slightly misleading, as we may specify, for example, that the values in a sequence be drawn exclusively from the set of natural numbers—we can specify, a priori, the range of the sequence. The canonical example of a lawless sequence is the series of rolls of a die. We specify which die to use and, optionally, specify in advance the values of the first $k$ rolls (for $k\backslash in\; \backslash mathbb\; N$). Further, we restrict the values of the sequence to be in the set $\backslash$. This specification comprises the procedure for generating the lawless sequence in question. At no point, then, is any particular future value of the sequence known. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Choice sequence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.