翻訳と辞書 Words near each other ・ Wheel of the Year ・ Wheel of time ・ Wheel of time (disambiguation) ・ Wheel of Time (film) ・ Wheel offense ・ Wheel play ・ Wheel Rim, Kentucky ・ Wheel series ・ Wheel sizing ・ Wheel slide protection ・ Wheel speed sensor ・ Wheel spider ・ Wheel Squad ・ Wheel stud ・ Wheel tax ・ Wheel theory ・ Wheel tractor-scraper ・ Wheel train ・ Wheel truing stand ・ Wheel washing system ・ Wheel Wreck ・ Wheel, Kentucky ・ Wheel, Tennessee ・ Wheel-barrowing ・ Wheel-driven land speed record ・ Wheel-rail interface ・ Wheel-Trans ・ Wheelabrator ・ Wheelabrator Incinerator ・ Wheelbarrow 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 Wheel theory ： ウィキペディア英語版 Wheel theory Wheels are a type of algebra where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring. Also the Riemann sphere can be extended to a wheel by adjoining an element $0/0$. The Riemann sphere is an extension of the complex plane by an element $\backslash infty$, where $z/0=\backslash infty$ for any complex $z\backslash neq\; 0$. However, $0/0$ is still undefined on the Riemann sphere, but defined in wheels. == The algebra of wheels == Wheels discard the usual notion of division being a binary operator, replacing it with multiplication by a unary operator $/x$ similar (but not identical) to the multiplicative inverse $x^$, such that $a/b$ becomes shorthand for $a\; \backslash cdot\; /b\; =\; /b\; \backslash cdot\; a$, and modifies the rules of algebra such that * $0x\; \backslash neq\; 0\backslash$ in the general case. * $x\; -\; x\; \backslash neq\; 0\backslash$ in the general case. * $x/x\; \backslash neq\; 1\backslash$ in the general case, as $/x$ is not the same as the multiplicative inverse of $x$. Precisely, a wheel is an algebraic structure with operations binary addition $+$, multiplication $\backslash cdot$, constants 0, 1 and unary $/$, satisfying: * Addition and multiplication are commutative and associative, with 0 and 1 as their respective identities. * $/(xy)\; =\; /x/y\backslash$ and $//x\; =\; x\backslash$ * $xz\; +\; yz\; =\; (x\; +\; y)z\; +\; 0z\backslash$ * $(x\; +\; yz)/y\; =\; x/y\; +\; z\; +\; 0y\backslash$ * $0\backslash cdot\; 0\; =\; 0\backslash$ * $(x+0y)z\; =\; xz\; +\; 0y\backslash$ * $/(x+0y)\; =\; /x\; +\; 0y\backslash$ * $0/0\; +\; x\; =\; 0/0\backslash$ If there is an element $a$ with $1\; +\; a\; =\; 0$, then we may define negation by $-x\; =\; ax$ and $x\; -\; y\; =\; x\; +\; (-y)$. Other identities that may be derived are * $0x\; +\; 0y\; =\; 0xy\backslash$ * $x-x\; =\; 0x^2\backslash$ * $x/x\; =\; 1\; +\; 0x/x\backslash$ However, if $0x\; =\; 0$ and $0/x\; =\; 0$ we get the usual * $x-x\; =\; 0\backslash$ * $x/x\; =\; 1\backslash$ The subset $\backslash$ is always a commutative ring if negation can be defined as above, and every commutative ring is such a subset of a wheel. If $x$ is an invertible element of the commutative ring, then $x^=/x$. Thus, whenever $x^$ makes sense, it is equal to $/x$, but the latter is always defined, even when $x=0$. 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「Wheel theory」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.