Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Wed, 15 Feb 2023 09:13:48 -0800 Received: from [192.168.123.254] (port=40062 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1pSLLl-002udQ-PU for jbovlaste-admin@lojban.org; Wed, 15 Feb 2023 09:13:48 -0800 Received: by jiten.lojban.org (sSMTP sendmail emulation); Wed, 15 Feb 2023 17:13:45 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Added At Word socnrpanrnji'akobi -- By krtisfranks Date: Wed, 15 Feb 2023 17:13:45 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -2.9 (--) X-Spam_score: -2.9 X-Spam_score_int: -28 X-Spam_bar: -- In jbovlaste, the user krtisfranks has added a definition of "socnrpanrnji'akobi" in the language "English". New Data: Definition: $x_1$ is a binary operator in structure $x_2$ which exhibits the Jacobi property with respect to binary operator $x_3$ (which also endows $x_2$) and element/object $x_4$ (which is an element of the underlying set which form $x_2$). Notes: This word uses a classifier {brapagjvo} involving experimental gismu "{socni}". Let $x_1$ be denoted by "$f$", $x_2$ be denoted by "X", $x_3$ be denoted by "$+$", and $x_4$ be denoted by "e". Then $f$ exhibits the Jacobi property iff, for any $x, y, z$ in $X$, the following is true: $f(x, f(y, z)) + f(z, f(x, y)) + f(y, f(z, x)) = e$. Notice that $f$ may not be commutative; it may be necessary to further specify that $e$ is the identity element in $X$ for operstor '$+$', assuming that such is appropriate. Jargon: Gloss Keywords: Word: Jacobi property, In Sense: for binary operators; in a sense, it measures associativity. Place Keywords: You can go to to see it.