Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Thu, 21 Jul 2022 22:44:46 -0700 Received: from [192.168.123.254] (port=56646 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1oElSt-0008gd-Bc for jbovlaste-admin@lojban.org; Thu, 21 Jul 2022 22:44:45 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Fri, 22 Jul 2022 05:44:43 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word socni -- By krtisfranks Date: Fri, 22 Jul 2022 05:44:43 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -0.0 (/) X-Spam_score: -0.0 X-Spam_score_int: 0 X-Spam_bar: / In jbovlaste, the user krtisfranks has edited a definition of "socni" in the language "English". Differences: 5,5c5,5 < Denote $x_1$ by "♤"; for any elements x,y,z in the set of concern, if '♤' is associative, then (x♤y)♤z = x♤(y♤z), where equality is defined in the space and parenthetic grouping denotes higher prioritization/earlier application. An operator being associative usually results, notationally, in the dropping of explicit parentheses. "Associative property"/"associativity" = "ka(m)( )socni". Notice that a space is understood to support association (or 'be associative') under a given operator $x_1$ in the sense that its elements and equality relation are such that all ordered pairs can be exchanged in application under the operator while maintaining equality; this is similar to a space being endowed with identity element(s) under a given operator and also an operator have identity in a space - in English, associativity is often understood to be a property of a function and the existence of an identity to be a property of a space, but they are wed in Lojban, as they should be, for neither makes sense without the other and the property is a relationship between the operator and the space. See also: {cajni}, {sezni}, {dukni}, {facni}. --- > Denote $x_1$ by "♤"; for any elements x,y,z in the set of concern, '♤' is associative iff (x♤y)♤z = x♤(y♤z), where equality is defined in the space and parenthetic grouping denotes higher prioritization/earlier application. An operator being associative usually results, notationally, in the dropping of explicit parentheses. "Associative property"/"associativity" = "ka(m)( )socni". Notice that a space is understood to support association (or 'be associative') under a given operator $x_1$ in the sense that its elements and equality relation are such that all ordered pairs can be exchanged in application under the operator while maintaining equality; this is similar to a space being endowed with identity element(s) under a given operator and also an operator have identity in a space - in English, associativity is often understood to be a property of a function and the existence of an identity to be a property of a space, but they are wed in Lojban, as they should be, for neither makes sense without the other and the property is a relationship between the operator and the space. See also: {cajni}, {sezni}, {dukni}, {facni}. Old Data: Definition: $x_1$ is a binary operator which is associative in space/under conditions/on (or endowing) set $x_2$. Notes: Denote $x_1$ by "♤"; for any elements x,y,z in the set of concern, if '♤' is associative, then (x♤y)♤z = x♤(y♤z), where equality is defined in the space and parenthetic grouping denotes higher prioritization/earlier application. An operator being associative usually results, notationally, in the dropping of explicit parentheses. "Associative property"/"associativity" = "ka(m)( )socni". Notice that a space is understood to support association (or 'be associative') under a given operator $x_1$ in the sense that its elements and equality relation are such that all ordered pairs can be exchanged in application under the operator while maintaining equality; this is similar to a space being endowed with identity element(s) under a given operator and also an operator have identity in a space - in English, associativity is often understood to be a property of a function and the existence of an identity to be a property of a space, but they are wed in Lojban, as they should be, for neither makes sense without the other and the property is a relationship between the operator and the space. See also: {cajni}, {sezni}, {dukni}, {facni}. Jargon: Gloss Keywords: Word: associative operator, In Sense: Word: associative property, In Sense: Place Keywords: New Data: Definition: $x_1$ is a binary operator which is associative in space/under conditions/on (or endowing) set $x_2$. Notes: Denote $x_1$ by "♤"; for any elements x,y,z in the set of concern, '♤' is associative iff (x♤y)♤z = x♤(y♤z), where equality is defined in the space and parenthetic grouping denotes higher prioritization/earlier application. An operator being associative usually results, notationally, in the dropping of explicit parentheses. "Associative property"/"associativity" = "ka(m)( )socni". Notice that a space is understood to support association (or 'be associative') under a given operator $x_1$ in the sense that its elements and equality relation are such that all ordered pairs can be exchanged in application under the operator while maintaining equality; this is similar to a space being endowed with identity element(s) under a given operator and also an operator have identity in a space - in English, associativity is often understood to be a property of a function and the existence of an identity to be a property of a space, but they are wed in Lojban, as they should be, for neither makes sense without the other and the property is a relationship between the operator and the space. See also: {cajni}, {sezni}, {dukni}, {facni}. Jargon: Gloss Keywords: Word: associative operator, In Sense: Word: associative property, In Sense: Place Keywords: You can go to to see it.