Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Fri, 04 Nov 2022 04:14:33 -0700 Received: from [192.168.123.254] (port=34238 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1oquec-008C4y-Nw for jbovlaste-admin@lojban.org; Fri, 04 Nov 2022 04:14:33 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Fri, 04 Nov 2022 11:14:30 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word kei'i -- By krtisfranks Date: Fri, 4 Nov 2022 11:14:30 +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 edited a definition of "kei'i" in the language "English". Differences: 2,2c2,2 < non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: $X_{1} ^{C}$; binary: ${X_1}\setminus{X_2}$. --- > non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: $X_{2} ^{C}$; binary: ${X_1}\setminus{X_2}$. 5,5c5,5 < Each input must be a set or similar. The definition of the binary case expands to "the set of all elements which are in $X_1$ but not in $X_2$". This word and operator has ordered input: '$X_1$ kei'i $X_2$' is not generally equivalent to '$X_2$ kei'i $X_1$'; in other words, the operator is not commutative. If unary (meaning that $X_1$ is not explicitly specified in a hypothetical expression "${X_1}\setminus{X_2}$"), then $X_1$ is taken to be some universal set $O$ in/of the discourse (of which all other mentioned sets are subsets, at the least); in this case, the word operates as the set (absolute) complement of the explicitly mentioned set here (but not in the definition) designated as $X_2$ for clarity (id est: the output is $O\setminus{X_2}={X_2}^{C}$, where "$^{C}$" denotes the set absolute complement; in other words, it is the set of all elements which may be under consideration such that they are not elements of the explicitly specified set). When binary with both $X_1$ and $X_2$ explicitly specified, this word/operator is the set relative complement. Somewhat analogous to logical 'NOT' (just as set intersection is analogous to logical 'AND', and set union is analogous to logical '(AND/)OR'). The preferred description/name in English is "set (theoretic) exclusion". For reference: https://en.wikipedia.org/wiki/Complement_(set_theory) . --- > Each input must be a set or similar. The definition of the binary case expands to "the set of exactly those elements which are in $X_1$ but not in $X_2$". This word and operator has ordered input: '$X_1$ kei'i $X_2$' is not generally equivalent to '$X_2$ kei'i $X_1$'; in other words, the operator is not commutative. If unary (meaning that $X_1$ is not explicitly specified in a hypothetical expression "${X_1}\setminus{X_2}$"), then $X_1$ is taken to be some universal set $O$ in/of the discourse (of which all other mentioned or relevantly formable sets are subsets, at the least); in this latter case, the word operates as the set (absolute) complement of the explicitly mentioned set here designated as $X_2$ for clarity (id est: the output is $O\setminus{X_2}={X_2}^{C}$, where "$^{C}$" denotes the set absolute complement; in other words, it is the set of all elements which may be under consideration such that they are not elements of the explicitly specified set). When binary with both $X_1$ and $X_2$ explicitly specified, this word/operator is the set relative complement. This word is somewhat analogous to, depending on its arity, logical 'NOT' or 'AND NOT' (just as set intersection is analogous to logical 'AND', set union is analogous to logical '(AND/)OR' and set symmetric difference is analogous to 'XOR'). The preferred description/name in English is "set (theoretic) exclusion". For reference: https://en.wikipedia.org/wiki/Complement_(set_theory) . 18a19,20 \n> Word: relative complement, In Sense: set-theoretic operator/connective (cmavo) > Word: absolute complement, In Sense: set-theoretic operator/connective (cmavo) Old Data: Definition: non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: $X_{1} ^{C}$; binary: ${X_1}\setminus{X_2}$. Notes: Each input must be a set or similar. The definition of the binary case expands to "the set of all elements which are in $X_1$ but not in $X_2$". This word and operator has ordered input: '$X_1$ kei'i $X_2$' is not generally equivalent to '$X_2$ kei'i $X_1$'; in other words, the operator is not commutative. If unary (meaning that $X_1$ is not explicitly specified in a hypothetical expression "${X_1}\setminus{X_2}$"), then $X_1$ is taken to be some universal set $O$ in/of the discourse (of which all other mentioned sets are subsets, at the least); in this case, the word operates as the set (absolute) complement of the explicitly mentioned set here (but not in the definition) designated as $X_2$ for clarity (id est: the output is $O\setminus{X_2}={X_2}^{C}$, where "$^{C}$" denotes the set absolute complement; in other words, it is the set of all elements which may be under consideration such that they are not elements of the explicitly specified set). When binary with both $X_1$ and $X_2$ explicitly specified, this word/operator is the set relative complement. Somewhat analogous to logical 'NOT' (just as set intersection is analogous to logical 'AND', and set union is analogous to logical '(AND/)OR'). The preferred description/name in English is "set (theoretic) exclusion". For reference: https://en.wikipedia.org/wiki/Complement_(set_theory) . Jargon: Gloss Keywords: Word: \, In Sense: set theoretic operator (mekso, connective): set exclusion Word: C, In Sense: set theoretic operator (mekso, connective): set complement Word: exclusion, In Sense: set theoretic operator (mekso, connective) Word: set complement, In Sense: set theoretic operator (mekso, connective): relative or absolute Word: set difference, In Sense: set theoretic operator (mekso, connective) Word: set exclusion, In Sense: set theoretic operator (mekso, connective) Word: set minus, In Sense: set theoretic operator (mekso, connective) Word: set subtraction, In Sense: set theoretic operator (mekso, connective) Place Keywords: New Data: Definition: non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: $X_{2} ^{C}$; binary: ${X_1}\setminus{X_2}$. Notes: Each input must be a set or similar. The definition of the binary case expands to "the set of exactly those elements which are in $X_1$ but not in $X_2$". This word and operator has ordered input: '$X_1$ kei'i $X_2$' is not generally equivalent to '$X_2$ kei'i $X_1$'; in other words, the operator is not commutative. If unary (meaning that $X_1$ is not explicitly specified in a hypothetical expression "${X_1}\setminus{X_2}$"), then $X_1$ is taken to be some universal set $O$ in/of the discourse (of which all other mentioned or relevantly formable sets are subsets, at the least); in this latter case, the word operates as the set (absolute) complement of the explicitly mentioned set here designated as $X_2$ for clarity (id est: the output is $O\setminus{X_2}={X_2}^{C}$, where "$^{C}$" denotes the set absolute complement; in other words, it is the set of all elements which may be under consideration such that they are not elements of the explicitly specified set). When binary with both $X_1$ and $X_2$ explicitly specified, this word/operator is the set relative complement. This word is somewhat analogous to, depending on its arity, logical 'NOT' or 'AND NOT' (just as set intersection is analogous to logical 'AND', set union is analogous to logical '(AND/)OR' and set symmetric difference is analogous to 'XOR'). The preferred description/name in English is "set (theoretic) exclusion". For reference: https://en.wikipedia.org/wiki/Complement_(set_theory) . Jargon: Gloss Keywords: Word: \, In Sense: set theoretic operator (mekso, connective): set exclusion Word: C, In Sense: set theoretic operator (mekso, connective): set complement Word: exclusion, In Sense: set theoretic operator (mekso, connective) Word: set complement, In Sense: set theoretic operator (mekso, connective): relative or absolute Word: set difference, In Sense: set theoretic operator (mekso, connective) Word: set exclusion, In Sense: set theoretic operator (mekso, connective) Word: set minus, In Sense: set theoretic operator (mekso, connective) Word: set subtraction, In Sense: set theoretic operator (mekso, connective) Word: relative complement, In Sense: set-theoretic operator/connective (cmavo) Word: absolute complement, In Sense: set-theoretic operator/connective (cmavo) Place Keywords: You can go to to see it.