Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Thu, 03 Nov 2022 23:36:49 -0700 Received: from [192.168.123.254] (port=59988 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1oqqJq-008BL7-4l for jbovlaste-admin@lojban.org; Thu, 03 Nov 2022 23:36:48 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Fri, 04 Nov 2022 06:36:46 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word kei'i -- By gleki Date: Fri, 4 Nov 2022 06:36:45 +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 gleki 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: $X_1 - X_2$. --- > non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: $X_{1} ^{C}$; binary: $X_1\setminusX_2$. 5,5c5,5 < In the definition and in this note, due to parsing constraints, "-" represents set exclusion; this is typically denoted as a backslash elsewhere. 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 "$X_1 - X_2$"), 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 $O - X_2 = X_{2} ^{C}$, 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 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 "$X_1\setminusX_2$"), 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 $O\setminusX_2=X_{2}^{C}$, 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) . 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: $X_1 - X_2$. Notes: In the definition and in this note, due to parsing constraints, "-" represents set exclusion; this is typically denoted as a backslash elsewhere. 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 "$X_1 - X_2$"), 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 $O - X_2 = X_{2} ^{C}$, 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: $X_{1} ^{C}$; binary: $X_1\setminusX_2$. 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 "$X_1\setminusX_2$"), 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 $O\setminusX_2=X_{2}^{C}$, 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: You can go to to see it.