Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Tue, 04 Oct 2022 23:54:15 -0700 Received: from [192.168.123.254] (port=38980 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1ofyIG-005BrC-1x for jbovlaste-admin@lojban.org; Tue, 04 Oct 2022 23:54:15 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Wed, 05 Oct 2022 06:54:11 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word bi'oi -- By krtisfranks Date: Wed, 5 Oct 2022 06:54:11 +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 "bi'oi" in the language "English". Differences: 5,5c5,5 < This word is a member of selma'o BIhI. The space must be ordered or directed in some sense. Let the space X be the traditionally-ordered field of real numbers, and x and y be in X (or x be a geometric point which is represented in such manner and which belongs to a specified line/ray which has a defined positive direction and a specification of the meaning of the length of 1 unit); then, "x bi'oi y" represents the interval between x and x + y, where y is signed. In other words, this interval is like the body of the string in the scenario in which one of its endpoints is tacked down at x and the other is dragged out a distance y therefrom in the directions specified by the signum of y (with the string being pulled taut and being of length exactly y). Maintaining the same notation and continuing discussion of "x bi'oi y": if the clusivity for the first term (or 'on the left') is specified, then x is or is not included in the referenced interval as specified; if the clusivity for the second term (or 'on the right') is specified, then x + y is or is not included in the referenced interval as specified (note: this does not generally indicate whether y is included in the referenced interval). Units, particularly for y, must be explicit when appropriate. In an acyclic possibly-directed graph, x would be a node and y would be the graph-geodesic distance therefrom in the direction (if y is positive) or in the opposite direction (if y is negative). This definition enables the ISO 8601 standard for time interval specification in the cases (1) of a starting time/pastward endpoint (namely x) and a duration (y: y > 0), and (2) of an ending time/futureward endpoint (namely x) and a duration (y: y < 0), where notation for "x" and "y" (in the usage "x bi'oi y") is continued from earlier in this note; note that, in this usage case, x is a point in time (a timestamp) and y is a duration (elapsed time or measure of time, and which thus has explicitly specified units or something akin to the ISO 8601 standard notation for durations). See this proposal for more information on related topics: https://mw.lojban.org/papri/Proposal:_loi_lerfu_tcita_detri;_the_final_word_on_the_problem_of_dates_and_times%3F . Importantly, the ISO 8601 standard in the case of an ending time and a duration has the terms expressed in the order of y followed by x with y being positive; when this word is used for such purposes, y must be negative, but the order of x and y may be exchanged via usage of "{se}" (resulting in "{sebi'oi}"). See also: "{bi'o}", "{bi'i}", "{mi'i}", and https://mw-live.lojban.org/papri/Extended_Dimensionality_of_Interval_cmavo . --- > This word is a member of selma'o BIhI. The space must be ordered or directed in some sense. Let the space X be the traditionally-ordered field of real numbers, and x and y be in X (or x be a geometric point which is represented in such manner and which belongs to a specified line/ray which has a defined positive direction and a specification of the meaning of the length of 1 unit); then, "x bi'oi y" represents the interval between x and x + y, where y is signed. In other words, this interval is like the body of the string in the scenario in which one of its endpoints is tacked down at x and the other is dragged out a distance y therefrom in the directions specified by the signum of y (with the string being pulled taut and being of length exactly y). Maintaining the same notation and continuing discussion of "x bi'oi y": if the clusivity for the first term (or 'on the left') is specified, then x is or is not included in the referenced interval as specified; if the clusivity for the second term (or 'on the right') is specified, then x + y is or is not included in the referenced interval as specified (note: this does not generally indicate whether y is included in the referenced interval). Units, particularly for y, must be explicit when appropriate. In a connected acyclic directed graph, x would be a node and y would be the graph-geodesic distance therefrom in the direction (if y is positive), or in the opposite direction (if y is negative), of the graph. This definition enables the ISO 8601 standard for time interval specification in the cases (1) of a starting time/pastward endpoint (namely x) and a duration (y: y > 0), and (2) of an ending time/futureward endpoint (namely x) and a duration (y: y < 0), where notation for "x" and "y" (in the usage "x bi'oi y") is continued from the earlier discussion in this note in the case of the number lines or the real; note that, in this usage case, x is a point in time (a timestamp) and y is a duration (elapsed time or measure of time, and which thus has explicitly specified units or something akin to the ISO 8601 standard notation for durations). See this proposal for more information on related topics: https://mw.lojban.org/papri/Proposal:_loi_lerfu_tcita_detri;_the_final_word_on_the_problem_of_dates_and_times%3F . Importantly, the ISO 8601 standard in the case of an ending time and a duration has the terms expressed in the order of y followed by x with y being positive; when this word is used for such purposes, y must be negative, but the order of x and y may be exchanged via usage of "{se}" (resulting in "{sebi'oi}"). Generally, the distinction between points/'positions' (represented by x) and measures/vectors/'displacements' (represented by y) must be maintained when using this word. See also: "{bi'o}", "{bi'i}", "{mi'i}", and https://mw-live.lojban.org/papri/Extended_Dimensionality_of_Interval_cmavo . Old Data: Definition: non-logical interval connective: ordered interval with specified endpoint/terminus $x_1$ and signed measure/length/duration $x_2$; interval between $x_1$ and $x_1 + x_2$ according to the ordering of the space. Notes: This word is a member of selma'o BIhI. The space must be ordered or directed in some sense. Let the space X be the traditionally-ordered field of real numbers, and x and y be in X (or x be a geometric point which is represented in such manner and which belongs to a specified line/ray which has a defined positive direction and a specification of the meaning of the length of 1 unit); then, "x bi'oi y" represents the interval between x and x + y, where y is signed. In other words, this interval is like the body of the string in the scenario in which one of its endpoints is tacked down at x and the other is dragged out a distance y therefrom in the directions specified by the signum of y (with the string being pulled taut and being of length exactly y). Maintaining the same notation and continuing discussion of "x bi'oi y": if the clusivity for the first term (or 'on the left') is specified, then x is or is not included in the referenced interval as specified; if the clusivity for the second term (or 'on the right') is specified, then x + y is or is not included in the referenced interval as specified (note: this does not generally indicate whether y is included in the referenced interval). Units, particularly for y, must be explicit when appropriate. In an acyclic possibly-directed graph, x would be a node and y would be the graph-geodesic distance therefrom in the direction (if y is positive) or in the opposite direction (if y is negative). This definition enables the ISO 8601 standard for time interval specification in the cases (1) of a starting time/pastward endpoint (namely x) and a duration (y: y > 0), and (2) of an ending time/futureward endpoint (namely x) and a duration (y: y < 0), where notation for "x" and "y" (in the usage "x bi'oi y") is continued from earlier in this note; note that, in this usage case, x is a point in time (a timestamp) and y is a duration (elapsed time or measure of time, and which thus has explicitly specified units or something akin to the ISO 8601 standard notation for durations). See this proposal for more information on related topics: https://mw.lojban.org/papri/Proposal:_loi_lerfu_tcita_detri;_the_final_word_on_the_problem_of_dates_and_times%3F . Importantly, the ISO 8601 standard in the case of an ending time and a duration has the terms expressed in the order of y followed by x with y being positive; when this word is used for such purposes, y must be negative, but the order of x and y may be exchanged via usage of "{se}" (resulting in "{sebi'oi}"). See also: "{bi'o}", "{bi'i}", "{mi'i}", and https://mw-live.lojban.org/papri/Extended_Dimensionality_of_Interval_cmavo . Jargon: Gloss Keywords: Word: ordered interval given by endpoint and signed measure, In Sense: Word: tack-and-drag ordered interval, In Sense: Place Keywords: Word: endpoint/terminus of interval, In Sense: , For Place: 1 Word: signed measure of interval, In Sense: , For Place: 2 New Data: Definition: non-logical interval connective: ordered interval with specified endpoint/terminus $x_1$ and signed measure/length/duration $x_2$; interval between $x_1$ and $x_1 + x_2$ according to the ordering of the space. Notes: This word is a member of selma'o BIhI. The space must be ordered or directed in some sense. Let the space X be the traditionally-ordered field of real numbers, and x and y be in X (or x be a geometric point which is represented in such manner and which belongs to a specified line/ray which has a defined positive direction and a specification of the meaning of the length of 1 unit); then, "x bi'oi y" represents the interval between x and x + y, where y is signed. In other words, this interval is like the body of the string in the scenario in which one of its endpoints is tacked down at x and the other is dragged out a distance y therefrom in the directions specified by the signum of y (with the string being pulled taut and being of length exactly y). Maintaining the same notation and continuing discussion of "x bi'oi y": if the clusivity for the first term (or 'on the left') is specified, then x is or is not included in the referenced interval as specified; if the clusivity for the second term (or 'on the right') is specified, then x + y is or is not included in the referenced interval as specified (note: this does not generally indicate whether y is included in the referenced interval). Units, particularly for y, must be explicit when appropriate. In a connected acyclic directed graph, x would be a node and y would be the graph-geodesic distance therefrom in the direction (if y is positive), or in the opposite direction (if y is negative), of the graph. This definition enables the ISO 8601 standard for time interval specification in the cases (1) of a starting time/pastward endpoint (namely x) and a duration (y: y > 0), and (2) of an ending time/futureward endpoint (namely x) and a duration (y: y < 0), where notation for "x" and "y" (in the usage "x bi'oi y") is continued from the earlier discussion in this note in the case of the number lines or the real; note that, in this usage case, x is a point in time (a timestamp) and y is a duration (elapsed time or measure of time, and which thus has explicitly specified units or something akin to the ISO 8601 standard notation for durations). See this proposal for more information on related topics: https://mw.lojban.org/papri/Proposal:_loi_lerfu_tcita_detri;_the_final_word_on_the_problem_of_dates_and_times%3F . Importantly, the ISO 8601 standard in the case of an ending time and a duration has the terms expressed in the order of y followed by x with y being positive; when this word is used for such purposes, y must be negative, but the order of x and y may be exchanged via usage of "{se}" (resulting in "{sebi'oi}"). Generally, the distinction between points/'positions' (represented by x) and measures/vectors/'displacements' (represented by y) must be maintained when using this word. See also: "{bi'o}", "{bi'i}", "{mi'i}", and https://mw-live.lojban.org/papri/Extended_Dimensionality_of_Interval_cmavo . Jargon: Gloss Keywords: Word: ordered interval given by endpoint and signed measure, In Sense: Word: tack-and-drag ordered interval, In Sense: Place Keywords: Word: endpoint/terminus of interval, In Sense: , For Place: 1 Word: signed measure of interval, In Sense: , For Place: 2 You can go to to see it.