Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Wed, 12 Oct 2022 23:38:03 -0700 Received: from [192.168.123.254] (port=39796 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1oirqy-005wmh-Gh for jbovlaste-admin@lojban.org; Wed, 12 Oct 2022 23:38:03 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Thu, 13 Oct 2022 06:38:00 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word bi'oi'au -- By krtisfranks Date: Thu, 13 Oct 2022 06:38:00 +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'au" in the language "English". Differences: 5,5c5,5 < Given a well-formed digit string "$x_{n} x_{n-1} ... x_{m}$ bi'oi'au $x_{m-1} x_{m-2} ...$", where "$x_i$" is a member of selma'o PA (other than this word; including at most one instance of "{pi}") for all $i$ and the string represents a finite number in base $b$ (taken to be ten by cultural convention in most human cases unless specified otherwise), the usage of this word in the digit string yields an output of the interval $[\sum_{i = 0}^{\infty}{(x_{n-i} b^{n-i})}, \sum_{i = n-m+1}^{\infty}{(x_{n-i} b^{n-i})} + (x_{m} + 1)b^{m} + \sum_{i = m+1}^{n}{(x_{i} b^{i})})$. Importantly this generates an interval, not a specific number - meaning that equality to such an expression would mean set equality, not numeric equality, among other things. As an example, where "b" represents this word: "2b000" yields [2000, 3000); "20b00" yields [2000, 2100). This is useful for dates (example: "the 2000s"), ages (example: "they are in their twenties"), or any estimate wherein the significant digits are known. Note that, for example, this functionality supports simple calendrical centuries (example: "1900 to 2000, exclusive of the latter only"), canonical calendrical centuries (example: "1901 to 2001, exclusive of the latter only"), and complicated century-long time intervals (example: "1969 to 2069, exclusive of the latter only"); and analogy applies, of course. The interval which is generated in a complete (math jargon) subset of the real numbers - there are no gaps and, in particular, the interval is not discrete (for example: it is not restricted to only the integers). --- > Given a well-formed digit string "$x_{n} x_{n-1} ... x_{m}$ bi'oi'au $x_{m-1} x_{m-2} ...$", where "$x_i$" is a member of selma'o PA (other than this word; including at most one instance of "{pi}") for all $i$ and the string represents a finite number in base $b$ (taken to be ten by cultural convention in most human cases unless specified otherwise), the usage of this word in the digit string yields an output of the interval $[\sum_{i = 0}^{\infty}{(x_{n-i} b^{n-i})}, \sum_{i = n-m+1}^{\infty}{(x_{n-i} b^{n-i})} + (x_{m} + 1)b^{m} + \sum_{i = m+1}^{n}{(x_{i} b^{i})})$. Importantly, usage of this word generates an interval, not a specific number - meaning, among other things, that equality to such an expression would be set equality, and not numeric equality. Note that the interval which is generated includes the lesser (left) endpoint but excludes the greater (right) endpoint. As an example, where "B" represents this word: "2B000" yields [2000, 3000); meanwhile, "20B00" yields [2000, 2100). This word/function is useful for dates (example: "the 2000s"), ages (example: "they are in their twenties"), or any estimate wherein the significant digits are known. Note that, for example, this functionality supports simple calendrical centuries (example: "1900 to 2000, exclusive of the latter only"), canonical calendrical centuries (example: "1901 to 2001, exclusive of the latter only"), and complicated century-long time intervals (example: "1969 to 2069, exclusive of the latter only"); and analogy applies, of course. The interval which is generated in a complete (math jargon) subset of the real numbers - there are no gaps and, in particular, the interval is not discrete (for example: it is not restricted to only the integers). See also: "{bi'oi}", "{mi'i'au}", "{su'ai}". Old Data: Definition: digit/number: $$ interval/range indicator for significant digits (determined by lesser endpoint). Notes: Given a well-formed digit string "$x_{n} x_{n-1} ... x_{m}$ bi'oi'au $x_{m-1} x_{m-2} ...$", where "$x_i$" is a member of selma'o PA (other than this word; including at most one instance of "{pi}") for all $i$ and the string represents a finite number in base $b$ (taken to be ten by cultural convention in most human cases unless specified otherwise), the usage of this word in the digit string yields an output of the interval $[\sum_{i = 0}^{\infty}{(x_{n-i} b^{n-i})}, \sum_{i = n-m+1}^{\infty}{(x_{n-i} b^{n-i})} + (x_{m} + 1)b^{m} + \sum_{i = m+1}^{n}{(x_{i} b^{i})})$. Importantly this generates an interval, not a specific number - meaning that equality to such an expression would mean set equality, not numeric equality, among other things. As an example, where "b" represents this word: "2b000" yields [2000, 3000); "20b00" yields [2000, 2100). This is useful for dates (example: "the 2000s"), ages (example: "they are in their twenties"), or any estimate wherein the significant digits are known. Note that, for example, this functionality supports simple calendrical centuries (example: "1900 to 2000, exclusive of the latter only"), canonical calendrical centuries (example: "1901 to 2001, exclusive of the latter only"), and complicated century-long time intervals (example: "1969 to 2069, exclusive of the latter only"); and analogy applies, of course. The interval which is generated in a complete (math jargon) subset of the real numbers - there are no gaps and, in particular, the interval is not discrete (for example: it is not restricted to only the integers). Jargon: Gloss Keywords: Word: interval-from-number determined by lesser endpoint, In Sense: Place Keywords: New Data: Definition: digit/number: $$ interval/range indicator for significant digits (determined by lesser endpoint). Notes: Given a well-formed digit string "$x_{n} x_{n-1} ... x_{m}$ bi'oi'au $x_{m-1} x_{m-2} ...$", where "$x_i$" is a member of selma'o PA (other than this word; including at most one instance of "{pi}") for all $i$ and the string represents a finite number in base $b$ (taken to be ten by cultural convention in most human cases unless specified otherwise), the usage of this word in the digit string yields an output of the interval $[\sum_{i = 0}^{\infty}{(x_{n-i} b^{n-i})}, \sum_{i = n-m+1}^{\infty}{(x_{n-i} b^{n-i})} + (x_{m} + 1)b^{m} + \sum_{i = m+1}^{n}{(x_{i} b^{i})})$. Importantly, usage of this word generates an interval, not a specific number - meaning, among other things, that equality to such an expression would be set equality, and not numeric equality. Note that the interval which is generated includes the lesser (left) endpoint but excludes the greater (right) endpoint. As an example, where "B" represents this word: "2B000" yields [2000, 3000); meanwhile, "20B00" yields [2000, 2100). This word/function is useful for dates (example: "the 2000s"), ages (example: "they are in their twenties"), or any estimate wherein the significant digits are known. Note that, for example, this functionality supports simple calendrical centuries (example: "1900 to 2000, exclusive of the latter only"), canonical calendrical centuries (example: "1901 to 2001, exclusive of the latter only"), and complicated century-long time intervals (example: "1969 to 2069, exclusive of the latter only"); and analogy applies, of course. The interval which is generated in a complete (math jargon) subset of the real numbers - there are no gaps and, in particular, the interval is not discrete (for example: it is not restricted to only the integers). See also: "{bi'oi}", "{mi'i'au}", "{su'ai}". Jargon: Gloss Keywords: Word: interval-from-number determined by lesser endpoint, In Sense: Place Keywords: You can go to to see it.