Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Sat, 12 Nov 2022 14:25:28 -0800 Received: from [192.168.123.254] (port=55768 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1otywH-008XTk-VO for jbovlaste-admin@lojban.org; Sat, 12 Nov 2022 14:25:28 -0800 Received: by jiten.lojban.org (sSMTP sendmail emulation); Sat, 12 Nov 2022 22:25:25 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word modju -- By krtisfranks Date: Sat, 12 Nov 2022 22:25:25 +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 "modju" in the language "English". Differences: 5,5c5,5 < In order to be clear (in case of poor display), ($x_1$ - $x_2$)/$x_3$ is an integer, possibly (but not necessarily) nonpositive. Traditionally, but not necessarily, $x_3$ is a strictly positive integer (in particular, $x_3$ is nonzero) and is called "(the) modulus"; if $x_3 = 1$, then $x_1$ and $x_2$ differ only by an integer amount - in other words, they have the same fractional part. Technically, $x_1$ and $x_2$ are symmetric under mutual exchange and can even be equivalent; however, in a manner morally analogous to "{srana}", $x_2$ is canonically/traditionally either the common residue (the unique element in the space which is congruent to $x_1$ mod $x_3$ and which is greater than or equal to 0 and strictly less than $x_3$) or the minimal residue (denoting the common residue by $c$, the minimal residue is either $c$ xor $c - x_3$, whichever is strictly less than the other in absolute value), and this may even be considered as its contextless default meaning (such as in "lo se modju"). See also: {dilcu}, {dunli}, {mintu}, {simsa}, {panra}, {dilma} (a particularly close relative and generalization of this word with slightly different focus). This word is essentially identical with {dilcrmadjulu}; consider this word to be its gismu equivalent. It is not the modulus operator; for that, use {veldilcu}. It is a specific type of {terpanryziltolju'i}, although both occupy the word "modulo" in English. --- > In order to be clear (in case of poor display), ($x_1$ - $x_2$)/$x_3$ is an integer, possibly (but not necessarily) nonpositive. Traditionally, but not necessarily, $x_3$ is a strictly positive integer (in particular, $x_3$ is nonzero) and is called "(the) modulus"; if $x_3 = 1$, then $x_1$ and $x_2$ differ only by an integer amount - in other words, they have the same fractional part. Technically, $x_1$ and $x_2$ are symmetric under mutual exchange and can even be equivalent; however, in a manner morally analogous to "{srana}", $x_2$ is canonically/traditionally either the common residue (the unique element in the space which is congruent to $x_1$ mod $x_3$ and which is greater than or equal to 0 and strictly less than $x_3$) or the minimal residue (denoting the common residue by $c$, the minimal residue is either $c$ xor $c - x_3$, whichever is strictly less than the other in absolute value), and this may even be considered as its contextless default meaning (such as in "lo se modju"). See also: {dilcu}, {dunli}, {mintu}, {simsa}, {panra}, {dilma} (a particularly close relative and generalization of this word with slightly different focus). This word is essentially identical with {dilcrmadjulu}; consider this word to be its gismu equivalent. It is not the modulus operator; for that, use {veldilcu} or {vei'u}. It is a specific type of {terpanryziltolju'i}, although both occupy the word "modulo" in English. 13a14,18 \n> Word: n-parity, In Sense: > Word: 2-parity, In Sense: > Word: kuller, In Sense: 3-parity > Word: color, In Sense: 3-parity > Word: integer-part, In Sense: Old Data: Definition: $x_1$ (li; number) is congruent to $x_2$ (li; number; see description for canonical/traditional/contextless default usage) modulo $x_3$ (li; number); $\frac{(x_1 - x_2)}{x_3}$ is an integer. Notes: In order to be clear (in case of poor display), ($x_1$ - $x_2$)/$x_3$ is an integer, possibly (but not necessarily) nonpositive. Traditionally, but not necessarily, $x_3$ is a strictly positive integer (in particular, $x_3$ is nonzero) and is called "(the) modulus"; if $x_3 = 1$, then $x_1$ and $x_2$ differ only by an integer amount - in other words, they have the same fractional part. Technically, $x_1$ and $x_2$ are symmetric under mutual exchange and can even be equivalent; however, in a manner morally analogous to "{srana}", $x_2$ is canonically/traditionally either the common residue (the unique element in the space which is congruent to $x_1$ mod $x_3$ and which is greater than or equal to 0 and strictly less than $x_3$) or the minimal residue (denoting the common residue by $c$, the minimal residue is either $c$ xor $c - x_3$, whichever is strictly less than the other in absolute value), and this may even be considered as its contextless default meaning (such as in "lo se modju"). See also: {dilcu}, {dunli}, {mintu}, {simsa}, {panra}, {dilma} (a particularly close relative and generalization of this word with slightly different focus). This word is essentially identical with {dilcrmadjulu}; consider this word to be its gismu equivalent. It is not the modulus operator; for that, use {veldilcu}. It is a specific type of {terpanryziltolju'i}, although both occupy the word "modulo" in English. Jargon: Gloss Keywords: Word: congruent, In Sense: modulo Word: modulo, In Sense: divison remainder congruence Word: modulus, In Sense: of a congruence relation Place Keywords: New Data: Definition: $x_1$ (li; number) is congruent to $x_2$ (li; number; see description for canonical/traditional/contextless default usage) modulo $x_3$ (li; number); $\frac{(x_1 - x_2)}{x_3}$ is an integer. Notes: In order to be clear (in case of poor display), ($x_1$ - $x_2$)/$x_3$ is an integer, possibly (but not necessarily) nonpositive. Traditionally, but not necessarily, $x_3$ is a strictly positive integer (in particular, $x_3$ is nonzero) and is called "(the) modulus"; if $x_3 = 1$, then $x_1$ and $x_2$ differ only by an integer amount - in other words, they have the same fractional part. Technically, $x_1$ and $x_2$ are symmetric under mutual exchange and can even be equivalent; however, in a manner morally analogous to "{srana}", $x_2$ is canonically/traditionally either the common residue (the unique element in the space which is congruent to $x_1$ mod $x_3$ and which is greater than or equal to 0 and strictly less than $x_3$) or the minimal residue (denoting the common residue by $c$, the minimal residue is either $c$ xor $c - x_3$, whichever is strictly less than the other in absolute value), and this may even be considered as its contextless default meaning (such as in "lo se modju"). See also: {dilcu}, {dunli}, {mintu}, {simsa}, {panra}, {dilma} (a particularly close relative and generalization of this word with slightly different focus). This word is essentially identical with {dilcrmadjulu}; consider this word to be its gismu equivalent. It is not the modulus operator; for that, use {veldilcu} or {vei'u}. It is a specific type of {terpanryziltolju'i}, although both occupy the word "modulo" in English. Jargon: Gloss Keywords: Word: congruent, In Sense: modulo Word: modulo, In Sense: divison remainder congruence Word: modulus, In Sense: of a congruence relation Word: n-parity, In Sense: Word: 2-parity, In Sense: Word: kuller, In Sense: 3-parity Word: color, In Sense: 3-parity Word: integer-part, In Sense: Place Keywords: You can go to to see it.