Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Thu, 05 Aug 2021 00:06:08 -0700 Received: from [192.168.123.254] (port=40512 helo=web.digitalkingdom.org) by stodi.digitalkingdom.org with smtp (Exim 4.94) (envelope-from ) id 1mBXSA-00B0Ek-02 for jbovlaste-admin@lojban.org; Thu, 05 Aug 2021 00:06:08 -0700 Received: by web.digitalkingdom.org (sSMTP sendmail emulation); Thu, 05 Aug 2021 07:06:05 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word te'o'a -- By gleki Date: Thu, 5 Aug 2021 07:06:05 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -2.8 (--) X-Spam_score: -2.8 X-Spam_score_int: -27 X-Spam_bar: -- In jbovlaste, the user gleki has edited a definition of "te'o'a" in the language "English". Differences: 5,5c5,5 < Approximately equivalent to "{se} {te'a} {te'o}" possibly with {ma'o} included somewhere. This is mostly useful for abbreviation and for being careful in distinguishing functions from numbers (since $e^x$ is a number and not a function; this word is $e^{#}$ using Wolfram notation). For example: Let $D$ be the differentiation operator with respect to the first variable of its argument. Then $D(e^x)=0$ at best, strictly speaking, because $x$ must be just a number and so the differentiand is a constant (in fact and at worst, it may not even be a function, in which case the derivative is not even defined); we accept this notation to mean something else (which will be shown momentarily) because few other notations are convenient. However, what we really mean, and what this word facilitates, is: $D(exp)=exp$; this is true because the differentiand is a differentiable (and special) function. This word is related to {te'a} in a fashion analgpus to the ordered relation between {fa'i} (resp. {va'a}) and {fi'u} (resp. {vu'u}). The domain and codomain sets are purposefully vague. --- > Approximately equivalent to "{se} {te'a} {te'o}" possibly with {ma'o} included somewhere. This is mostly useful for abbreviation and for being careful in distinguishing functions from numbers (since $e^x$ is a number and not a function; this word is $e^{\#}$ using Wolfram notation). For example: Let $D$ be the differentiation operator with respect to the first variable of its argument. Then $D(e^x)=0$ at best, strictly speaking, because $x$ must be just a number and so the differentiand is a constant (in fact and at worst, it may not even be a function, in which case the derivative is not even defined); we accept this notation to mean something else (which will be shown momentarily) because few other notations are convenient. However, what we really mean, and what this word facilitates, is: $D(exp)=exp$; this is true because the differentiand is a differentiable (and special) function. This word is related to {te'a} in a fashion analgpus to the ordered relation between {fa'i} (resp. {va'a}) and {fi'u} (resp. {vu'u}). The domain and codomain sets are purposefully vague. Old Data: Definition: unary mekso operator: natural exponentiation operator exp, where $exp(a) = e^a \forall a$. Notes: Approximately equivalent to "{se} {te'a} {te'o}" possibly with {ma'o} included somewhere. This is mostly useful for abbreviation and for being careful in distinguishing functions from numbers (since $e^x$ is a number and not a function; this word is $e^{#}$ using Wolfram notation). For example: Let $D$ be the differentiation operator with respect to the first variable of its argument. Then $D(e^x)=0$ at best, strictly speaking, because $x$ must be just a number and so the differentiand is a constant (in fact and at worst, it may not even be a function, in which case the derivative is not even defined); we accept this notation to mean something else (which will be shown momentarily) because few other notations are convenient. However, what we really mean, and what this word facilitates, is: $D(exp)=exp$; this is true because the differentiand is a differentiable (and special) function. This word is related to {te'a} in a fashion analgpus to the ordered relation between {fa'i} (resp. {va'a}) and {fi'u} (resp. {vu'u}). The domain and codomain sets are purposefully vague. Jargon: Gloss Keywords: Word: exp, In Sense: Word: natural exponentiation function, In Sense: Place Keywords: New Data: Definition: unary mekso operator: natural exponentiation operator exp, where $exp(a) = e^a \forall a$. Notes: Approximately equivalent to "{se} {te'a} {te'o}" possibly with {ma'o} included somewhere. This is mostly useful for abbreviation and for being careful in distinguishing functions from numbers (since $e^x$ is a number and not a function; this word is $e^{\#}$ using Wolfram notation). For example: Let $D$ be the differentiation operator with respect to the first variable of its argument. Then $D(e^x)=0$ at best, strictly speaking, because $x$ must be just a number and so the differentiand is a constant (in fact and at worst, it may not even be a function, in which case the derivative is not even defined); we accept this notation to mean something else (which will be shown momentarily) because few other notations are convenient. However, what we really mean, and what this word facilitates, is: $D(exp)=exp$; this is true because the differentiand is a differentiable (and special) function. This word is related to {te'a} in a fashion analgpus to the ordered relation between {fa'i} (resp. {va'a}) and {fi'u} (resp. {vu'u}). The domain and codomain sets are purposefully vague. Jargon: Gloss Keywords: Word: exp, In Sense: Word: natural exponentiation function, In Sense: Place Keywords: You can go to to see it.