Received: from [192.168.123.254] (port=47850 helo=jukni.digitalkingdom.org) by stodi.digitalkingdom.org with smtp (Exim 4.92) (envelope-from ) id 1i6qFC-00031Q-QZ for jbovlaste-admin@lojban.org; Sat, 07 Sep 2019 23:00:17 -0700 Received: by jukni.digitalkingdom.org (sSMTP sendmail emulation); Sat, 07 Sep 2019 23:00:14 -0700 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word fa'ai'ai -- By krtisfranks Date: Sat, 7 Sep 2019 23:00:14 -0700 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 "fa'ai'ai" in the language "English". Differences: 2,2c2,2 < mekso binary or ternary operator: ordered input $(f, g, S)$ where $f$ and $g$ are functions and $S$ is a set of positive integers or "ro" (="all"); output is a function equivalent to the function $f$ as applied to an input ordered tuple with $g$ applied to the entries/terms with indices in $S$ (or to all entries/terms if $S$="ro"). --- > mekso k-ary operator, for natural k and 1 < k < 5: ordered input $(f, g, S, m)$ where $f$ and $g$ are functions, $S$ is a set of positive integers or "ro" (="all"), and $m$ is 0 or 1 (as a toggle); output is a function equivalent to the function $f$ as applied to an input ordered tuple with $g$ applied to the entries/terms with indices in $S$ (or to all entries/terms if $S$="ro") if $m=0$, or $g$ left-composed with the same if $m=1$. 5,5c5,5 < $S$="ro" is default case (making this operator binary); use "{mau'au}" and "{zai'ai}" in order to quote $f$ and $g$ each; the indices in the implicit tuple mentioned in the definition are positive natural numbers such that said tuple is of form $(x_1, x_2, x_3, ..., x_n, ...)$. For example, maintaining this notation, if $S$="ro", then the output is $f(g(x_1), g(x_2), ..., g(x_n), ...)$; if $S$ = Set(1, 3, 23), then the output is $f(g(x_1), x_2, g(x_3), x_4, x_5, ..., x_{21}, x_{22}, g(x_{23}), x_{24}, x_{25}, ..., x_n, ...)$; vel sim. Obviously, in order to be meaningful, the output of each step along the way must be defined. If $S$ is the empty set and $g$ is defined, then the output is just the function $f$. The output of this operator is a function, so it must have explicit input supplied to it ("it" here referring to the output of this operator) in order to actually have an explicit and concrete result; use mathematical brackets around this operator and its inputs when doing so, particularly when $S$ is omitted (as being equal to the default "ro"). --- > $S$="ro" is default case (making this operator binary or ternary); $S$ must be a set or "ro" (no bare integers); $m$ = 0 is the default case (making this operator binary or ternary); use "{mau'au}" and "{zai'ai}" in order to quote $f$ and $g$ each; the indices in the implicit tuple mentioned in the definition are positive natural numbers such that said tuple is of form $(x_1, x_2, x_3, ..., x_n, ...)$. For example, maintaining this notation, if $S$="ro" and $m=0$, then the output is $f(g(x_1), g(x_2), ..., g(x_n), ...)$; if $S$ = Set(1, 3, 23) and $m=0$, then the output is $f(g(x_1), x_2, g(x_3), x_4, x_5, ..., x_{21}, x_{22}, g(x_{23}), x_{24}, x_{25}, ..., x_n, ...)$; vel sim. If $h$ is the function output by this expression when $m=0$, then for the same inputs (ignoring $m$), $g \circ h$ is the function output by the same expression but with $m=1$. Obviously, in order to be meaningful, the output of each step along the way must be defined. If $S$ is the empty set and $g$ is defined, then the output is just the function $f$. The output of this operator is a function, so it must have explicit input supplied to it ("it" here referring to the output of this operator) in order to actually have an explicit and concrete result; use mathematical brackets around this operator and its inputs when doing so, particularly when $S$ is omitted (as being equal to the default "ro"). Old Data: Definition: mekso binary or ternary operator: ordered input $(f, g, S)$ where $f$ and $g$ are functions and $S$ is a set of positive integers or "ro" (="all"); output is a function equivalent to the function $f$ as applied to an input ordered tuple with $g$ applied to the entries/terms with indices in $S$ (or to all entries/terms if $S$="ro"). Notes: $S$="ro" is default case (making this operator binary); use "{mau'au}" and "{zai'ai}" in order to quote $f$ and $g$ each; the indices in the implicit tuple mentioned in the definition are positive natural numbers such that said tuple is of form $(x_1, x_2, x_3, ..., x_n, ...)$. For example, maintaining this notation, if $S$="ro", then the output is $f(g(x_1), g(x_2), ..., g(x_n), ...)$; if $S$ = Set(1, 3, 23), then the output is $f(g(x_1), x_2, g(x_3), x_4, x_5, ..., x_{21}, x_{22}, g(x_{23}), x_{24}, x_{25}, ..., x_n, ...)$; vel sim. Obviously, in order to be meaningful, the output of each step along the way must be defined. If $S$ is the empty set and $g$ is defined, then the output is just the function $f$. The output of this operator is a function, so it must have explicit input supplied to it ("it" here referring to the output of this operator) in order to actually have an explicit and concrete result; use mathematical brackets around this operator and its inputs when doing so, particularly when $S$ is omitted (as being equal to the default "ro"). Jargon: Gloss Keywords: Word: extended functional composition, In Sense: Place Keywords: New Data: Definition: mekso k-ary operator, for natural k and 1 < k < 5: ordered input $(f, g, S, m)$ where $f$ and $g$ are functions, $S$ is a set of positive integers or "ro" (="all"), and $m$ is 0 or 1 (as a toggle); output is a function equivalent to the function $f$ as applied to an input ordered tuple with $g$ applied to the entries/terms with indices in $S$ (or to all entries/terms if $S$="ro") if $m=0$, or $g$ left-composed with the same if $m=1$. Notes: $S$="ro" is default case (making this operator binary or ternary); $S$ must be a set or "ro" (no bare integers); $m$ = 0 is the default case (making this operator binary or ternary); use "{mau'au}" and "{zai'ai}" in order to quote $f$ and $g$ each; the indices in the implicit tuple mentioned in the definition are positive natural numbers such that said tuple is of form $(x_1, x_2, x_3, ..., x_n, ...)$. For example, maintaining this notation, if $S$="ro" and $m=0$, then the output is $f(g(x_1), g(x_2), ..., g(x_n), ...)$; if $S$ = Set(1, 3, 23) and $m=0$, then the output is $f(g(x_1), x_2, g(x_3), x_4, x_5, ..., x_{21}, x_{22}, g(x_{23}), x_{24}, x_{25}, ..., x_n, ...)$; vel sim. If $h$ is the function output by this expression when $m=0$, then for the same inputs (ignoring $m$), $g \circ h$ is the function output by the same expression but with $m=1$. Obviously, in order to be meaningful, the output of each step along the way must be defined. If $S$ is the empty set and $g$ is defined, then the output is just the function $f$. The output of this operator is a function, so it must have explicit input supplied to it ("it" here referring to the output of this operator) in order to actually have an explicit and concrete result; use mathematical brackets around this operator and its inputs when doing so, particularly when $S$ is omitted (as being equal to the default "ro"). Jargon: Gloss Keywords: Word: extended functional composition, In Sense: Place Keywords: You can go to to see it.