Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Sun, 28 Apr 2024 21:46:27 -0700 Received: from [192.168.123.254] (port=38448 helo=jiten.lojban.org) by 11bda84a326c with smtp (Exim 4.96) (envelope-from ) id 1s1IuE-000Eoq-12 for jbovlaste-admin@lojban.org; Sun, 28 Apr 2024 21:46:27 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Mon, 29 Apr 2024 04:46:21 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word ci'ai'u -- By krtisfranks Date: Mon, 29 Apr 2024 04:46:21 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: 0.0 (/) X-Spam_score: 0.0 X-Spam_score_int: 0 X-Spam_bar: / In jbovlaste, the user krtisfranks has edited a definition of "ci'ai'u" in the language "English". Differences: 2,2c2,2 < unary or binary mex operator: $n$-set or integer interval; in unary form, it maps a nonnegative integer $X_1 = n$ to the set $\{1, \dots , n\}$ (fully, officially, and precisely: the intersection of the set of exactly all positive with the closed ordered interval [$1, n$] such that $n \geq 1$); in binary form, it maps ordered inputs $(X_1, X_2) = (m, n)$ to the intersection of the set of exactly all integers with the closed interval [$m, n$]. --- > Mekso unary or binary operator: $n$-set or integer interval; in unary form, it maps a nonnegative integer $X_1 = n$ to the set $\{1, \dots , n\}$ (fully, officially, and precisely: the intersection of (a) the set of exactly all positive integers with (b) the closed ordered interval [$1, n$] such that $n \geq 1$); in binary form, it maps ordered inputs $(X_1, X_2) = (m, n)$ to the intersection of (a) the set of exactly all integers with (b) the closed interval [$m, n$]. Old Data: Definition: unary or binary mex operator: $n$-set or integer interval; in unary form, it maps a nonnegative integer $X_1 = n$ to the set $\{1, \dots , n\}$ (fully, officially, and precisely: the intersection of the set of exactly all positive with the closed ordered interval [$1, n$] such that $n \geq 1$); in binary form, it maps ordered inputs $(X_1, X_2) = (m, n)$ to the intersection of the set of exactly all integers with the closed interval [$m, n$]. Notes: $0$ on its own induces the unary form of this word and thus maps to the empty set ∅. Inputting infinity (for the unary form) produces the set of exactly positive integers (natural numbers), $Z^{+} = N$. The upper bound is always specified; when the lower bound is not specified, it defaults to $1$ and the upper bound must equal or exceed $1$ (else the output is ∅). If this word is represented by $f$, and $Z$ represents the set of exactly all integers, and $(n, m \in Z \cup$ Set$(\pm \infty$)$: m \leq n)$, then: $f(m, n) = Z \cap [m, n]$, and furthermore: if $1 \leq n$, then $f(n) = f(1, n) = Z \cap [1, n]$, else $f(n) =$ ∅. The definition extends naturally (and with only trivial modification) to non-integer real-valued $n, m$, but it is recommended to keep them as integers when possible. $Z$ excludes $\pm \infty$. Jargon: Gloss Keywords: Word: integer interval, In Sense: Word: natural number interval, In Sense: Word: n-set, In Sense: Place Keywords: New Data: Definition: Mekso unary or binary operator: $n$-set or integer interval; in unary form, it maps a nonnegative integer $X_1 = n$ to the set $\{1, \dots , n\}$ (fully, officially, and precisely: the intersection of (a) the set of exactly all positive integers with (b) the closed ordered interval [$1, n$] such that $n \geq 1$); in binary form, it maps ordered inputs $(X_1, X_2) = (m, n)$ to the intersection of (a) the set of exactly all integers with (b) the closed interval [$m, n$]. Notes: $0$ on its own induces the unary form of this word and thus maps to the empty set ∅. Inputting infinity (for the unary form) produces the set of exactly positive integers (natural numbers), $Z^{+} = N$. The upper bound is always specified; when the lower bound is not specified, it defaults to $1$ and the upper bound must equal or exceed $1$ (else the output is ∅). If this word is represented by $f$, and $Z$ represents the set of exactly all integers, and $(n, m \in Z \cup$ Set$(\pm \infty$)$: m \leq n)$, then: $f(m, n) = Z \cap [m, n]$, and furthermore: if $1 \leq n$, then $f(n) = f(1, n) = Z \cap [1, n]$, else $f(n) =$ ∅. The definition extends naturally (and with only trivial modification) to non-integer real-valued $n, m$, but it is recommended to keep them as integers when possible. $Z$ excludes $\pm \infty$. Jargon: Gloss Keywords: Word: integer interval, In Sense: Word: natural number interval, In Sense: Word: n-set, In Sense: Place Keywords: You can go to to see it.