Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Sun, 28 Apr 2024 21:40:36 -0700 Received: from [192.168.123.254] (port=34078 helo=jiten.lojban.org) by 11bda84a326c with smtp (Exim 4.96) (envelope-from ) id 1s1IoY-000EoS-2P for jbovlaste-admin@lojban.org; Sun, 28 Apr 2024 21:40:35 -0700 Received: by jiten.lojban.org (sSMTP sendmail emulation); Mon, 29 Apr 2024 04:40:29 +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 04:40:29 +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: 5,5c5,5 < $0$ 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 $1$. If this word is represented by $f$, $Z$ represents the set of exactly all integers, and $(n, m \in Z \cup$ {$\pm \infty$}$: m \leq n)$, 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. --- > $0$ 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. 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 $\{1, \dots , n\}$ (the intersection of the set of exactly all positive with the closed ordered interval [$1, n$] such that $n$ geq $1$); in binary torm, it maps ordered inputs $(X_1, X_2) = (m, n)$ to intersection of the set of exactly all integers with [$m, n$]. 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 $1$. If this word is represented by $f$, $Z$ represents the set of exactly all integers, and $(n, m \in Z \cup$ {$\pm \infty$}$: m \leq n)$, 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. Jargon: Gloss Keywords: Word: integer interval, In Sense: Word: natural number interval, In Sense: Word: n-set, In Sense: Place Keywords: New 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 $\{1, \dots , n\}$ (the intersection of the set of exactly all positive with the closed ordered interval [$1, n$] such that $n$ geq $1$); in binary torm, it maps ordered inputs $(X_1, X_2) = (m, n)$ to intersection of the set of exactly all integers with [$m, n$]. 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. 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.