https://wiki.lojban.io/index.php?action=history&feed=atom&title=ci%27ai%27uci'ai'u - Revision history2026-05-07T17:23:50ZRevision history for this page on the wikiMediaWiki 1.45.3https://wiki.lojban.io/index.php?title=ci%27ai%27u&diff=2328&oldid=prevNalvaizmiku: Import words via API2026-01-13T14:30:30Z<p>Import words via API</p>
<p><b>New page</b></p><div>==== valsi ====<br />
ci'ai'u<br />
==== type ====<br />
experimental cmavo<br />
==== creator ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== time entered ====<br />
Sun Sep 14 20:26:02 2014<br />
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== English ==<br />
=== Definition #57413 - Preferred ===<br />
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==== selma'o ====<br />
VUhU<br />
==== definition ====<br />
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Mekso unary or binary operator: <span class="MATH"><i>n</i></span>-set or integer interval; in unary form, it maps a nonnegative integer <span class="MATH"><i>X</i><sub>1</sub> = <i>n</i></span> to the set MATH<br />
$\{1, \dots , n\}$<br />
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<span class="MATH">{1,..., <i>n</i>}</span> (fully, officially, and precisely: the intersection of (a) the set of exactly all positive integers with (b) the closed ordered interval [<span class="MATH">1, <i>n</i></span>] such that <span class="MATH"><i>n</i>≥1</span>; see notes for other <span class="MATH"><i>n</i></span>); in binary form, it maps ordered inputs MATH<br />
$(X_1, X_2) = (m, n)$<br />
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<span class="MATH">(<i>X</i><sub>1</sub>, <i>X</i><sub>2</sub>) = (<i>m</i>, <i>n</i>)</span> to the intersection of (a) the set of exactly all integers with (b) the closed ordered interval [<span class="MATH"><i>m</i>, <i>n</i></span>].<br />
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==== notes ====<br />
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<span class="MATH">0</span> 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 all positive integers (sometimes also onown as: natural numbers), <span class="MATH"><i>Z</i><sup>+</sup> = <i>N</i></span>. The upper bound is always specified; when the lower bound is not specified, it defaults to <span class="MATH">1</span> and the upper bound must equal or exceed <span class="MATH">1</span> (else the output is ∅). If this word is represented by <span class="MATH"><i>f</i></span>, and <span class="MATH"><i>Z</i></span> represents the set of exactly all integers, and MATH<br />
$(n, m \in Z \cup$<br />
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<span class="MATH">(<i>n</i>, <i>m</i>∈<i>Z</i>∪</span> Set MATH<br />
$(\pm \infty$<br />
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<span class="MATH">(±∞</span>) MATH<br />
$: m \leq n)$<br />
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<span class="MATH">: <i>m</i>≤<i>n</i>)</span>, then: MATH<br />
$f(m, n) = Z \cap [m, n]$<br />
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<span class="MATH"><i>f</i> (<i>m</i>, <i>n</i>) = <i>Z</i>∩[<i>m</i>, <i>n</i>]</span>, and furthermore: if <span class="MATH">1≤<i>n</i></span>, then MATH<br />
$f(n) = f(1, n) = Z \cap [1, n]$<br />
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<span class="MATH"><i>f</i> (<i>n</i>) = <i>f</i> (1, <i>n</i>) = <i>Z</i>∩[1, <i>n</i>]</span>, else <span class="MATH"><i>f</i> (<i>n</i>) =</span> ∅. The definition extends naturally (and with only trivial modification) to non-integer real-valued <span class="MATH"><i>n</i>, <i>m</i></span>, but it is recommended to keep them as integers when possible. <span class="MATH"><i>Z</i></span> excludes MATH<br />
$\pm \infty$<br />
<br />
<span class="MATH">±∞</span>.<br />
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==== gloss words ====<br />
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<ul><li>[[natlang/en/integer interval|integer interval]]</li><li>[[natlang/en/natural number interval|natural number interval]]</li><li>[[natlang/en/n-set|n-set]]</li></ul><br />
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==== created by ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== vote information ====<br />
2<br />
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==== time ====<br />
Mon Apr 29 04:49:49 2024<br />
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<br/><font size="+1">Examples</font><br />
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=== Etymology ===</div>Nalvaizmiku