https://wiki.lojban.io/index.php?action=history&feed=atom&title=kei%27ikei'i - Revision history2026-05-02T21:45:55ZRevision history for this page on the wikiMediaWiki 1.45.3https://wiki.lojban.io/index.php?title=kei%27i&diff=8356&oldid=prevNalvaizmiku: Import words via API2026-01-13T15:23:21Z<p>Import words via API</p>
<p><b>New page</b></p><div>==== valsi ====<br />
kei'i<br />
==== type ====<br />
experimental cmavo<br />
==== creator ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== time entered ====<br />
Wed Dec 24 22:33:07 2014<br />
<br />
== English ==<br />
=== Definition #63968 - Preferred ===<br />
<br />
==== selma'o ====<br />
KEIhI<br />
==== definition ====<br />
<br />
non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: MATH<br />
$X_{2} ^{C}$<br />
<br />
<span class="MATH"><i>X</i><sub>2</sub><sup>C</sup></span>; binary: MATH<br />
${X_1}\setminus{X_2}$<br />
<br />
<span class="MATH"><i>X</i><sub>1</sub> <img alt="$\setminus$" src="/jbovlaste_export/vj83eWeBWw/img1.png" style="height: 2.38ex; vertical-align: -0.70ex; "/> <i>X</i><sub>2</sub></span>.<br />
<br />
==== notes ====<br />
<br />
Each input must be a set or similar. The definition of the binary case expands to "the set of exactly those elements which are in <span class="MATH"><i>X</i><sub>1</sub></span> but not in <span class="MATH"><i>X</i><sub>2</sub></span>". This word and operator has ordered input: '<span class="MATH"><i>X</i><sub>1</sub></span> kei'i <span class="MATH"><i>X</i><sub>2</sub></span>' is not generally equivalent to '<span class="MATH"><i>X</i><sub>2</sub></span> kei'i <span class="MATH"><i>X</i><sub>1</sub></span>'; in other words, the operator is not commutative. If unary (meaning that <span class="MATH"><i>X</i><sub>1</sub></span> is not explicitly specified in a hypothetical expression " MATH<br />
$<a class="undefined" href="../dict/X_1?bg=1;langidarg=2">X_1</a>\setminus<a class="undefined" href="../dict/X_2?bg=1;langidarg=2">X_2</a>$<br />
<br />
<span class="MATH"><i>X</i><sub>1</sub> <img alt="$\setminus$" src="/jbovlaste_export/b0131tpoQq/img1.png" style="height: 2.38ex; vertical-align: -0.70ex; "/> <i>X</i><sub>2</sub></span>"), then <span class="MATH"><i>X</i><sub>1</sub></span> is taken to be some universal set <span class="MATH"><i>O</i></span> in/of the discourse (of which all other mentioned or relevantly formable sets are subsets, at the least); in this latter case, the word operates as the set (absolute) complement of the explicitly mentioned set here designated as <span class="MATH"><i>X</i><sub>2</sub></span> for clarity (id est: the output is MATH<br />
$O\setminus<a class="undefined" href="../dict/X_2?bg=1;langidarg=2">X_2</a>=<a class="undefined" href="../dict/X_2?bg=1;langidarg=2">X_2</a>^<a class="undefined" href="../dict/C?bg=1;langidarg=2">C</a>$<br />
<br />
<span class="MATH"><i>O</i> <img alt="$\setminus$" src="/jbovlaste_export/b0131tpoQq/img1.png" style="height: 2.38ex; vertical-align: -0.70ex; "/> <i>X</i><sub>2</sub> = <i>X</i><sub>2</sub><sup>C</sup></span>, where "<span class="MATH"><sup>C</sup></span>" denotes the set absolute complement; in other words, it is the set of all elements which may be under consideration such that they are not elements of the explicitly specified set). When binary with both <span class="MATH"><i>X</i><sub>1</sub></span> and <span class="MATH"><i>X</i><sub>2</sub></span> explicitly specified, this word/operator is the set relative complement. This word is somewhat analogous to, depending on its arity, logical 'NOT' or 'AND NOT' (just as set intersection is analogous to logical 'AND', set union is analogous to logical '(AND/)OR' and set symmetric difference is analogous to 'XOR'). The preferred description/name in English is "set (theoretic) exclusion". See also: "[[kleivmu|kleivmu]]". For reference: https://en.wikipedia.org/wiki/Complement_(set_theory) .<br />
<br />
==== gloss words ====<br />
<br />
<ul><li>[[natlang/en/\|\ ; set theoretic operator (mekso, connective): set exclusion]]</li><li>[[natlang/en/absolute complement|absolute complement ; set-theoretic operator/connective (cmavo)]]</li><li>[[natlang/en/C|C ; set theoretic operator (mekso, connective): set complement]]</li><li>[[natlang/en/exclusion|exclusion ; set theoretic operator (mekso, connective)]]</li><li>[[natlang/en/relative complement|relative complement ; set-theoretic operator/connective (cmavo)]]</li><li>[[natlang/en/set complement|set complement ; set theoretic operator (mekso, connective): relative or absolute]]</li><li>[[natlang/en/set difference|set difference ; set theoretic operator (mekso, connective)]]</li><li>[[natlang/en/set exclusion|set exclusion ; set theoretic operator (mekso, connective)]]</li><li>[[natlang/en/set minus|set minus ; set theoretic operator (mekso, connective)]]</li><li>[[natlang/en/set subtraction|set subtraction ; set theoretic operator (mekso, connective)]]</li></ul><br />
<br />
==== created by ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== vote information ====<br />
2<br />
<br />
==== time ====<br />
Fri Nov 4 11:17:20 2022<br />
<br />
[[comments.html?valsi=27870;definition=63968|[View<br />
Comments For This Definition]]] <br />
<br />
<br/><font size="+1">Examples</font><br />
<hr/><br />
<dl><br />
</dl><br />
<br />
=== Etymology ===</div>Nalvaizmiku