https://wiki.lojban.io/index.php?action=history&feed=atom&title=tamseingutamseingu - Revision history2026-04-27T07:22:14ZRevision history for this page on the wikiMediaWiki 1.45.3https://wiki.lojban.io/index.php?title=tamseingu&diff=18235&oldid=prevNalvaizmiku: Import words via API2026-01-13T16:47:16Z<p>Import words via API</p>
<p><b>New page</b></p><div>==== valsi ====<br />
tamseingu<br />
==== type ====<br />
fu'ivla<br />
==== creator ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== time entered ====<br />
Thu Jan 16 05:21:49 2025<br />
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== English ==<br />
=== Definition #73722 - Preferred ===<br />
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==== definition ====<br />
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Target node <span class="MATH"><i>x</i><sub>1</sub></span> and primary subject node <span class="MATH"><i>x</i><sub>4</sub></span> belong to the same (single) strictly-directed, connected tree graph/network/hierarchy or are related by relation scheme <span class="MATH"><i>x</i><sub>5</sub></span> such that <span class="MATH"><i>x</i><sub>1</sub></span> has coordinates MATH<br />
$(x_2, x_3)$<br />
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<span class="MATH">(<i>x</i><sub>2</sub>, <i>x</i><sub>3</sub>)</span> and <span class="MATH"><i>x</i><sub>4</sub></span> has coordinates <span class="MATH">(0, 0)</span> according to the labelling scheme which is described in the notes hereof.<br />
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==== notes ====<br />
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This word makes all basic familial relationships easily expressible and regular. <span class="MATH"><i>x</i><sub>2</sub></span> is a nonnegative integer; <span class="MATH"><i>x</i><sub>3</sub></span> is an integer (potentially of any signum a priori). <span class="MATH"><i>x</i><sub>5</sub></span> is directed and thus admits descriptions such as "rootward", "parent", "superior"/"ancestor", "leafward", "child", and "descendant"/"subordinate". <span class="MATH"><i>x</i><sub>4</sub></span> is a node which is identified and singled out as being special in the tree, and thus the relationship is not entirely symmetric under exchange of <span class="MATH"><i>x</i><sub>4</sub></span> with any other node. For any target node <span class="MATH"><i>v</i></span> in <span class="MATH"><i>x</i><sub>5</sub></span>, the coördinate label for <span class="MATH"><i>v</i></span> is determined as follows: For the sake of ease and uniformity of notation, denote <span class="MATH"><i>x</i><sub>4</sub></span> by "<span class="MATH">μ</span>"; likewise denote <span class="MATH"><i>x</i><sub>5</sub></span> by "<span class="MATH"><i>G</i></span>". Let/require/assume that the most-recent common direct ancestor of <span class="MATH">μ</span> and <span class="MATH"><i>v</i></span> in/according to <span class="MATH"><i>G</i></span> be essentially-unique and denoted by "mrcda MATH<br />
$_<a class="undefined" href="../dict/G?bg=1;langidarg=2">G</a>(μ, v)$<br />
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<span class="MATH"><sub>G</sub>(μ, <i>v</i>)</span>"; let <span class="MATH">δ</span> be the Kronecker delta function on the nodes of <span class="MATH"><i>G</i></span>; let <span class="MATH">ρ</span> be a binary function on the Cartesian square of the set of nodes of <span class="MATH"><i>G</i></span> mapped to the nonnegative intergers or positive infinity, and be the undirected graph-geodesic distance between its inputs. Let the coördinate label assigned to <span class="MATH"><i>v</i></span> be coörd MATH<br />
$_<a class="undefined" href="../dict/G%2c%20%3bc?bg=1;langidarg=2">G, μ</a>(v) = (ξ_<a class="undefined" href="../dict/G%2c%20%3bc?bg=1;langidarg=2">G, μ</a>(v), υ_<a class="undefined" href="../dict/G%2c%20%3bc?bg=1;langidarg=2">G, μ</a>(v)) = (ξ, υ) = ((1 - δ(v,$<br />
<br />
<span class="MATH"><sub>G,μ</sub>(<i>v</i>) = (ξ<sub>G,μ</sub>(<i>v</i>),υ<sub>G,μ</sub>(<i>v</i>)) = (ξ,υ) = ((1 - δ(<i>v</i>,</span> mrcda MATH<br />
$_<a class="undefined" href="../dict/G?bg=1;langidarg=2">G</a>(μ, v))) ρ(μ,$<br />
<br />
<span class="MATH"><sub>G</sub>(μ, <i>v</i>)))ρ(μ,</span> mrcda MATH<br />
$_<a class="undefined" href="../dict/G?bg=1;langidarg=2">G</a>(μ, v)), ρ(v,$<br />
<br />
<span class="MATH"><sub>G</sub>(μ, <i>v</i>)),ρ(<i>v</i>,</span> mrcda MATH<br />
$_<a class="undefined" href="../dict/G?bg=1;langidarg=2">G</a>(μ, v)) - ρ(μ,$<br />
<br />
<span class="MATH"><sub>G</sub>(μ, <i>v</i>)) - ρ(μ,</span> mrcda MATH<br />
$_<a class="undefined" href="../dict/G?bg=1;langidarg=2">G</a>(μ, v)))$<br />
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<span class="MATH"><sub>G</sub>(μ, <i>v</i>)))</span>. Under these conditions, unique relations/path-shapes which connect <span class="MATH">μ</span> to <span class="MATH"><i>v</i></span> are bijective with the labels; under these conditions, the mapping from labels to nodes should be injective. For example: Assume that <span class="MATH"><i>x</i><sub>4</sub></span> is oneself for simplicity and that <span class="MATH"><i>x</i><sub>5</sub></span> is one's family tree under the assumption that it records only human genetic relationships due to binary sexual reproduction/inheritance and excludes incest (regardless of the graph-geodesic distance otherwise between the participants), marriage or similar relationships, co-parenting, in-law relationships, half or other partial family relationships, step-familial relationships, adoptions, cross-generational co-parenting, distinctions according to age alone or comparisons thereof, and distinctions according to gender/sex alone or comparisons thereof. In this case, if oneself is labelled by <span class="MATH">(0, 0)</span>, then: one's children are labelled by <span class="MATH">(0, 1)</span>, one's grandchildren are labelled by <span class="MATH">(0, 2)</span>, one's <span class="MATH"><i>n</i></span>th-great-grandchildren are labelled by <span class="MATH">(0, 2 + <i>n</i>)</span>, one's parents are labelled by <span class="MATH">(0, - 1)</span>, one's grandparents are labelled by <span class="MATH">(0, - 2)</span>, one's <span class="MATH"><i>nth</i></span>-great-grandparents are labelled by MATH<br />
$(0, -(2 + n))$<br />
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<span class="MATH">(0, - (2 + <i>n</i>))</span>, one's siblings are labelled by <span class="MATH">(1, 0)</span>, one's niblings (children of siblings) are labelled by <span class="MATH">(1, 1)</span>, one's nibling's children are labelled <span class="MATH">(1, 2)</span>, one's neams (siblings of parents) are labelled by <span class="MATH">(2, - 1)</span>, one's 1st cousins 0 times removed (children of neams) are labelled by <span class="MATH">(2, 0)</span>, one's first cousins once removed via neams are labelled by <span class="MATH">(2, 1)</span>, etc. Notice that corporate organization charts, as directed from CEO (root) toward subordinates, can have similar labels. See also: "[[tamne|tamne]]", ".[[anseingu|anseingu]]", "[[grafnseljimcnkipliiu|grafnseljimcnkipliiu]]".<br />
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==== gloss words ====<br />
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<ul><li>[[natlang/en/canonical marked-quipyew co�rdinate|canonical marked-quipyew coördinate ; kinship/cousin labelling system]]</li></ul><br />
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==== created by ====<br />
[[personal/krtisfranks|krtisfranks]]<br />
==== vote information ====<br />
1<br />
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==== time ====<br />
Thu Jan 16 05:30:53 2025<br />
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<br/><font size="+1">Examples</font><br />
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=== Etymology ===</div>Nalvaizmiku