View source for tseingu

==== valsi ====
tseingu
==== type ====
fu'ivla
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Mon Nov 23 22:48:30 2015
 
== English ==
=== Definition #68108 - Preferred ===
 
==== definition ====

<span class="MATH"><i>x</i><sub>1</sub></span> (node in a tree graph) and <span class="MATH"><i>x</i><sub>2</sub></span> (node in the same tree graph) have an essentially unique most recent (graph-nearest) common ancestor node A such that <span class="MATH"><i>x</i><sub>3</sub></span> [nonnegative integer; li] is the minimum element of the set consisting only of <span class="MATH"><i>d</i> (</span>A<span class="MATH">, <i>x</i><sub>1</sub>)</span> and of <span class="MATH"><i>d</i> (</span>A<span class="MATH">, <i>x</i><sub>2</sub>)</span>, and such that <span class="MATH"><i>x</i><sub>4</sub></span> [integer; li] is <span class="MATH"><i>d</i> (</span>A MATH
 $, x_1) - d($
 
<span class="MATH">, <i>x</i><sub>1</sub>) - <i>d</i> (</span>A<span class="MATH">, <i>x</i><sub>2</sub>)</span>, where <span class="MATH"><i>d</i></span> is the graph geodesic distance (defined to be infinite if nodes are not connected in the correct direction).

==== notes ====

While technically not good, this definition also employs the convention that <span class="MATH"><i>x</i><sub>3</sub></span> is positive (countable) infinity if <span class="MATH"><i>A</i></span> does not exist, meaning that <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span> belong to mutually disjoint trees (or if at least one of them is undefined); in this case, <span class="MATH"><i>x</i><sub>4</sub></span> is not well-defined (see: "[[zi'au|zi'au]]"). This word can be used to specify the concept of "<span class="MATH"><i>n</i></span>th cousin <span class="MATH"><i>m</i></span>-times removed"-ness; <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span> would be the cousins, <span class="MATH"><i>x</i><sub>3</sub> - 1 = <i>n</i></span>, and <span class="MATH"><i>x</i><sub>4</sub></span> is closely related to <span class="MATH"><i>m</i></span> but is signed. If one views the tree graphs to which <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span> belong with the viewing perspective such that siblings and spouses are mutually separated horizontally and such that ancestors are separated from their descendants vertically (with ancestors in the positive direction relative to their descendants), then <span class="MATH"><i>x</i><sub>3</sub></span> is the unsigned horizontal distance between <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span>. Additionally, <span class="MATH"><i>x</i><sub>4</sub></span> is, approximately, the signed generational offset/difference between subjects <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span>; it is their signed 'vertical' difference under the aforementioned viewing perspective and sign convention. The relationship need not actually be cousinhood  (as perceived by English); direct ancestor-descendant pairs, (aunt/uncle)-(niece/nephew) pairs, and in fact any pair of family members with a well-specified most recent common ancestor (that is known) have this relationship to one another. This word can be used for specifying the number of "great"'s in the title of a relationship between <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span> (with some calculational forethought). The tree diagram can be more generic than a family tree though; thus cousinhood is just a way to put it into context/application and is not really essential to the meaning except through analogy. Notice the ordering of all terms; if the graph is directed, the arguments of the distance matters. The graph should probably be a tree locally if it is to be a well-defined relationship. <span class="MATH"><i>x</i><sub>3</sub></span> is unchanged but <span class="MATH"><i>x</i><sub>4</sub></span> is negated (multiplied by <span class="MATH">-1</span>) by/under exchange of <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span>. The ordered pair  MATH
 $(x_3, x_4)$
 
<span class="MATH">(<i>x</i><sub>3</sub>, <i>x</i><sub>4</sub>)</span> is named "consanguistance between <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span> (in that order)" by Curtis Franks. For a normal family tree and fixed <span class="MATH"><i>x</i><sub>1</sub></span> therein, consanguistance produces countably many equivalence classes of nodes. It does not recognize the difference between half or full relatives, marriages/parentings are either unsupported (when <span class="MATH"><i>x</i><sub>3</sub> &gt; 0</span>) or are reduced to be equivalent (when <span class="MATH"><i>x</i><sub>3</sub> = 0</span> and  MATH
 $x_4 \neq 0$
 
<span class="MATH"><i>x</i><sub>4</sub>≠ 0</span>), and gender/sex are ignored/reduced to equivalence. The set of nodes <span class="MATH"><i>x</i><sub>2</sub></span> with <span class="MATH"><i>x</i><sub>3</sub> = 0</span> is called <span class="MATH"><i>x</i><sub>1</sub></span>'s (the subject's) genealogical line (id est: if <span class="MATH"><i>x</i><sub>3</sub> = 0</span>, then <span class="MATH"><i>x</i><sub>1</sub></span> re'au'e ja se dzena <span class="MATH"><i>x</i><sub>2</sub></span> according to the edge relation on the graph or <span class="MATH"><i>x</i><sub>1</sub> = <i>x</i><sub>2</sub></span>); the set of nodes with <span class="MATH"><i>x</i><sub>3</sub> &gt; 0</span> are sibling/branch/side lines, which could be labelled and ordered, but doing so would be somewhat difficult with this word. This word focuses on the relationship between <span class="MATH"><i>x</i><sub>1</sub></span> and <span class="MATH"><i>x</i><sub>2</sub></span>, not the relationship between each of them and A; for that, see ".[[anseingu|anseingu]]". The underlying tree graph is, modulo an equivalence relation involving tseingu, a 'quipyew' tree graph (see "[[grafnkipliiu|grafnkipliiu]]"). This concept is fairly unnatural and convoluted, so it is probably [[malgli|malgli]] except for the purpose of translations; in a natural, culturally-neutral Lojbanic context, ".anseingu" is preferred.

==== gloss words ====

<ul><li>[[natlang/en/consanguinity values|consanguinity values]]</li><li>[[natlang/en/consanguistance|consanguistance ; C. Franks' neologism, genealogy]]</li><li>[[natlang/en/cousin degree|cousin degree]]</li><li>[[natlang/en/cousin order|cousin order ; ordinal of cousin relationship]]</li><li>[[natlang/en/cousin removal|cousin removal]]</li><li>[[natlang/en/degree of removal|degree of removal ; cousin relationship]]</li><li>[[natlang/en/kinship number|kinship number]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
1
     
==== time ====
Fri Aug  3 06:39:16 2018

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=== Etymology ===