Nalvaizmiku: Import words via API

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Import words via API

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==== valsi ====
fi'au
==== type ====
experimental cmavo
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Mon Apr 2 06:25:33 2018

== English ==
=== Definition #70585 - Preferred ===

==== definition ====

mekso operator: continued fraction, Kettenbruch notation; for ordered input MATH
$(X_1, X_2, X_3, X_4)$

(X1, X2, X3, X4), where: X1 is an ordered pair of functions and X2 is a free or dummy variable/input/index which ranges through set X3 in order(ing) X4, the result is MATH
$K_{(X_2, (X_3, X_4))} (X_1(X_2))$

K(X2,(X3, X4))(X1(X2)) for Kettenbruch notation K.

==== notes ====

X1 will be an ordered pair of functions defined on X3 and with input X2. Let MATH
$X_1 = (a, b)$

X1 = (a, b) where 'a' and b are each functions (defined on X_3), X3 be the set of all nonnegative integers which are strictly less than some positive integer or positive infinity (denoted by "n+1") as determined by the context/problem, and X4 be the standard ordering on X3; then the output will be: a(0) + b(0)/(a(1) + b(1)/(a(2) + b(2)/(.../(a(n-1) + b(n-1)/(a(n) + b(n)))))), where division has higher operator priority than addition and where, if n is positive infinity, then the expression never terminates and convergence of subfractions is necessary for well-definition; the inputs of 'a' and b technically can be ordered tuples so long as they symbolically include X2 and all other parameters are specified.� In general, MATH
$a(min(X_3))$

a(min(X3)), for min being defined according to the ordering X4, will be the formally 'integer'-part of the expression (even if it evaluates to a fraction) - in other words, it is the number which is entirely outside of the nested fractions. This operator is intended to be maximally general; some definition for X3 being the empty set can be devised, or 'a' or b could be function-valued or otherwise exotic-valued functions (so long as their outputs have sum, division, and closure properties), etc. See also: "[[se'au|se'au]]". If diphthong "eu" is ever accepted into Lojban, this definition would preferably be moved to "[[fi'eu|fi'eu]]" (because the "eu" would also be etymologically tied to "Kettenbruch", and the "au" diphthong is more basic and should be reserved for higher-priority words).

==== gloss words ====

<ul><li>[[natlang/en/continued fraction|continued fraction ; operator/big operator K]]</li><li>[[natlang/en/Kettenbruch|Kettenbruch ; operator/big operator K]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
1

==== time ====
Mon Apr 2 06:27:46 2018

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=== Etymology ===

fi'au - Revision history

Nalvaizmiku: Import words via API