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valsi 
fi'au 
type 
experimental cmavo 
creator 
krtisfranks 
time entered 
Mon Apr 2 06:25:33 2018 
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English


Definition #70585
 Preferred
[edit]


definition 
mekso operator: continued fraction, Kettenbruch notation; for ordered input
(X_{1}, X_{2}, X_{3}, X_{4}), where: X_{1} is an ordered pair of functions and X_{2} is a free or dummy variable/input/index which ranges through set X_{3} in order(ing) X_{4}, the result is
K_{(X2,(X3, X4))}(X_{1}(X_{2})) for Kettenbruch notation K.

notes 
X_{1} will be an ordered pair of functions defined on X_{3} and with input X_{2}. Let
X_{1} = (a, b) where 'a' and b are each functions (defined on X_3), X_{3} 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 X_{4} be the standard ordering on X_{3}; then the output will be: a(0) + b(0)/(a(1) + b(1)/(a(2) + b(2)/(.../(a(n1) + b(n1)/(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 welldefinition; the inputs of 'a' and b technically can be ordered tuples so long as they symbolically include X_{2} and all other parameters are specified. In general,
a(min(X_{3})), for min being defined according to the ordering X_{4}, 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 X_{3} being the empty set can be devised, or 'a' or b could be functionvalued or otherwise exoticvalued functions (so long as their outputs have sum, division, and closure properties), etc. See also: "se'au". If diphthong "eu" is ever accepted into Lojban, this definition would preferably be moved to "fi'eu" (because the "eu" would also be etymologically tied to "Kettenbruch", and the "au" diphthong is more basic and should be reserved for higherpriority words).

gloss words 

created by 
krtisfranks 
vote information 
1

time 
Mon Apr 2 06:27:46 2018 

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