# fi'au experimental cmavo

mekso operator: continued fraction, Kettenbruch notation; for ordered input (X1, X, 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 K(X for Kettenbruch notation K.

X1 will be an ordered pair of functions defined on X3 and with input X2. Let 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, 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". 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 higher-priority words).