
Definition #71498
 Preferred
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selma'o 
VUhU 
definition 
mekso kary operator, for natural k and 1 < k < 5: ordered input
(f, g, S, m) where f and g are functions, S is a set of positive integers or "ro" (="all"), and m is 0 or 1 (as a toggle); output is a function equivalent to the function f as applied to an input ordered tuple with g applied to the entries/terms with indices in S (or to all entries/terms if S="ro") if m = 0, or g leftcomposed with the same if m = 1.

notes 
S="ro" is default case (making this operator binary or ternary); S must be a set or "ro" (no bare integers); m = 0 is the default case (making this operator binary or ternary); use "mau'au" and "zai'ai" in order to quote f and g each; the indices in the implicit tuple mentioned in the definition are positive natural numbers such that said tuple is of form
(x_{1}, x_{2}, x_{3},..., x_{n},...); thus, notationally, a concrete output of this function, as applied to the aforementioned concrete input tuple, is of form (fa'ai'ai
(f, g, S, m))(x_{1}, x_{2},..., x_{n},...). For example, maintaining this notation, if S="ro" and m = 0, then the output is
f (g(x_{1}), g(x_{2}),..., g(x_{n}),...); if S = Set(1, 3, 23) and m = 0, then the output is
f (g(x_{1}), x_{2}, g(x_{3}), x_{4}, x_{5},..., x_{21}, x_{22}, g(x_{23}), x_{24}, x_{25},..., x_{n},...); vel sim. If h is the function output by this expression when m = 0, then for the same inputs (ignoring m), goh is the function output by the same expression but with m = 1. Obviously, in order to be meaningful, the output of each step along the way must be defined. If S is the empty set and g is defined, then the output is just the function f if m = 0. The output of this operator is a function, so it must have explicit input supplied to it ("it" here referring to the output of this operator) in order to actually have an explicit and concrete result; use mathematical brackets around this operator and its inputs when doing so, particularly when S or m is omitted (as being equal to the default "ro" or 0 resp.).

gloss words 

created by 
krtisfranks 
vote information 
1

time 
Sat Sep 7 23:07:04 2019 

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