# kei'ai PEhO …KUhE experimental cmavo

mekso style converter: elementwise application of operator

Prefixed to an operator/function that operates on numbers, thereby transforming it into a set operator (thus its arguments must be sets where before they were numbers), as defined in a given structure; the result is a function of the same arity. Produces the set of all numbers that are given by some ordered tuple of elements (the nth term of which belongs to the nth set specified, for all n) with the operator acting on them/the tuple (per the rules of that operator). The set produced may include empty terms and/or infinity. Let "@" represent the operator and "xi" represent a set for all i; then x1 kei'ai @ x2 boi x3 boi x4 boi \dots = Set(@(t1, t: ti in xi for all i); the ordered Cartesian product of the operands of 'kei'ai @' must be a subset of the domain set of '@'. If f is unitary and we convert it to a set operator 'kei'ai f' = F, then for any good set A, F(A) = \operatornameimgf (A), which is the image of A under the function/map f. See also kei'au for a similar but different word.

## In notes:

kei'au
mekso operator: finite result set derived from/on set A with/due to operator/function B under ordering of application C