View source for kei'ai

==== valsi ====
kei'ai
==== type ====
experimental cmavo
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Wed Dec 17 06:40:33 2014
 
== English ==
=== Definition #63936 - Preferred ===
 
==== selma'o ====
PEhO
==== definition ====
mekso style converter: elementwise application of operator
==== notes ====

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 "<span class="MATH"><i>x</i><sub>i</sub></span>" represent a set for all i; then <span class="MATH"><i>x</i><sub>1</sub></span> kei'ai @ <span class="MATH"><i>x</i><sub>2</sub></span> boi <span class="MATH"><i>x</i><sub>3</sub></span> boi <span class="MATH"><i>x</i><sub>4</sub></span> boi <span class="MATH">...</span> = Set(@ MATH
 $(t_1, t_2, t_3, t_4, \dots)$
 
<span class="MATH">(<i>t</i><sub>1</sub>, <i>t</i><sub>2</sub>, <i>t</i><sub>3</sub>, <i>t</i><sub>4</sub>,...)</span>: <span class="MATH"><i>t</i><sub>i</sub></span> in <span class="MATH"><i>x</i><sub>i</sub></span> 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,  MATH
 $F(A) = \operatorname<a class="undefined" href="../dict/img?bg=1;langidarg=2">img</a>_f (A)$
 
<span class="MATH"><i>F</i>(<i>A</i>) = <img alt="$\operatorname$" src="/jbovlaste_export/f_74mqwZub/img1.png" style=""/><i>img</i><sub>f</sub>(<i>A</i>)</span>, which is the image of A under the function/map f.  See also [[kei'au|kei'au]] for a similar but different word.

==== gloss words ====

<ul><li>[[natlang/en/difference set|difference set ; mekso; generalized]]</li><li>[[natlang/en/image under f|image under f ; image of a function on a set]]</li><li>[[natlang/en/set of results of operator|set of results of operator ; mekso]]</li><li>[[natlang/en/sum set|sum set ; mekso; generalized]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
2
     
==== time ====
Mon Jul 24 07:25:35 2017

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=== Etymology ===