View source for ci'ai'u

==== valsi ====
ci'ai'u
==== type ====
experimental cmavo
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Sun Sep 14 20:26:02 2014
 
== English ==
=== Definition #57413 - Preferred ===
 
==== selma'o ====
VUhU
==== definition ====

Mekso unary or binary operator: <span class="MATH"><i>n</i></span>-set or integer interval; in unary form, it maps a nonnegative integer <span class="MATH"><i>X</i><sub>1</sub> = <i>n</i></span> to the set  MATH
 $\{1, \dots , n\}$
 
<span class="MATH">{1,..., <i>n</i>}</span> (fully, officially, and precisely: the intersection of (a) the set of exactly all positive integers with (b) the closed ordered interval [<span class="MATH">1, <i>n</i></span>] such that <span class="MATH"><i>n</i>≥1</span>; see notes for other <span class="MATH"><i>n</i></span>); in binary form, it maps ordered inputs  MATH
 $(X_1, X_2) = (m, n)$
 
<span class="MATH">(<i>X</i><sub>1</sub>, <i>X</i><sub>2</sub>) = (<i>m</i>, <i>n</i>)</span> to the intersection of (a) the set of exactly all integers with (b) the closed ordered interval [<span class="MATH"><i>m</i>, <i>n</i></span>].

==== notes ====

<span class="MATH">0</span> on its own induces the unary form of this word and thus maps to the empty set ∅. Inputting infinity (for the unary form) produces the set of exactly all positive integers (sometimes also onown as: natural numbers), <span class="MATH"><i>Z</i><sup>+</sup> = <i>N</i></span>. The upper bound is always specified; when the lower bound is not specified, it defaults to <span class="MATH">1</span> and the upper bound must equal or exceed <span class="MATH">1</span> (else the output is ∅). If this word is represented by <span class="MATH"><i>f</i></span>, and <span class="MATH"><i>Z</i></span> represents the set of exactly all integers, and  MATH
 $(n, m \in Z \cup$
 
<span class="MATH">(<i>n</i>, <i>m</i>∈<i>Z</i>∪</span> Set MATH
 $(\pm \infty$
 
<span class="MATH">(±∞</span>) MATH
 $: m \leq n)$
 
<span class="MATH">: <i>m</i>≤<i>n</i>)</span>, then:  MATH
 $f(m, n) = Z \cap [m, n]$
 
<span class="MATH"><i>f</i> (<i>m</i>, <i>n</i>) = <i>Z</i>∩[<i>m</i>, <i>n</i>]</span>, and furthermore: if <span class="MATH">1≤<i>n</i></span>, then  MATH
 $f(n) = f(1, n) = Z \cap [1, n]$
 
<span class="MATH"><i>f</i> (<i>n</i>) = <i>f</i> (1, <i>n</i>) = <i>Z</i>∩[1, <i>n</i>]</span>, else <span class="MATH"><i>f</i> (<i>n</i>) =</span> ∅. The definition extends naturally (and with only trivial modification) to non-integer real-valued <span class="MATH"><i>n</i>, <i>m</i></span>, but it is recommended to keep them as integers when possible. <span class="MATH"><i>Z</i></span> excludes  MATH
 $\pm \infty$
 
<span class="MATH">±∞</span>.

==== gloss words ====

<ul><li>[[natlang/en/integer interval|integer interval]]</li><li>[[natlang/en/natural number interval|natural number interval]]</li><li>[[natlang/en/n-set|n-set]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
2
     
==== time ====
Mon Apr 29 04:49:49 2024



<br/><font size="+1">Examples</font>
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=== Etymology ===