ci'ai'u
valsi
ci'ai'u
type
experimental cmavo
creator
time entered
Sun Sep 14 20:26:02 2014
English
Definition #57413 - Preferred
selma'o
VUhU
definition
Mekso unary or binary operator: n-set or integer interval; in unary form, it maps a nonnegative integer X1 = n to the set MATH
$\{1, \dots , n\}$
{1,..., n} (fully, officially, and precisely: the intersection of (a) the set of exactly all positive integers with (b) the closed ordered interval [1, n] such that n≥1; see notes for other n); in binary form, it maps ordered inputs MATH
$(X_1, X_2) = (m, n)$
(X1, X2) = (m, n) to the intersection of (a) the set of exactly all integers with (b) the closed ordered interval [m, n].
notes
0 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), Z+ = N. The upper bound is always specified; when the lower bound is not specified, it defaults to 1 and the upper bound must equal or exceed 1 (else the output is ∅). If this word is represented by f, and Z represents the set of exactly all integers, and MATH
$(n, m \in Z \cup$
(n, m∈Z∪ Set MATH
$(\pm \infty$
(±∞) MATH
$: m \leq n)$
: m≤n), then: MATH
$f(m, n) = Z \cap [m, n]$
f (m, n) = Z∩[m, n], and furthermore: if 1≤n, then MATH
$f(n) = f(1, n) = Z \cap [1, n]$
f (n) = f (1, n) = Z∩[1, n], else f (n) = ∅. The definition extends naturally (and with only trivial modification) to non-integer real-valued n, m, but it is recommended to keep them as integers when possible. Z excludes MATH
$\pm \infty$
±∞.
gloss words
created by
vote information
2
time
Mon Apr 29 04:49:49 2024
Examples