modju

valsi

modju

type

experimental gismu

creator

krtisfranks

time entered

Wed Jul 26 02:54:38 2017  

English

Definition #69775 - Preferred

 

definition

x₁ (li; number) is congruent to x₂ (li; number; see description for canonical/traditional/contextless default usage) modulo x₃ (li; number); MATH

$\frac{(x_1 - x_2)}{x_3}$

<img alt="${\fracTemplate:(x 1 - x 2)Template:x 3}$" src="/jbovlaste_export/inez29tiq9/img1.png" style="height: 3.50ex; vertical-align: -1.15ex; "/> is an integer.

notes

In order to be clear (in case of poor display), (x₁ - x₂)/x₃ is an integer, possibly (but not necessarily) nonpositive. Traditionally, but not necessarily, x₃ is a strictly positive integer (in particular, x₃ is nonzero) and is called "(the) modulus"; if x₃ = 1, then x₁ and x₂ differ only by an integer amount - in other words, they have the same fractional part. Technically, x₁ and x₂ are symmetric under mutual exchange and can even be equivalent; however, in a manner morally analogous to "srana", x₂ is canonically/traditionally either the common residue (the unique element in the space which is congruent to x₁ mod x₃ and which is greater than or equal to 0 and strictly less than x₃) or the minimal residue (denoting the common residue by c, the minimal residue is either c xor c - x₃, whichever is strictly less than the other in absolute value), and this may even be considered as its contextless default meaning (such as in "lo se modju"). See also: dilcu, dunli, mintu, simsa, panra, dilma (a particularly close relative and generalization of this word with slightly different focus). This word is essentially identical with dilcrmadjulu; consider this word to be its gismu equivalent. It is not the modulus operator; for that, use veldilcu or vei'u. It is a specific type of terpanryziltolju'i, although both occupy the word "modulo" in English. This word does not have direct access to "integer-part" but does to "fractional-part".

gloss words

• 2-parity
• color ; 3-parity
• congruent ; modulo
• fractional-part
• integer-part
• kuller ; 3-parity
• modulo ; divison remainder congruence
• modulus ; of a congruence relation
• n-parity

created by

krtisfranks

vote information

3

time

Sat Nov 12 22:50:06 2022

Examples

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