kei'i

valsi

kei'i

type

experimental cmavo

creator

krtisfranks

time entered

Wed Dec 24 22:33:07 2014  

English

Definition #63968 - Preferred

 

selma'o

KEIhI

definition

non-logical connective/mekso operator - of arity only 1 xor 2: set (absolute) complement, or set exclusion (relative complement). Unary: MATH

$X_{2} ^{C}$

X₂^C; binary: MATH

${X_1}\setminus{X_2}$

X₁ <img alt="$\setminus$" src="/jbovlaste_export/vj83eWeBWw/img1.png" style="height: 2.38ex; vertical-align: -0.70ex; "/> X₂.

notes

Each input must be a set or similar. The definition of the binary case expands to "the set of exactly those elements which are in X₁ but not in X₂". This word and operator has ordered input: 'X₁ kei'i X₂' is not generally equivalent to 'X₂ kei'i X₁'; in other words, the operator is not commutative. If unary (meaning that X₁ is not explicitly specified in a hypothetical expression " MATH

$<a class="undefined" href="../dict/X_1?bg=1;langidarg=2">X_1</a>\setminus<a class="undefined" href="../dict/X_2?bg=1;langidarg=2">X_2</a>$

X₁ <img alt="$\setminus$" src="/jbovlaste_export/b0131tpoQq/img1.png" style="height: 2.38ex; vertical-align: -0.70ex; "/> X₂"), then X₁ is taken to be some universal set O in/of the discourse (of which all other mentioned or relevantly formable sets are subsets, at the least); in this latter case, the word operates as the set (absolute) complement of the explicitly mentioned set here designated as X₂ for clarity (id est: the output is MATH

$O\setminus<a class="undefined" href="../dict/X_2?bg=1;langidarg=2">X_2</a>=<a class="undefined" href="../dict/X_2?bg=1;langidarg=2">X_2</a>^<a class="undefined" href="../dict/C?bg=1;langidarg=2">C</a>$

O <img alt="$\setminus$" src="/jbovlaste_export/b0131tpoQq/img1.png" style="height: 2.38ex; vertical-align: -0.70ex; "/> X₂ = X₂^C, where "^C" denotes the set absolute complement; in other words, it is the set of all elements which may be under consideration such that they are not elements of the explicitly specified set). When binary with both X₁ and X₂ explicitly specified, this word/operator is the set relative complement. This word is somewhat analogous to, depending on its arity, logical 'NOT' or 'AND NOT' (just as set intersection is analogous to logical 'AND', set union is analogous to logical '(AND/)OR' and set symmetric difference is analogous to 'XOR'). The preferred description/name in English is "set (theoretic) exclusion". See also: "kleivmu". For reference: https://en.wikipedia.org/wiki/Complement_(set_theory) .

gloss words

• \ ; set theoretic operator (mekso, connective): set exclusion
• absolute complement ; set-theoretic operator/connective (cmavo)
• C ; set theoretic operator (mekso, connective): set complement
• exclusion ; set theoretic operator (mekso, connective)
• relative complement ; set-theoretic operator/connective (cmavo)
• set complement ; set theoretic operator (mekso, connective): relative or absolute
• set difference ; set theoretic operator (mekso, connective)
• set exclusion ; set theoretic operator (mekso, connective)
• set minus ; set theoretic operator (mekso, connective)
• set subtraction ; set theoretic operator (mekso, connective)

created by

krtisfranks

vote information

2

time

Fri Nov 4 11:17:20 2022

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