In constructive mathematics, an apartness relation is a constructive form of inequality, and is often taken to be more basic than equality.
An apartness relation is often written as (⧣ in unicode) to distinguish from the negation of equality (the denial inequality), which is weaker. In the literature, the symbol is found to be used for either of these.
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also follows that every apartnessrelation is the complement of an equivalence relation, and the only tight apartnessrelation on a given set is the complement...
Johansson Apart (Léon album), 2020 album by Swedish singer Léon Apartnessrelation This disambiguation page lists articles associated with the title Apart. If...
correspond to the normal subgroups). Any equivalence relation is the negation of an apartnessrelation, though the converse statement only holds in classical...
f(x)<\left(g(x)\right)^{2}} Look up inequation in Wiktionary, the free dictionary. Apartnessrelation — a form of inequality in constructive mathematics Equation Equals...
line by some means, a collection extending the rationals and with an apartnessrelation definable from an asymmetric order structure. Center stage takes a...
is the primorial of n. In constructive mathematics, # denotes an apartnessrelation. In computational complexity theory, #P denotes a complexity class...
the classical notion of a field. It is essentially a field with an apartnessrelation. A commutative ring is a Heyting field if it is a field in the sense...
constructive mathematics, one often takes a setoid with an apartnessrelation instead of an equivalence relation, called a constructive setoid. One sometimes also...
generalizes more easily. Mathematically, in wave mechanics, the uncertainty relation between position and momentum arises because the expressions of the wavefunction...
may on any set A {\displaystyle A} define the logically positive apartnessrelation x # A y := ∃ ( f ∈ N A ) . f ( x ) ≠ f ( y ) {\displaystyle x\,\#_{A}\...
canonically identified with the quotient topology under the equivalence relation defined by f. Dually, for a function f from a set S to a topological space...
whether they inhere in the subject or not: Primary categories: Substance, Relation, Quantity and Quality Secondary categories: Place, Time, Situation, Condition...
word קֹדֶשׁ, transliterated as qodesh, is used in the Torah to mean 'set-apartness' and 'separateness', as well as 'holiness' and 'sacredness'. The Torah...
on inter-religious dialogue, also with focus on current issues and in relation with parliamentary works. The chair of European Parliament Mediator for...
The new club has no relation to the defunct Clube Desportivo das Aves or its phoenix club Clube Desportivo das Aves 1930 apart from the sharing of its...
explains that quarks carry what is called a color charge, although it has no relation to visible color. Quarks with unlike color charge attract one another as...
back on the 2011 NBA Finals but also has a strong focus on Nowitzki's relation to his hometown Würzburg and his career progression which began there....
composer Frédéric Chopin and the female novelist George Sand had an "unusual" relation that would be called LAT nowadays. The LAT relationship between philosopher...
even though one is connected and the other is discrete. The equivalence relation of quasi-isometry is important in geometric group theory: the Švarc–Milnor...
ancient times was a simpler relation than modern forms of citizenship, although this view has come under scrutiny. The relation of citizenship has not been...
Philosophies (2011). Vol. 4: Historical Perspectives, Poets/Teachers/Saints, Relation to Other Religions and Traditions, Hinduism and Contemporary Issues (2012)...
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