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also follows that every apartness relation is the complement of an equivalence relation, and the only tight apartness relation on a given set is the complement
Apartness_relation
Topics referred to by the same term
Johansson Apart (Léon album), 2020 album by Swedish singer Léon Apartness relation This disambiguation page lists articles associated with the title Apart. If
Apart
Mathematical concept for comparing objects
correspond to the normal subgroups). Any equivalence relation is the negation of an apartness relation, though the converse statement only holds in classical
Equivalence_relation
Mathematical analysis
line by some means, a collection extending the rationals and with an apartness relation definable from an asymmetric order structure. Center stage takes a
Constructive_analysis
the classical notion of a field. It is essentially a field with an apartness relation. A commutative ring is a Heyting field if it is a field in the sense
Heyting_field
Mathematical statement that two values are not equal
f(x)<\left(g(x)\right)^{2}} Look up inequation in Wiktionary, the free dictionary. Apartness relation — a form of inequality in constructive mathematics Equation Equals
Inequation
Typographic symbol (#)
is the primorial of n. In constructive mathematics, # denotes an apartness relation. In computational complexity theory, #P denotes a complexity class
Number_sign
expressed as negation of apartness. Note that the negation of equality is in general merely the double-negation of apartness. Now the disjunctive syllogism
Pseudo-order
Mathematical construction of a set with an equivalence relation
constructive mathematics, one often takes a setoid with an apartness relation instead of an equivalence relation, called a constructive setoid. One sometimes also
Setoid
Axiomatic set theories based on the principles of mathematical constructivism
needed, this notion of infinitude can also be expressed in terms of an apartness relation on the set in question. Being not Kuratowski-finite implies being
Constructive_set_theory
Foundational principle in quantum physics
generalizes more easily. Mathematically, in wave mechanics, the uncertainty relation between position and momentum arises because the expressions of the wavefunction
Uncertainty_principle
Set of tuples consisting of values indexed by attributes
In database theory, a relation, as originally defined by E. F. Codd, is a set of tuples (d1,d2,...,dn), where each element dj is a member of Dj, a data
Relation_(database)
Ways how entities stand to each other
entity with itself. The adicity of a relation is the number of entities it connects. The direction of a relation is the order in which the elements are
Relation_(philosophy)
Physics concept expressed as E = mc²
to many fields of physics, including nuclear and particle physics. Some relation between mass and energy was explored in the late 1800s under the term electromagnetic
Mass–energy_equivalence
Portuguese association football club
championships. The 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
AVS_Futebol_SAD
1885 encyclical on Church-State relations
instinct moves him to live in civil society, for he cannot, if dwelling apart, provide himself with the necessary requirements of life, nor procure the
Immortale_Dei
Social media platform owned by Meta
Chloe L. (2019). ""Let me take another selfie": Further examination of the relation between narcissism, self-perception, and instagram posts". Psychology of
Philosophy terms referring to an observer versus the thing observed
exercises agency, undergoes conscious experiences, and is situated in relation to other things that exist outside itself; thus, a subject is any individual
Subject and object (philosophy)
Subject_and_object_(philosophy)
Prime Minister of the United Kingdom since 2024
Huhne would be prosecuted for perverting the course of justice, stating in relation to the case that "[w]here there is sufficient evidence we do not shy away
Keir_Starmer
Educational programming environment
offers a basic scripting language that consists of a concise set of rules. Apart from commands to make the robot perform basic movement instructions, the
RoboMind
Association football tournament in Qatar
Two FIFA executive committee members were suspended before the vote in relation to allegations of corruption regarding their votes. The decision to host
2022_FIFA_World_Cup
Living arrangement for couples
as well as couples who prefer to (or must) live apart, for various reasons. The term lat-relation became popular in the 1970's in the Netherlands, due
Living_apart_together
Mathematical optimization problem
programming, since we optimize a linear function, and all constraints are linear. Apart from that, many combinatorial algorithms exist. Some of them are generalizations
Minimum-cost_flow_problem
Poor thinking inferred from speech and language usage
only appearing as a response to a question or prompt.[failed verification] Apart from the lack of content in a reply, the manner in which the person delivers
Alogia
Mughal emperor from 1556 to 1605
including several accounts by Parsis, Jains, and Jesuit missionaries, apart from contemporary accounts by Brahminical and Muslim orthodoxy. Existing
Akbar
Infinitesimal calculus on functions defined on a geometric algebra
\wedge e_{i_{k}}\right)dx^{i_{1}}dx^{i_{2}}\cdots dx^{i_{k}}.\end{aligned}}} Apart from a subtle difference in meaning for the exterior product with respect
Geometric_calculus
Colombian singer-songwriter (born 1977)
the government to return the over €60 million in fines and interest in relation to fines that were wrongly imposed in 2021. Magia (1991) Peligro (1993)
Shakira
Geometric operation which truncates the edges of polyhedra
vertices inward). Oppositely, similar to expansion, it moves the faces apart outward, and adds a new face between each two adjacent faces; but contrary
Chamfer_(geometry)
American political activist (1993–2025)
the successful U.S. Senate campaign of Illinois Republican Mark Kirk (no relation). Also during his junior year, he began listening to The Rush Limbaugh
Charlie_Kirk
Interpretation of sensory information
applications of this process in the human sphere. Research has focused on the relation of this to other kinds of learning, and whether it takes place in peripheral
Perception
Compact astronomical body
only plausible explanation. In 1999, David Merritt proposed the M–sigma relation, which related the dispersion of the velocity of matter in the centre bulge
Black_hole
Spacing between equally-spaced square numbers
z {\displaystyle z} ) are three square numbers that are equally spaced apart from each other, then the spacing between them, y 2 − x 2 = z 2 − y 2 {\displaystyle
Congruum
instances in which the soap film breaks as the circular wires are stretched apart. However, in a physical soap film, the connecting line segment would not
Minimal_surface_of_revolution
Martial artist and actor (1940–1973)
witnessed the match include Cadwell, James Lee (Bruce Lee's associate, no relation), and William Chen, a teacher of tai chi.[citation needed] Wong and William
Bruce_Lee
Country in northwestern Europe
is that the UK Parliament has not renounced legislative sovereignty in relation to the three nations concerned. For example, the Scottish Parliament is
United_Kingdom
Christian government in which society is ruled by divine law
to the nation of Israel, it is stated, is continuously binding, although apart from what he considers to be surrounding cultural connotations specific
Theonomy
American singer and actress (born 1993)
TikTok. She commented on the post, writing: "Please do not use my music in relation to this barbaric, inhumane, heinous nonsense." The White House later told
Ariana_Grande
Astronomical principle
period-luminosity relation is a relationship linking the luminosity of pulsating variable stars with their pulsation period. The best-known relation is the direct
Period-luminosity_relation
American football player and commentator (born 1977)
politics these days." In 2018, Brady endorsed Republican Helen Brady (no relation) for State Auditor of Massachusetts. Brady's health regimen includes transcendental
Tom_Brady
1961 novel by Alan Sillitoe
subsequent novels are interrelated, even though some were published decades apart. Thus, for example, Brian Seaton, the semi-autobiographical protagonist
Key_to_the_Door
Study of general and fundamental questions
philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation. Indian philosophy combines the spiritual
Philosophy
American multinational technology company
upholding the fine of around €4.1 billion for abusing its dominant position in relation to the Android operating system. In March 2024, a former Google software
Strong, deep, or close association or acquaintance between two or more people
In social psychology, an interpersonal relation (or interpersonal relationship) describes a social association, connection, or affiliation between two
Interpersonal_relationship
Prime Minister of the United Kingdom from 2010 to 2016
resigned as the paper's editor following the conviction of a reporter in relation to illegal phone hacking, although stating that he knew nothing about it
David_Cameron
English rock band
label Ariola-Hansa on 18 May 1977. In September 1977, Peter O'Toole (no relation to the actor), who had been the group's vocalist for several months, left
The_Cure
Mathematical function
Alternatively, H n {\displaystyle H_{n}} can be calculated using the recurrence relation (for n ≥ 0 {\displaystyle n\geq 0} ) H n + 1 ( y ) = y 2 H n ( y ) − (
Dawson_function
Increase in postsynaptic potential by impulses
absolute refractory period was reached when intervals were about 10 ms apart. To examine facilitation during shorter intervals, Katz and Miledi directly
Neural_facilitation
Largest living species of dolphin
unbaited lines as decoys. Once, fishermen placed their boats several miles apart, taking turns retrieving small amounts of their catch, in the hope that
Orca
Fulfilling life guided by a purpose
meaningful lives is that they are guided by a purpose. This highlights the relation to importance: in working towards realizing this purpose, the agent usually
Meaningful_life
Country in South Asia
this assumed that other Muslim states would take the same view of the relation between religion and nationality." Haqqani (2010, p. 18) "Pakistan's pan-Islamic
Pakistan
1871 book by Charles Darwin
The Descent of Man, and Selection in Relation to Sex is a book by English naturalist Charles Darwin, first published in 1871, which applies evolutionary
The Descent of Man, and Selection in Relation to Sex
The_Descent_of_Man,_and_Selection_in_Relation_to_Sex
Religion of the Jewish people
place in the World to Come....Getting circumcised apart from desiring to be obedient to HaShem, and apart from accepting Yeshua as your King, is nothing
Judaism
Algorithm to transform a regular expression into a finite automaton
concatenation of the regular expression E and let s be the number of symbols apart from parentheses — that is, |, *, a and ε. Then, the number of states of
Thompson's_construction
Time coordinate used in cosmology
that two events separated in space (say, two lightning strikes 10 meters apart) occurred at the same time, while another observer in (relative) motion
Cosmic_time
British racing driver (born 1985)
was made in bad faith and that it was contrary to "fair competition" in relation to 44IP's existing "LEWIS HAMILTON" mark. In 2020 the case was heard before
Lewis_Hamilton
Extinct genus of cartilaginous fish
of ctenacanthiforms and other chondrichthyans. There is no ornamentation apart from randomly oriented furrows which extend over its entire area. The base
Cladoselache
German-born theoretical physicist (1879–1955)
that edition was prepared by Alfred Einstein, who may have been a distant relation. Mozart was a special favorite; he said that "Mozart's music is so pure
Albert_Einstein
Canadian pornographic video-sharing website
of such content. Pornhub has also reported on traffic trends and their relation to large events. Traffic was below usual levels during the solar eclipse
Pornhub
Convex shape with one stable and one unstable position of equilibrium
thickness, the discovered mono-monostatic bodies are the most sphere-like, apart from the sphere itself.[clarification needed] Because of this, they were
Gömböc
First-century Jewish preacher and religious leader
by some contemporaries as having broken the law himself, for example in relation to Sabbath observance. When asked what the greatest commandment is, Jesus
Jesus
1929 book by Alfred North Whitehead
member. Every member (apart from the earliest) is a causal consequence of the earliest member of the nexus, and every member (apart from the last) of such
Process_and_Reality
American singer and actress (born 1969)
Lopez has been the subject of considerable academic analysis, including in relation to ethnicity, class, "body politics", race, Latin culture, and gender.
Jennifer_Lopez
Philosophical concept
present as parts are present in a whole, but being incapable of existence apart from the said subject." (Aristotle, Categories 1a24–26). Owen, G. E. L.
Inherence
Country in North Africa
encourage broader reparation. Tensions between Algeria and Morocco in relation to the Western Sahara have been an obstacle to tightening the Arab Maghreb
Algeria
Class of lobe-finned fishes
consumers. As a result, living coelacanths have no real commercial value apart from being coveted by museums and private collectors. Because of their remote
Coelacanth
1993 television film directed by Don Lusk
impressed but there is not time to take it all in as the pant contiues to fall apart. As the group near the exit, Jonny is separated from the rest of Team Quest
Jonny's_Golden_Quest
Model of airborne disease transmission
an infection. These infectious doses are sometimes called 'quanta' - no relation to quantum physics. The doses are breathed out or otherwise emitted by
Wells-Riley_model
2024 film by Michael Showalter
in the south of France, Solène becomes uncomfortable about her age in relation to the other women traveling with them. Hayes's bandmate Ollie and the
The_Idea_of_You
arcsine is the inverse of sine). Implicit function: defined implicitly by a relation between the argument(s) and the value. Piecewise function: is defined by
List_of_types_of_functions
resolvable into actions between pairs." This specific type of triadic relation is fundamental to Peirce's understanding of logic as formal semiotic. By
Semiotic theory of Charles Sanders Peirce
Semiotic_theory_of_Charles_Sanders_Peirce
Bilateral relations
Kashmiri separatists. It was one of the most prominent attacks against India apart from on the Indian Parliament in December 2001. The dead bodies of the terrorists
India–Pakistan_relations
f-vector and the h-vector uniquely determine each other through the linear relation ∑ i = 0 d f i − 1 ( t − 1 ) d − i = ∑ k = 0 d h k t d − k , {\displaystyle
H-vector
Island country in the Pacific Ocean
2011. McGlone, M. S. (1989). "The Polynesian settlement of New Zealand in relation to environmental and biotic changes" (PDF). New Zealand Journal of Ecology
New_Zealand
School of critical theory developed in the US
decision, but not that it is impossible to tell judicial and legislative acts apart. Rather, CLS have argued that while the form may differ, both are based
Critical_legal_studies
King of Macedon from 336 to 323 BC
proclaimed that it did not matter how the knot was undone, and hacked it apart with his sword. In spring 333 BC, Alexander crossed the Taurus into Cilicia
Alexander_the_Great
Repeated joining and separation of Earth's continents
is generally low when the continents are together and high when they are apart. For example, sea level was low at the time of formation of Pangaea (Permian)
Supercontinent_cycle
Country in Southeast Asia and Oceania
quarter-century under Indonesian rule, a period discussed in scholarship in relation to genocide and occupation. In the post-Suharto era, Indonesia introduced
Indonesia
Mostly submerged continental crust area in Oceania
New Zealand New Zealand Subantarctic Islands "Figure 8.1: New Zealand in relation to the Indo-Australian and Pacific Plates". The State of New Zealand's
Zealandia
Near-Earth asteroid of the Atira group
share identical orbits and spectral types, which suggest that they split apart from a single parent body over 10,500 years ago. The splitting of the parent
2025_GN1
Range of movement of the mandible
population, centric occlusion is said to be averagely 1 mm anterior to centric relation in the natural dentition. Intermediate zone of the articular disk lies
Posselt's_envelope_of_motion
Canadian comedy television series
Pine, a right wing player for the Bulldogs Jordan Nolan as Jim Pine (no relation), a left wing player for the Bulldogs Eliana Jones as Mercedes Policetri
Shoresy
1977 aviation accident in Mississippi, USA
Aviation Administration (FAA) as taking legal action against L & J Company in relation to the operator responsibility, and the analysis section concludes by asking
Lynyrd_Skynyrd_plane_crash
Mathematical statistics distance measure
between P and Q, but this fails to convey the fundamental asymmetry in the relation. Sometimes, as in this article, it may be described as the divergence of
Kullback–Leibler_divergence
Study of meaning in language
of the relation between language and meaning. Cognitive semantics examines meaning from a psychological perspective and assumes a close relation between
Semantics
Biblical figure and Israelite monarch
original on 2018-12-25. Retrieved 2016-01-07. Eynikel, Erik (2000). "The Relation Between the Eli Narrative and the Ark Narratives". In Johannes Cornelis
David
Thai actor, model and singer (born 1994)
promotional activities along with vlogs and collaboration with other artists. Apart from having an active acting career, Poompat also co-owns an Artist Management
Poompat_Iam-samang
Mathematical series
{1}{n^{s}}},} whose analytic continuation to C {\displaystyle \mathbb {C} } (apart from a simple pole at s = 1 {\displaystyle s=1} ) is the Riemann zeta function
Dirichlet_series
German philosopher and socialist (1818–1883)
Paul (2015). "Marx's scientific and political criticism: The internal relation". Capital & Class. 39: 65–78. doi:10.1177/0309816814564657. Annelien de
Karl_Marx
Professional network website
allows authors to better track the traffic that their posts receive. In relation to this functionality, LinkedIn has gained more users over the years in
Measure words in Chinese
several hundred, depending on how they are counted. The classifier gè (个; 個), apart from being the standard classifier for many nouns, also serves as a general
Chinese_classifier
Effectiveness of radiation in radiobiology
are spaced by several hundred nanometers (several tenths of a micrometer) apart, along their path. In contrast, the much more massive alpha particles and
Relative biological effectiveness
Relative_biological_effectiveness
Problem optimization method
problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems
Dynamic_programming
Country in West Asia
requirement of a male guardian. The amendment also granted women rights in relation to the guardianship of minor children. Previously, girls and women were
Saudi_Arabia
When sun appears directly over equator
virtually horizontally on or above the horizon, not obviously rising or setting apart from the movement in "declination" (and hence altitude) of a little under
September_equinox
the border between the Soviet Union and Iran, and kept the Azerbaijanis apart from one another. Literature and history courses in Azerbaijan have incorporated
Azerbaijani_nationalism
English guitarist (born 1944)
want to go into it because it's a personal thing and isn't in relation to anything apart from the fact that I've employed his system in my own day to day
Jimmy_Page
Polish-British historian and Marxist (1907–1967)
confirmed me in my view that the Fourth International was a non-starter... Apart from Trotsky himself the Fourth International was a zero." Germany invaded
Isaac_Deutscher
King of Scotland from 1306 to 1329
Declaration of Arbroath of 1320 strengthened his position, particularly in relation to the Papacy, and Pope John XXII eventually lifted Bruce's excommunication
Robert_the_Bruce
Subgenus of fishes
depths. Mantas may forage on the ocean floor with the cephalic fins splayed apart. During filter feeding, the gills may get clogged up, forcing mantas to
Manta_ray
Mathematical function with no sudden changes
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
Continuous_function
APARTNESS RELATION
APARTNESS RELATION
Boy/Male
Indian, Punjabi, Sikh
Gem of Awareness
Boy/Male
Indian, Marathi
Awarness
Boy/Male
Hindu, Indian, Punjabi, Sikh
One Absorbed in Awareness
Boy/Male
Tamil
Awareness
Boy/Male
Hindu, Indian
Universal Awareness
Boy/Male
Hindu, Indian
Awareness
Boy/Male
Hindu, Indian
Awareness
Girl/Female
Hindu, Indian
Self Awareness
Girl/Female
Tamil
Vigilance, Awareness
Boy/Male
Indian, Punjabi, Sikh
Spiritual Awareness
Girl/Female
Hindu
Vigilance, Awareness
Girl/Female
Tamil
Vigilance, Awareness
Boy/Male
Gujarati, Hindu, Indian
Awaken; Awareness
Surname or Lastname
English (Cumbria)
English (Cumbria) : unexplained.
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Sindhi, Tamil, Telugu
Awareness; Awakening; Vigilance
Girl/Female
Hindu
Vigilance, Awareness
Girl/Female
Hindu, Indian
Smartness
Girl/Female
Indian, Tamil
Smartness
Boy/Male
Hindu, Indian
Smartness; Attitude; Lord of Ganesha
Boy/Male
Indian, Punjabi, Sikh
Of Exalted Mind and Awareness
APARTNESS RELATION
APARTNESS RELATION
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Excelling the Moon
Girl/Female
Gujarati, Hindu, Indian, Kannada, Sindhi, Telugu, Traditional
Full of Water
Girl/Female
Indian
Queen of Love
Girl/Female
Tamil
Girl/Female
Arabic
Excellent; Pure; Beautiful; Blessing
Boy/Male
Indian, Telugu
Chocolate
Surname or Lastname
English and Scottish
English and Scottish : habitational name from any of the numerous and widespread places so called. The majority of these are named with Old English middel ‘middle’ + tūn ‘enclosure’, ‘settlement’; a smaller group, with examples in Cumbria, Kent, Northamptonshire, Northumbria, Nottinghamshire, and Staffordshire, have as their first element Old English mylen ‘mill’.
Boy/Male
Arabic
Truth
Girl/Female
Hindu, Indian
A River
Boy/Male
Arabic, Farsi, Iranian, Muslim, Parsi
Admiral; Big Gate
APARTNESS RELATION
APARTNESS RELATION
APARTNESS RELATION
APARTNESS RELATION
APARTNESS RELATION
n.
Fitness; suitableness; appropriateness; as, the aptness of things to their end.
n.
Roughness to the taste; sourness; tartness.
n.
Readiness in learning; docility; aptness.
n.
Aptness to break; fragility.
n.
Tartness; sourness, as of disposition.
n.
Openness; frankness.
n.
Pertness; sauciness.
n.
Fineness; spruceness; smartness.
n.
Quickness of apprehension; readiness in learning; docility; as, an aptness to learn is more observable in some children than in others.
n.
The quality or state of being lean or thin; leanness.
n.
The quality of being alert or on the alert; briskness; nimbleness; activity.
n.
The quality or state of being smart.
n.
Proneness; tendency; as, the aptness of iron to rust.
v. i.
To behave with pertness.
n.
Disposition of the mind; propensity; as, the aptness of men to follow example.
n.
Forwardness; pertness; petulance.
n.
The quality or state of being swart.
n.
Tartness; sourness.
n.
Aptness to start.
n.
The quality of standing apart.