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Subset of a preorder that contains all larger elements
S. Upper sets and lower sets are also known by many other names. An upper set may also be called an upward closed set, an up-set, an isotone set, or
Upper_and_lower_sets
Majorant and minorant in mathematics
mathematical literature for sets that have upper (respectively lower) bounds. For example, 5 is a lower bound for the set S = {5, 8, 42, 34, 13934} (as
Upper_and_lower_bounds
Property of functions which is weaker than continuity
, and upper semi-continuous if − f {\displaystyle -f} is lower semi-continuous. A function is continuous if and only if it is both upper and lower semicontinuous
Semi-continuity
∩{open sets containing x}. ↓x = {y ∈ X : y ≤ x} = ∩{closed sets containing x} = cl{x}. The lower set ↓x is always closed; however, the upper set ↑x need
Specialization_preorder
Two regions of Ancient Egypt
Egyptian history, the Upper and Lower Egypt period (also known as The Two Lands) was the final stage of prehistoric Egypt and directly preceded the unification
Upper_and_Lower_Egypt
Greatest lower bound and least upper bound
other upper bound). We can also define suprema and infima without restricting to sets. For example, there is no set containing all cardinal numbers (and there
Infimum_and_supremum
Varied organ found in many animals and used for palpation and manipulation
snails, which usually have two sets of tentacles on the head: when extended the upper pair have eyes at their tips; the lower pair are chemoreceptors. Both
Tentacle
Special kind of square matrix
square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly, a square matrix is called upper triangular if all the
Triangular_matrix
Uppercase or lowercase
distinguish between the upper- and lowercase have two parallel sets of letters: each in the majuscule set has a counterpart in the minuscule set. Some counterpart
Letter_case
Austria-Hungarian World War I flying boat
in the interplane gap. The pilot and observer sat side by side in an open cockpit, and both the upper and lower sets of wings featured sweepback. The
Lohner_L
strict upper contour set of x {\displaystyle x} is { y ∍ y ≻ x } {\displaystyle \left\{y~\backepsilon ~y\succ x\right\}} and the strict lower contour
Contour_set
Structure of the respiratory system
tract is divided into the upper airways and lower airways. The upper airways or upper respiratory tract includes the nose and nasal passages, paranasal
Respiratory_tract
1910s British float plane project
the pilot and observer being seated ahead of the wings in a streamlined lightweight nacelle mounted in the gap between the upper and lower sets of wings
AD_Navyplane
Semicontinuity for set-valued functions
mathematics, upper hemicontinuity and lower hemicontinuity are extensions of the notions of upper and lower semicontinuity of single-valued functions to set-valued
Hemicontinuity
Flag officer rank of the USN, USCG, USPHS, and NOAA Corps
single-point-up stars on blue fields for the lower half or upper half, respectively. The flags of restricted line officers and staff corps officers have blue stars
Rear_admiral_(United_States)
Vertebrate organ through which food passes to the stomach
predominates in its upper third. It has two muscular rings or sphincters in its wall, one at the top and one at the bottom. The lower sphincter helps to
Esophagus
Automotive independent suspension design
unequal-length double wishbone suspension. The upper arm is typically an A-arm and is shorter than the lower link, which is an A-arm or an L-arm, or sometimes
Double_wishbone_suspension
Concept in number theory
} The set of numbers whose decimal expansion begins with the digit 1 similarly has no natural density: the lower density is 1/9 and the upper density
Natural_density
Representations of imprecise probability
Upper and lower probabilities are representations of imprecise probability. Whereas probability theory uses a single number, the probability, to describe
Upper_and_lower_probabilities
Topology on a partially ordered set
the upper topology is the least order consistent topology in which all open sets are up-sets. However, not all up-sets must necessarily be open sets. The
Upper_topology
Statistic which divides data into four same-sized parts for analysis
about both the center and the spread of the data. Knowing the lower and upper quartile provides information on how big the spread is and if the dataset is
Quartile
Region of Sydney, New South Wales, Australia
the Upper North Shore. Buses on the Lower North Shore are mainly operated by the Busways out of Willoughby Bus Depot. Significant commercial and retail
North_Shore_(Sydney)
Class of electric multiple unit operating in Sydney, Australia
first set entered service as 8 car R1 (not used for 6 car trains until 1984). When R sets later started to include sets made up of older Comeng and Goninan
New_South_Wales_K_set
Branch of mathematics
smallest set that contains all of the sets. Hence, we have found the least upper bound of a set of sets. This concept is also called supremum or join, and for
Order_theory
Approximation of a mathematical set
Pawlak (1991), the lower- and upper-approximation sets are crisp sets, but in other variations, the approximating sets may be fuzzy sets. The following section
Rough_set
in the interplane gap. The pilot and observer sat side by side in an open cockpit, and both the upper and lower sets of wings featured sweepback. Austria-Hungary
Lohner_M
Shape that blocks all lines of sight
opaque set is a system of curves or other set in the plane that blocks all lines of sight across a polygon, circle, or other shape. Opaque sets have also
Opaque_set
Partial order with joins
The greatest lower bound of the set {x, y} is called the meet of x and y, denoted x ∧ y. Replacing "greatest lower bound" with "least upper bound" results
Semilattice
Place in Norrbotten, Sweden
1989) semi-retired Swedish mixed martial arts fighter, competed in the UFC Anders Nilsson (born 1990) a Swedish professional ice hockey goaltender Alexander
Luleå
District of New France
included two regions, now known as Upper Louisiana (la Haute-Louisiane), which began north of the Arkansas River, and Lower Louisiana (la Basse-Louisiane)
Louisiana_(New_France)
Method of determining fractal dimension
limit capacity or upper Minkowski dimension, while the lower box dimension is also called the lower Minkowski dimension. The upper and lower box dimensions
Minkowski–Bouligand_dimension
The Set animal (Seth) Nome 12: Viper mountain Nome 13: Upper pomegranate tree (Upper Sycamore and Viper) Nome 14: Lower pomegranate tree (Lower Sycamore
List of ancient Egyptian sites
List_of_ancient_Egyptian_sites
of the lower or upper envelope can be bounded using Davenport–Schinzel sequences, and these envelopes can be computed efficiently by a divide-and-conquer
Lower_envelope
Burning within well-defined lower and upper bounds
Dusts also have upper and lower explosion limits, though the upper limits are hard to measure and of little practical importance. Lower flammability limits
Flammability_limit
Smallest convex set containing a given set
sets, and in time matching the worst-case output complexity given by the upper bound theorem in higher dimensions. As well as for finite point sets,
Convex_hull
Topological relational characteristic
first define the upper and lower sets of x. These are both defined with respect to the specialization preorder discussed above. The lower set of x is just
Topological indistinguishability
Topological_indistinguishability
Oxyaenid genus from upper Eocene Epoch
anteriorly-placed canines. Both the upper and lower sets of premolars were large, and formed rectilinear cutting blades. The second upper one was offset into a position
Sarkastodon
Theory of Islamic legal limits developed by Muhammad Shahrur
hundred lashes as both the lower and upper limit, so the punishment cannot be reduced or increased. God sets both a lower and an upper boundary. Human action
Theory_of_limits_in_Islam
Signal processing effect
filters (AAF) to the input signal before sampling and when converting a signal from a higher to a lower sampling rate. Suitable reconstruction filtering
Aliasing
Set of descriptive statistics
of a single set of data there are two related statistics called the upper and lower quartiles. If data are placed in order, then the lower quartile is
Five-number_summary
Two volcanic plateaus in Oregon, US
Upper Table Rock and Lower Table Rock are two prominent volcanic mesas located just north of the Rogue River in Jackson County, Oregon, U.S. Created by
Upper_and_Lower_Table_Rock
Smallest complete lattice containing a partial order
Therefore, the set of cuts, partially ordered by inclusion on the lower set of the cut (or the reverse of the inclusion relation on the upper set), gives an
Dedekind–MacNeille_completion
Property of a partially ordered set
a partially ordered set X has the least-upper-bound property if every non-empty subset of X with an upper bound has a least upper bound (supremum) in
Least-upper-bound_property
1990 book on mathematical order theory
lattices, every set) has a greatest lower bound and a least upper bound. This chapter includes the construction of a lattice from the lower sets of any partial
Introduction to Lattices and Order
Introduction_to_Lattices_and_Order
Integral constructed using Darboux sums
and only if the upper and lower integrals are equal. The upper and lower integrals are in turn the infimum and supremum, respectively, of upper and lower
Darboux_integral
Populated place in Arizona, United States
this name, the other being a CDP in Gila County. In 1909, the US Government set up an irrigation project to assist the Navajo residents. It is a chapter
Wheatfields, Apache County, Arizona
Wheatfields,_Apache_County,_Arizona
Educational year group in the UK and some Commonwealth countries
education and not to vocational education. Sixth Form describes the two school years that are called by many schools the lower sixth (L6) and upper sixth
Sixth_form
Species of gastropod
conic spire; suture canaliculate, deep and narrow; columellar area with a strong raised callus, an upper and lower set of columellar plications; lip about
Olivella_watermani
Retired class of electric multiple unit train
similar looking K sets and C sets. Their stainless steel appearance is shared with the intercity V sets and U sets. All remaining sets were withdrawn from
New_South_Wales_S_set
Vacuum-tube 1950s computer system
lower and upper accumulators with a common sign. Arithmetic was performed by a one-digit adder. The console (10 digit switches, one sign switch, and 10
IBM_650
Education between primary and higher education
Level 2 (lower secondary education, less commonly junior secondary education) is the second and final phase of basic education, and Level 3 (upper secondary
Secondary_education
Social stratification conferring status
meaning many universities are at a far lower rate than legislated. These reservation systems have backlash from upper caste groups, who claim that people
Caste
Facial feature
of the top and bottom eyelids, spanning outwards and away from the eyes. The lashes grow in up to six layers on each of the upper and lower eyelids. Eyelashes
Eyelash
Meteorological optical phenomenon
conditions are right, a distinct green spot is briefly visible above the Sun's upper limb; the green appearance usually lasts for no more than two seconds. Rarely
Green_flash
Collection of mathematical objects of finite size
called an upper bound of S. The terms bounded from below and lower bound are similarly defined. A set S is bounded if it has both upper and lower bounds
Bounded_set
Series of cataracts on the Congo River in the Democratic Republic of the Congo
explorer David Livingstone, are a succession of enormous rapids on the lower course of the Congo River in west equatorial Africa, downstream from Malebo
Livingstone_Falls
Longest river in Ulster, passing through Lough Neagh
Bann Wattèr) is the longest river in Northern Ireland, its length, Upper and Lower Bann combined, being 129 km (80 mi). The total length of the River
River_Bann
Medical condition
of the mouth, a pit in the upper lip, in which case it may be called a midline sinus of the upper lip, and pits in the lower lip, in which case it may
Congenital_lip_pit
Theorem in economics
{\displaystyle A\in X} , both lower and upper strict contour sets at A are topologically open; If the lower countour set of A is nonempty, then A is in
Utility representation theorem
Utility_representation_theorem
Subnational administrative division of ancient Egypt
ⲡⲑⲱϣ) are listed in separate tables for "Isti" - "the two Egypts" (Upper and Lower Egypt). Note: older or other variants of the name in square brackets
Nome_(Egypt)
1791–1841 British colony in North America
of Quebec (1763–1791) into the Province of Lower Canada and the Province of Upper Canada. The prefix "lower" in its name refers to its geographic position
Lower_Canada
Bisection of Euclidean space by a hyperplane
hyperplane are partitioned into two convex sets (i.e., half-spaces), such that any subspace connecting a point in one set to a point in the other must intersect
Half-space_(geometry)
Normal series of subgroups which indicate almost-commutativity
A general group possesses a lower central series and upper central series (also called the descending central series and ascending central series, respectively)
Central_series
Strip of land on the Nile valley between Nubia and Lower Egypt
El-Ayait, which places modern-day Cairo in Lower Egypt. The northern (downriver) part of Upper Egypt, between Sohag and El-Ayait, is also known as Middle Egypt
Upper_Egypt
Historic building complex and art museum in Vienna, Austria
historic building complex and art museum in Vienna, Austria. The complex consists of two Baroque palaces, the Upper and Lower Belvedere, together with
Belvedere,_Vienna
This is a list of former Universal Studios Hollywood Attractions. Upper Lot Time Travelers Depot (Back to the Future: The Ride) removed in 2003, now Kwik-E-Mart
List of former Universal Studios Hollywood attractions
List_of_former_Universal_Studios_Hollywood_attractions
Village in Gloucestershire, England
proper. It comprises the districts of Lower Lydbrook, Upper Lydbrook, Joys Green and Worrall Hill. It has a mile and a half long high street, reputed to
Lydbrook
Class of electric multiple unit operating in Sydney, Australia
previous Intercity Tangara G sets. Currently operating as 55 four-carriage sets, the H sets now operate on the South Coast line, and numerous suburban lines
New_South_Wales_H_set
Exercise equipment
the main variables used to lower or increase the intensity of the workout. In 2014, researchers found that the bench press and the resistance band push-up
Resistance_band
Measure of statistical dispersion
the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile
Interquartile_range
Particular correspondence between two partially ordered sets
categories that arise from partially ordered sets. In this context, the upper adjoint is the right adjoint while the lower adjoint is the left adjoint. However
Galois_connection
Technique in dentistry
alignment of the teeth in the upper and lower jaw, leading to optimal function, comfort, and aesthetics. Various methods and materials are used to record
Bite_registration
Existence of certain infima or suprema of a given poset
the great importance of suprema (least upper bounds, joins, " ∨ {\displaystyle \vee } ") and infima (greatest lower bounds, meets, " ∧ {\displaystyle \wedge
Completeness_(order_theory)
Approximation technique in integral calculus
between x i − 1 {\displaystyle x_{i-1}} and x i {\displaystyle x_{i}} ) is contained between the lower and upper Darboux sums. This forms the basis of the
Riemann_sum
American dental notation system
continues along the upper teeth to the left side. Then the count begins at the mandibular left third molar, designated number 17, and continues along the
Universal_Numbering_System
Algebra whose elements are stable matchings
matchings have a unique greatest lower bound and a unique least upper bound. Together, the greatest lower bound and least upper bound operations obey the distributive
Lattice_of_stable_matchings
Lithostratigraphic layer of the Stormberg Group in South Africa
Neck, Hill Top, Quthing, and near the capital, Maseru. The Elliot Formation is further divided into the lower (LEF) and upper (UEF) Elliot formations to
Elliot_Formation
River in Galway, Ireland
known as the Upper Corrib. The weir, a set of weir gates also built during the above navigation scheme, was originally built from stone and timber but now
River_Corrib
Japanese high speed train type
on 18 March 2007. The first two sets were withdrawn in April 2012: M1 on 2 April and M2 on 14 April. The remaining sets were withdrawn from service with
E1_Series_Shinkansen
Mathematical ordering with upper bounds
ordered sets) are directed sets as well, but not conversely. Likewise, lattices are directed sets both upward and downward. In topology, directed sets are
Directed_set
Buddhist temple in Pingyao County, Shanxi, China
two pillars are of the 5th degree. The hall has no ceiling, and the upper and lower set of rafters are exposed. Nancy Steinhardt speculates that the
Zhenguo_Temple
First set of teeth in diphyodonts
midline and then spreads back into the posterior region. By the time the embryo is eight weeks old, there are ten buds on the upper and lower arches that
Deciduous_teeth
Infectious disease affecting nose, throat and lungs
diseases involving the lower or upper respiratory tract. An infection of this type usually is further classified as an upper respiratory tract infection
Respiratory_tract_infection
Mathematical set containing no elements
subset of any ordered set, every member of that set will be an upper bound and lower bound for the empty set. For example, when considered as a subset of
Empty_set
Points with no three in a line
{\displaystyle c^{n}} for a constant c < 2 {\displaystyle c<2} . The upper bounds on cap sets imply lower bounds on certain types of algorithms for matrix multiplication
Cap_set
Tooth numbering system
in front or behind the number. A plus (+) indicates upper position while minus (−) indicates lower. When the sign is in front of the number, it indicates
Palmer_notation
American trading card company
The Upper Deck Company, LLC (known colloquially as Upper Deck and Upper Deck Authenticated, Ltd. in the United Kingdom) is a private company primarily
Upper_Deck_Company
Type of sail on a square rigged vessel
above the upper topsail. The upper or only topgallant sail is set from the top of the topgallant mast. If there is a lower topgallant it is set from midway
Topgallant_sail
Set disjoint from its sumset with itself
{1}{3}}} , and conjectured that equality holds. This was proved in 2014 by Eberhard, Green, and Manners giving an upper bound matching Erdős' lower bound up
Sum-free_set
Types of special mathematical functions
In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to certain integrals. Their respective
Incomplete_gamma_function
Geometry; how many 3-point lines can n points form
achieving the same lower bound. In September 2013, Ben Green and Terence Tao published a paper in which they prove that for all point sets of sufficient size
Orchard-planting_problem
Two distinct indigenous peoples of the Pacific Northwest
two culturally and linguistically distinct indigenous peoples of the Pacific Northwest; the Lower Cowlitz or Cowlitz proper, and the Upper Cowlitz / Cowlitz
Cowlitz_people
Waterfall in the US state of Indiana
two sets of waterfalls on Mill Creek separated by about 1 mile (1.6 km). Both falls consist of a series of drops. The total height of the Upper Falls
Cataract_Falls_(Indiana)
Comprehensive list of Magic: The Gathering card sets since its inception in 1993
sets have been released per year, in addition to various spin-off products. Magic has made three types of sets since Alpha and Beta: base/core sets,
List of Magic: The Gathering sets
List_of_Magic:_The_Gathering_sets
Hamlet in South Buckinghamshire, England
(SSSI) with an array of wildlife including glow worms and the bee orchid. Up on Pulpit Hill, set within Pulpit Woods, are the remains of an Iron Age hill
Cadsden
Method for finding kth smallest value
{\displaystyle k} down or up, respectively: the lower median with k = n / 2 {\displaystyle k=n/2} and the upper median with k = n / 2 + 1 {\displaystyle k=n/2+1}
Selection_algorithm
Catholic church of the Order of Friars Minor Conventual in Assisi
interred. The interior of the Upper Church is an important early example of the Gothic style in Italy. The Upper and Lower Churches are decorated with frescoes
Basilica of Saint Francis of Assisi
Basilica_of_Saint_Francis_of_Assisi
Data visualization
indicating variability outside the upper and lower quartiles, thus, the plot is also called the box-and-whisker plot and the box-and-whisker diagram. Outliers
Box_plot
New York City Subway station in Brooklyn
the upper level and the local tracks on the lower one. The station was originally planned to be a conventional local station with four tracks and two
Nostrand Avenue station (IND Fulton Street Line)
Nostrand_Avenue_station_(IND_Fulton_Street_Line)
Measurement weight range for boxers
for boxers. The lower limit of a weight class is equal to the upper weight limit of the class below it. The top class, with no upper limit, is called
Weight_class_(boxing)
travel, tourism, insurance
UPPER AND-LOWER-SETS
UPPER AND-LOWER-SETS
UPPER AND-LOWER-SETS
UPPER AND-LOWER-SETS
UPPER AND-LOWER-SETS
UPPER AND-LOWER-SETS
UPPER AND-LOWER-SETS
UPPER AND-LOWER-SETS
UPPER AND-LOWER-SETS
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