
Review of Short Phrases and Links 
This Review contains major "Set" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 A set is the name for a collection of some number of elements.
 A set is a group or collection of objects or numbers, considered as an entity unto itself.
 A set is a collection of elements, and may be described in many ways.
 A set is a singleton if and only if its cardinality is 1.
 A set (which can also be referred to as a side) is a number of dancers in a particular arrangement for a dance.
 A digraph of a binary relation on a set can be simplified if the relation is a partial order.
 In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being "equivalent" in some way.
 This function allows you to set the aperture on your camera; the camera chooses the shutter speed for you.
 Av: AperturePriority AE In this mode you manually set the aperture and the camera automatically sets the shutter speed to ensure an accurate exposure.
 When objects are still you have all the time that you need to focus on the object and set the other camera parameters like shutter speed and aperture.
 Av (Aperture Priority)  Set the aperture to create the depth of field (the area of focus) and the camera automatically selects the shutter speed.
 Manual  you set both the shutter speed and aperture AV (Aperture priority)  the camera automatically selects a shutter speed to match the aperture you set.
 The reason the setting is called "priority" is that when you set the aperture, the camera adjusts the shutter speed so that the exposure is just right.
 Show that the cofinite (respectively, cocountable) topology on a set X equals the discrete topology if and only if X is finite (respectively, countable).
 In geometry, topology and related branches of mathematics, a closed set is a set whose complement is an open set.
 The trivial topology is the topology with the least possible number of open set s, since the definition of a topology requires these two sets to be open.
 By restricting the metric, any subset of a metric space is a metric space itself (a subspace) with a topology restricted to that set.
 Every metric space is automatically a topological space, the topology being the set of all open sets.
 To prove this fact, note that any open set in a metric space is the union of an increasing sequence of closed sets.
 Clijsters, two points away from defeat, stormed back to win the set in a tiebreak, before cruising through the last set.
 The game took another twist with Federer leading the second set 52, as Nadal rallied again to level the set at 55 as the set went to a tiebreak.
 Henin, who did not drop a set or face a tiebreak heading into the final, completed a stunning rally by breaking Petkovic in the ninth game.
 He overcame cramping in the fifth set, trying to push the set into a tiebreaker, but Agassi broke his serve in the last game.
 Federer dominated Haas in the first two sets but Haas stepped it up, forcing Federer into making errors and extending the match to a fifth set.
 Roddick paused briefly but continued the match, which went a record 30 games in the fifth set before Federer won.
 Mean That value of a variate such that the sum of deviations from it is zero, and thus it is the sum of a set of values divided by their number.
 The practical value of understanding the standard deviation of a set of values is in appreciating how much variation there is from the "average" (mean).
 It is calculated by applying a function (statistical algorithm) to the values of the items comprising the sample which are known together as a set of data.
 To calculate the mean, you simply add together all of the values in your data set, and divide that sum by the total number of values in the set of data.
 A data set can be viewed abstractly as a set of records, each consisting of values for a set of dimensions (variables).
 The median of a set of data values is the middle value once the data set has been arranged in order of its values.
 Tsonga hit a backhand into the net on break point to give Federer a 21 lead in the third set, and the match was all but over.
 He didn't face a break point until he was serving to take the match into a fourth set, when Federer pounced again.
 The 76thranked Zverev didn't allow Federer to see a break point until the 10th game of the first set, saving two set points to get to 55.
 Cheered on by his home crowd Luczak served for the opening set at 53, but Nadal broke to set up a tiebreak he did not lose a point in.
 Since losing the opening set in a tiebreak to Julien Benneteau in the first round, he has not dropped a set in the next 12 sets.
 Federer had noticed Djokovic was trying to deal with his foot problem in the locker room and later said he was surprised Nadal dropped the opening set.
 Cross over the next set of traffic lights and then at the final set, with a Caltex garage on your right, turn left on the R40 for Hazyview.
 Surviving 13 aces by Isner, Querrey won 94 percent of his first serve points in the final set to capture his second victory over his countryman this season.
 But Federer came through by winning the tiebreak in the first and third sets, and faced four break points before victory in the final set.
 Roddick saved a match point in the fourth set before going on to win that set and force a decisive fifth set.
 Roddick had a two set lead before Gasquet won the final 3 sets to book a semi final spot.
 Roddick then broke in the next game to take the set, closing with a deep backhand that forced a forehand error by Federer.
 The ordinal number of the set of all ordinals must be an ordinal and this leads to a contradiction.
 The cofinality of a set of ordinals or any other wellordered set is the cofinality of the order type of that set.
 And in fact, much more is true: Every set of ordinals is wellordered.
 In mathematics, an uncountable set is a set which is not countable.
 Cantor proved that the set of all secondclass ordinal numbers O 2 is the least uncountable set, i.e.
 For every uncountable set x of ordinals there is a constructible y such that x ⊂ y and y has the same cardinality as x.
 A good example of a set that is not compact is a bounded set of the rational numbers Q. It is not compact because it is not closed.
 The diameter of a bounded set is the least upper bound of the distances between two points in the set.
 Definition 2.1.16 A bounded set is a set for which there exists a positive number such that (i.e.
 However its closure (the closure of a compact set) is the entire space X and if X is infinite this is not compact (since any set {t,p} is open).
 In mathematics, a compact set is a set of points in a topological space such that every one of its (possibly infinite) open covers has a finite subcover.
 Summary. The following notions for real subsets are defined: open set, closed set, compact set, intervals and neighbourhoods.
 In the final against Roddick, Roger dominated the opening set, won the second in a tiebreaker, and closed the American out in the third 6–4.
 Roddick saved a break point with Murray leading 43 in the fourth set with a forehand winner, then came through with big serves in the tiebreaker.
 Blake saved two set points at 45 in the second and three more after falling behind 62 in the tiebreaker, but Federer cashed his sixth.
 For the first time all tournament, Smith dropped a set as Moneke won the second set in a tiebreaker to force a third and final set.
 At the second, in Charleston, lost 26 61 46 after leading 31 in the final set, and doublefaulting away the final two points of the match.
 Nadal ripped a backhand passing shot to break at love for a 31 lead in the final set, and erased two more break points to hold for 52.
 The number of elements in a particular set is a property known as cardinality, informally this is the size of a set.
 Perhaps the simplest is that any set can be a universe, so long as you are studying that particular set.
 Newton's Divided Difference is a way of finding an interpolation polynomial (a polynomial that fits a particular set of points or data).
 The security policy is a set of rules that state which packets are allowed to pass the network and which are not.
 A tiebreaker, played under a separate set of rules, allows one player to win one more game and thus the set, to give a final set score of 76.
 This game was taken back to England where the rules of badminton were set out.
 He set a qualifying record with a lap of 122.410 mph to break the record of 121.999 mph set a year ago by Harvick.
 One break of serve in each set was enough for Roddick, who didn't face a break point in the entire match.
 Months later, he set a new best in the event as the youngest man to break a world record.
 The United States finished the race in first place in a time of 3:08.24 and wins the gold medal and set a new World Record.
 In the games, she set a new world record in the 400meter freestyle event; this record would hold for 18 years until Laure Manaudou broke it in May 2006.
 In addition to that record, Hedrick marked other victories in 2005 as he: Set the world record in the 1,500 meter on Nov.
 Nadal won the third set easily and served for the match in the fourth set before Federer broke him and forced a tiebreaker.
 In that match, Blake managed to win his first set against Federer, winning the third set in a tiebreaker (11–9).
 Roddick was now under siege, saving a break point in the sixth game of the third set before another tiebreaker was required.
 Federer managed to win that set in a tiebreak, but Nadal was clearly the better player in the third set, winning 75, 67 (3), 63.
 Nadal also won his next three matches in straight sets, which set up another final with Federer, who had won this tournament the three previous years.
 Federer is capable of performing in high pressure situations, often saving break, set or match points during crucial times in a match.
 For example, (said alephnull or alephnaught) is the cardinality of the set of rational numbers or integers.
 Therefore, we can ask if there is a set whose cardinality is "between" that of the integers and that of the reals.
 For example, the set of integers under the operation of addition is a group.
 Properties If an uncountable set X is a subset of set Y, then Y is uncountable.
 The best known example of an uncountable set is the set R of all real number s; Cantor's diagonal argument shows that this set is uncountable.
 An uncountable set can be given the cocountable topology, in which a set is defined to be open if it is either empty or its complement is countable.
 Define a set to be a countable intersection of open sets, and an set to be a countable union of closed sets.
 The closed sets are the set complements of the members of T. Finally, the elements of the topological space X are called points.
 As a set take, and topologize by declaring the (nonempty, proper) closed sets to be those sets of the form for a positive integer.
 Definition of a closed set In a metric space, a set is closed if every limit point of the set is a point in the set.
 Closed set A set is closed if its complement is a member of the topology.
 In topology, a regular space is one in which points are closed and any point can be separated by open sets from any closed set of which it is not a member.
 A topological space is a set X equipped with a set of subsets of X, called open sets, which are closed under finite intersections and arbitrary unions.
 Indeed, a totally ordered set (with its order topology) is compact as a topological space if it is complete as a lattice.
 Let G be the functor from topological space s to set s that associates to every topological space its underlying set (forgetting the topology, that is).
 Any arbitrarily small neighborhood around that point contains an open set in the unit interval that is disjoint from the Cantor set.
 Since the set of endpoints of the removed intervals is countable, there must be uncountably many numbers in the Cantor set which are not interval endpoints.
 Tags: Cantor set, compact, connected set, continuity, homeomorphism,.
 The set of pathconnected components of a space X is denoted π 0(X). Point A point is an element of a topological space.
 In mathematics, a metric space is a set (or "space") where a distance between points is defined.
 If a set is given the discrete topology, all functions with that space as a domain are continuous.
 To qualify as a vector space, the set V and the operations of addition and multiplication have to adhere to a number of requirements called axioms.
 A functor from the category into the category of sets assigns a set to each type and a function to each function symbol satisfying the axioms.
 In order for a function to qualify as an inner product it must follow a set of axioms (u, v and w are vectors in vector space V, and c is any scalar): 1.
 In mathematics, a cocountable subset of a set X is a subset Y whose complement in X is a countable set.
 Some authors use countable set to mean a set with the same cardinality as the set of natural numbers.
 Hereditarily countable set  In set theory, a set is called hereditarily countable if and only if its transitive closure is a countable set.
 Cantor defined countable set Countable set In mathematics, a countable set is a set with the same cardinality as some subset of the set of natural numbers.
 Since the set of integers is a countable set, and any subset of a countable set is still countable, the set of perfect numbers must obviously be countable.
 A countable set is a set which is either finite or countably infinite.
 In the branch of mathematics known as set theory, the aleph numbers are a series of numbers used to represent the cardinality (or size) of infinite sets.
 Naive set theory was created at the end of the 19th century by Georg Cantor in order to allow mathematicians to work with infinite sets consistently.
 Moreover, Bolzano's definition was more accurately a relation which held between two infinite sets, rather than a definition of an infinite set per se.
 Infinite Sets: An infinite set is a set where the number of elements in the set cannot be counted.
 Any set which can be mapped onto an infinite set is infinite.
 An infinite set is a set with an infinite number of elements, while a finite set is a set with a finite number of elements.
 In fact, the cardinality of the reals is 2 ω (see cardinal numbers), i.e., the cardinality of the set of subsets of the natural numbers.
 A base (or basis) for a topology T of a set X is a collection B of subsets of X such that each element of T is the union of elements of B.
 The power set of a set S can be defined as the set of all subsets of S. This includes the subsets formed from the members of S and the empty set.
 Or if you take the discrete topology (every subset of R is open), then every set is *both* open and closed under that topology.
 The complement of a set A in X, denoted by A C, is (that is, the entire space except for A). A subset C is called closed if the set C C is open.
 A coordinate map is essentially a coordinate system for a subset of a given space with the property that each point has exactly one set of coordinates.
 Djokovic had an opportunity to take the 20 lead in the next set, but Nadal saved three break points and never looked back.
 In the end only Nadal, the lawn neophyte, took a set off Federer, and lost another narrowly in a tiebreak.
 Roddick fought back from a set down to beat Nadal 46, 63, 63 in just over two hours  gaining his first victory over Nadal since 2008.
 Federer drew first blood when he broke Agassi for a 42 lead in the first set, but putting that set away wasn't easy.
 After losing the first set, Dubois took charge in the second, catching Cirstea in the final game with a break to tie the match.
 Capturing one break of serve in the first set, Nadal battled through two nine minute plus games in the second set, while saving one break point.
 Monfils got his two break points of the match when leading 21 in the second, but Nadal won the next four points and cruised through the rest of the set.
 Roddick saved his best move for the end, when Chiudinelli was battling to send the match to another set in front of 14,723 fans.
 The match was a far cry from the Monte Carlo final two weeks ago, when Djokovic became the only player to take a set from Nadal on clay this year.
 In topology, open sets and closed sets are dual concepts: the complement of an open set is closed, and vice versa.
 In topology, a branch of mathematics, a discrete space is a topological space in which all sets are open, and a discrete set is a set of isolated points.
 The standard example of a space is the set of integers with the topology of open sets being those with finite complements.
 In short, by decategorifying the category of finite sets, the set of natural numbers was invented.
 To put this more formally, if is a set that can be written as a union for some collection of finite sets, then is countable.
 For example, the category FinSet, whose objects are finite sets and whose morphisms are functions, is a categorification of the set N of natural numbers.
 The set of values of a function when applied to elements of a finite set is finite.
 This is obviously not the case for finite sets, for if you remove n elements from a finite set the cardinality of that set will be reduced by n.
 Alternatively, consider the real numbers with the counting measure, which assigns to each finite set of reals the number of points in the set.
 The name "axiom of choice" refers to one such statement, namely that there exists a choice function for every set of nonempty sets.
 If the axiom of choice holds, then a set is hereditarily of cardinality less than κ if and only if its transitive closure is of cardinality less than κ.
 In fact the statement that every set can be wellordered is equivalent to the axiom of choice.
Categories
 Group
 Information > Science > Mathematics > Sets
 Life > Game > Points > Point
 Nature > Form > Part > Number
 First
Related Keywords
* Back
* Cardinality
* Case
* Different Set
* Elements
* Empty Set
* End
* First
* Form
* Game
* Group
* Help
* Information
* Music
* Name
* Number
* Order
* Part
* People
* Point
* Points
* Power
* Power Set
* Race
* Record
* Result
* Right
* Second
* Second Set
* Set Back
* Set Point
* Set Theory
* Teeth
* Time
* Type
* Way
* Work
* World
* Year
* Years

Books about "Set" in
Amazon.com


