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## set

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"set." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. 15 Dec. 2017 <http://www.encyclopedia.com>.

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## set

set
1. A collection of distinct objects of any sort. The objects in the set are called its members or elements. An element can occur at most once in a set and order or arrangement is unimportant. If x is a member of the set S it is customary to write xS

If x is not a member of S this can be expressed as xS

and is equivalent to NOT (xS)

i.e. ∈ and ∉ can be regarded as operators. When any element in set S is also in set T, and vice versa, the two sets are said to be identical or equal.

A finite set has a fixed finite number of members and a notation such as {Ada, Pascal, Cobol, C}

is possible; the members are separated by commas and here are just the names of various programming languages. When the number of elements is not finite, the set is said to be infinite and explicit enumeration of the elements is not then possible.

Infinite and finite sets can be described using a predicate or statement such as p(x) that involves x and is either true or false, thus {x | p(x)}

This is read as “the set of all elements x for which p(x) is true”, the elements being characterized by the common property p. Examples of sets described in this way are (letting R be the set of real numbers): {(x,y) | xR, yR and x + y = 9} {n | n is a prime number} {l | l is the name of a language}

There is an implicit assumption here that there is some algorithm for deciding whether p(x) is true or false in any particular case.

The idea of a set is fundamental to mathematics. It forms the basis for all ideas involving functions, relations, and indeed any kind of algebraic structure. Authors differ considerably in the way they define sets. A mathematical logician will distinguish carefully between classes and sets, basically to ensure that paradoxes such as Russell's paradox cannot occur in sets. However, the informal definition is adequate for most purposes.

2. Any data structure representing a set of elements. One example is a characteristic vector.

3. To cause the condition or state of a switch, signal, or storage location to change to the positive condition.

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# Set

In Egyptian mythology Set (or Seth) was the evil brother of the deities Osiris, Isis, and Nephthys. The son of the earth god Geb and the sky goddess Nut, Set tore himself from his mother's body before he was fully formed. For this reason, he used pieces of animals to complete his body. Among the many animals associated with Set were the pig, donkey, scorpion, antelope, hippopotamus, and crocodile.

deity god or goddess

Originally a sky and storm god, Set was highly regarded at first, and his cult was one of the oldest in Egypt. Each day he rode across the sky in the sun ship of the great god Ra*; each night as he traveled through the underworld, he killed the mighty serpent Aapep to protect Ra. In time, however, Set became jealous of the other gods, and his treachery against them turned him into one of the chief forces of evil.

Above all, Set envied his brother Osiris, who ruled as king of Egypt while Set served only as lord of the desert. Determined to destroy his brother, Set arranged a great feast to which he invited Osiris and the other gods. He had carpenters construct a large and magnificently decorated box, which he placed at the entrance hall of his palace. When Osiris arrived, Set tricked him into getting inside the box. As soon as Osiris stepped into the box, Set ordered his servants to nail down the lid, seal it with molten lead, and throw it into the Nile River. Osiris drowned.

Their sister Isis, who was also Osiris's wife, searched for her husband and eventually found the box. She brought Osiris back to life long enough to conceive a son, Horus. However, Set found Osiris's body and cut it into pieces. Then he scattered the pieces throughout Egypt. Nephthys, Set's wife and sister, helped Isis locate the pieces and resurrect Osiris. After that, Osiris went to rule the underworld as king of the dead.

Horus later fought Set to avenge his father's death. In a series of great battles, Horus defeated his evil uncle. He would have killed him except that Isis took pity on Set and asked Horus to spare his life. Ancient Egyptians viewed the battle between Horus and Set as the ultimate struggle between good and evil.

cult group bound together by devotion to a particular person, belief, or god

resurrect to raise from the dead

As the cult of Osiris grew in Egypt, worship of Set declined. Eventually, Egyptian priests declared Set to be an enemy of the gods. His name and image were removed from many monuments, and he became associated with Aapep (known also as Apopis), the monstrous serpent that he had once defeated each night to protect Ra.

See also Egyptian Mythology; Horus; Isis; Nut; Osiris; Ra (Re); Serpents and Snakes.

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"Set." Myths and Legends of the World. . Encyclopedia.com. 15 Dec. 2017 <http://www.encyclopedia.com>.

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## set

set In mathematics, a defined collection of objects. The objects are called the elements or members of the set. The number of members can be finite or infinite, or even be zero (the null set). Various relations can exist between two sets, A and B: A equals B if both sets contain exactly the same members; A is included in, or is a subset of, B if all members of A are members of B; disjoint sets have no members in common; overlapping sets have one or more common members. Operations on sets produce new sets: the union of A and B contains the members of both A and B; the intersection of A and B contains only those members common to both sets.

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"set." World Encyclopedia. . Encyclopedia.com. 15 Dec. 2017 <http://www.encyclopedia.com>.

"set." World Encyclopedia. . Encyclopedia.com. (December 15, 2017). http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/set

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# Set

a number of items of a similar nature usually used together; a group of persons who habitually meet socially or through some other contact.

Examples : set of acquaintances, 1779; of artisans, 1705; of bells, 1771; of books, 1596; of booksellers; of bowlsBrewer ; of chairs; of china; of customers, 1866; of eggs; of games; of golfclubsBrewer, of fishing hooks, 1867; of horses, 1687; of motives, 1897; of oysters (crop of young oysters in any locality), 1881; of pains, 1742; of punches, 1683; of shuttlecocks, 1711; of smugglers, 1815; of ushers.

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"Set." Dictionary of Collective Nouns and Group Terms. . Encyclopedia.com. 15 Dec. 2017 <http://www.encyclopedia.com>.

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## set

set. Term normally applied to atonal mus., meaning a small group of notes (a cell or a unit) which the composer or the analyst of the work concerned deems to be of structural significance, e.g. the notes B–C–F in the 4th of Webern's 5 Movements for str. qt. In a serial work the series or part of it may be considered as the set. And so can the opening notes of Beethoven's 5th Sym.!

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"set." The Concise Oxford Dictionary of Music. . Encyclopedia.com. 15 Dec. 2017 <http://www.encyclopedia.com>.

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## Set (in Egyptian religion)

Set or Seth (both: sĕt or sāt), in Egyptian religion, god of evil. Set was a sun god of predynastic Egypt, but he gradually degenerated from being a beneficent deity into being a god of evil and darkness. In a widespread Egyptian myth he murdered his brother Osiris and was in turn defeated by Horus, the son of Osiris. The Greeks identified Set with Typhon.

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## set (in mathematics)

set, in mathematics, collection of entities, called elements of the set, that may be real objects or conceptual entities. Set theory not only is involved in many areas of mathematics but has important applications in other fields as well, e.g., computer technology and atomic and nuclear physics.

Definition of Sets

A set must be well defined; i.e., for any given object, it must be unambiguous whether or not the object is an element of the set. For example, if a set contains all the chairs in a designated room, then any chair can be determined either to be in or not in the set. If there were no chairs in the room, the set would be called the empty, or null, set, i.e., one containing no elements. A set is usually designated by a capital letter. If A is the set of even numbers between 1 and 9, then A={2, 4, 6, 8}. The braces, {}, are commonly used to enclose the listed elements of a set. The elements of a set may be described without actually being listed. If B is the set of real numbers that are solutions of the equation x2=9, then the set can be written as B={x:x2=9} or B={x|x2=9}, both of which are read: B is the set of all x such that x2=9; hence B is the set {3,-3}.

Membership in a set is indicated by the symbol ∈ and nonmembership by ∉; thus, xA means that element x is a member of the set A (read simply as "x is a member of A" ) and yA means y is not a member of A. The symbols ⊂ and ⊃ are used to indicate that one set A is contained within or contains another set B;AB means that A is contained within, or is a subset of, B; and AB means that A contains, or is a superset of, B.

Operations on Sets

There are three basic set operations: intersection, union, and complementation. The intersection of two sets is the set containing the elements common to the two sets and is denoted by the symbol ∩. The union of two sets is the set containing all elements belonging to either one of the sets or to both, denoted by the symbol ∪. Thus, if C={1, 2, 3, 4} and D={3, 4, 5}, then CD={3, 4} and CD={1, 2, 3, 4, 5}. These two operations each obey the associative law and the commutative law, and together they obey the distributive law.

In any discussion the set of all elements under consideration must be specified, and it is called the universal set. If the universal set is U={1, 2, 3, 4, 5} and A={1, 2, 3}, then the complement of A (written A′) is the set of all elements in the universal set that are not in A, or A′={4, 5}. The intersection of a set and its complement is the empty set (denoted by ∅), or AA′=∅; the union of a set and its complement is the universal set, or AA′=U. See also symbolic logic.

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## set

set1 pt., pp. set cause to sit; (hence) place, put, with many spec. applications lit. and fig. OE.; †subside OE. (late); (of a luminary) go down, sink below the horizon XIII (prob. after ON. refl. setjask). OE. settan = OS. settian (Du. zetten), OHG. sezzan (G. setzen), ON. setja, Goth. satjan :- Gmc. *satjan, causative of *setjan SIT.

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"set." The Concise Oxford Dictionary of English Etymology. . Encyclopedia.com. 15 Dec. 2017 <http://www.encyclopedia.com>.

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## set

set2 set out one's stall display or show off one's abilities, attributes, or experience in order to convince someone of one's suitability for something. From a street trader's setting up a stall to display goods for sale.

See also set a beggar on horseback, set the world on fire, set the pace, set in stone, set a thief to catch a thief.

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## set

set3 number or group of persons XIV; number or collection of things XVI. orig., in sense ‘sect’ — OF. sette :- L. secta SECT, but in later developments infl. by SET1 and apprehended as ‘number set together’ (cf. SET2); the application to things may be partly due to MLG. gesette set or suite of things.

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## set

set2
A. setting of a luminary XIV;

B. in various applications of the senses ‘act of setting’, ‘manner or position in which a thing is set’, ‘something that is set’ from XV. Mainly f. SET1; but sense A may be in part due to ON. -setr, -seta (as in sǒlarsetr, -seta sunset).

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## set

set1 make a dead set at make a determined attempt to win the liking of; originally (early 19th century) a sporting idiom, referring to the manner in which a dog such as a setter or pointer stands stock still with its muzzle pointing in the direction of its prey.

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## Set

Set / set/ variant spelling of Seth.

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## set

setabet, aiguillette, anisette, Annette, Antoinette, arête, Arlette, ate, baguette, banquette, barbette, barrette, basinet, bassinet, beget, Bernadette, beset, bet, Bette, blanquette, Brett, briquette, brochette, brunette (US brunet), Burnett, cadet, caravanette, cassette, castanet, cigarette (US cigaret), clarinet, Claudette, Colette, coquette, corvette, couchette, courgette, croquette, curette, curvet, Debrett, debt, dinette, diskette, duet, epaulette (US epaulet), flageolet, flannelette, forget, fret, galette, gazette, Georgette, get, godet, grisette, heavyset, Jeanette, jet, kitchenette, La Fayette, landaulet, launderette, layette, lazaret, leatherette, let, Lett, lorgnette, luncheonette, lunette, Lynette, maisonette, majorette, maquette, Marie-Antoinette, marionette, Marquette, marquisette, martinet, met, minaret, minuet, moquette, motet, musette, Nanette, net, noisette, nonet, novelette, nymphet, octet, Odette, on-set, oubliette, Paulette, pet, Phuket, picquet, pillaret, pincette, pipette, piquet, pirouette, planchette, pochette, quartet, quickset, quintet, regret, ret, Rhett, roomette, rosette, roulette, satinette, septet, serviette, sestet, set, sett, sextet, silhouette, soubrette, spinet, spinneret, statuette, stet, stockinet, sublet, suffragette, Suzette, sweat, thickset, threat, Tibet, toilette, tret, underlet, upset, usherette, vedette, vet, vignette, vinaigrette, wagonette, wet, whet, winceyette, yet, Yvette •quodlibet • alphabet •ramjet, scramjet •propjet • turbojet • etiquette • outlet •triolet • calumet • cermet