set
Intuitively a set is a collection of entities, called its members or elements, itself considered as a single object. The fundamental principle of the theory of sets is the principle of extensionality : sets are identical if and only if they have the same members. The union of two sets is the set A ? B that has as members all the things that are members of A or B (or both). The intersection A n B is the set of things that are members of both. Sets are disjoint when they have no common members. The complement of a set B within a set A, A – B, is the set of elements that are in A but not in B. A set A is a subset of a set B when all the things that belong to A belong to B. This makes A itself a subset of A; a subset of A not itself identical with A is a proper subset of A. Sets are all members of the set-theoretic hierarchy. To obtain this we start with a list of elements: things that are not themselves sets (in case this sounds mathematically impure, we can start simply with Ø, the null set). At the bottom level we have the set of all these. At the next level we add all sets of atoms; at each level we have everything from the previous level, plus all sets of them. We then take the infinite union of all these sets, and continue ‘forever’. In fact, if we start with the null set at the lowest level, each ascending level becomes the power set of the set that constitutes the previous level.

Philosophy dictionary. . 2011.

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  • set — set …   Dictionnaire des rimes

  • Set — (s[e^]t), v. t. [imp. & p. p. {Set}; p. pr. & vb. n. {Setting}.] [OE. setten, AS. setton; akin to OS. settian, OFries. setta, D. zetten, OHG. sezzen, G. setzen, Icel. setja, Sw. s[ a]tta, Dan. s?tte, Goth. satjan; causative from the root of E.… …   The Collaborative International Dictionary of English

  • Set — (s[e^]t), v. t. [imp. & p. p. {Set}; p. pr. & vb. n. {Setting}.] [OE. setten, AS. setton; akin to OS. settian, OFries. setta, D. zetten, OHG. sezzen, G. setzen, Icel. setja, Sw. s[ a]tta, Dan. s?tte, Goth. satjan; causative from the root of E.… …   The Collaborative International Dictionary of English

  • set — /set/, v., set, setting, n., adj., interj. v.t. 1. to put (something or someone) in a particular place: to set a vase on a table. 2. to place in a particular position or posture: Set the baby on his feet. 3. to place in some relation to something …   Universalium

  • set — [ sɛt ] n. m. • 1893; mot anglais I ♦ Anglic. Manche d un match de tennis, de ping pong, de volley ball. Gagner le premier set. Partie de tennis en cinq sets. Balle de set, qui décide du gain du set. II ♦ Set ou set de table : ensemble des… …   Encyclopédie Universelle

  • set — [set] vt. set, setting [ME setten < OE settan (akin to Ger setzen & Goth satjan < Gmc * satjan), caus. formation “to cause to sit” < base of SIT] 1. to place in a sitting position; cause to sit; seat 2. a) to cause (a fowl) to sit on… …   English World dictionary

  • set*/*/*/ — [set] (past tense and past participle set) verb I 1) [T] to put someone or something in a position, or to be in a particular place or position Tea s ready, he told them and set down the tray.[/ex] She set the baby on the floor to play.[/ex] 2)… …   Dictionary for writing and speaking English

  • set — Ⅰ. set [1] ► VERB (setting; past and past part. set) 1) put, lay, or stand in a specified place or position. 2) put, bring, or place into a specified state. 3) cause or instruct (someone) to do something. 4) give someone (a task) …   English terms dictionary

  • Set — (s[e^]t), v. i. 1. To pass below the horizon; to go down; to decline; to sink out of sight; to come to an end. [1913 Webster] Ere the weary sun set in the west. Shak. [1913 Webster] Thus this century sets with little mirth, and the next is likely …   The Collaborative International Dictionary of English

  • Set — has 464 separate definitions in the Oxford English Dictionary, the most of any English word; its full definition comprises 10,000 words making it the longest definition in the OED. Set may refer to:In mathematics and science:*Set (mathematics), a …   Wikipedia

  • Set! — jeu de société Trouverez vous les 4 sets ? (solution en bas de page) {{{licence}}} Auteur Marsha Falco Éditeur …   Wikipédia en Français

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