# Set

(redirected from*Mathematical set*)

Also found in: Dictionary, Thesaurus, Medical, Legal.

## 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**Osiris**

, in Egyptian religion, legendary ruler of predynastic Egypt and god of the underworld. He was the son of the sky goddess Nut and the earth god Geb. The great benefactor of mankind, Osiris brought to the people knowledge of agriculture and civilization.

**.....**Click the link for more information. and was in turn defeated by Horus, the son of Osiris. The Greeks identified Set with Typhon.

## 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 *x*^{2}=9, then the set can be written as *B*={*x*:*x*^{2}=9} or *B*={*x*|*x*^{2}=9}, both of which are read: *B* is the set of all *x* such that *x*^{2}=9; hence *B* is the set {3,−3}.

Membership in a set is indicated by the symbol ∈ and nonmembership by ∉; thus, *x*∈*A* means that element *x* is a member of the set *A* (read simply as "*x* is a member of *A*") and *y*∉*A* 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;* *A*⊂*B* means that *A* is contained within, or is a subset of, *B;* and *A*⊃*B* 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 *C*∩*D*={3, 4} and *C*∪*D*={1, 2, 3, 4, 5}. These two operations each obey the associative law**associative law,**

in mathematics, law holding that for a given operation combining three quantities, two at a time, the initial pairing is arbitrary; e.g., using the operation of addition, the numbers 2, 3, and 4 may be combined (2+3)+4=5+4=9 or 2+(3+4)=2+7=9.**.....** Click the link for more information. and the commutative law**commutative law,**

in mathematics, law holding that for a given binary operation (combining two quantities) the order of the quantities is arbitrary; e.g., in addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7.**.....** Click the link for more information. , and together they obey the distributive law**distributive law.**

In mathematics, given any two operations, symbolized by * and +, the first operation, *, is distributive over the second, +, if *a**(*b*+*c*)=(*a***b*)+(*a***c*) for all possible choices of *a, b,* and *c.***.....** Click the link for more information. .

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 *A*∩*A′*=∅; the union of a set and its complement is the universal set, or *A*∪*A′*=*U.* See also symbolic logic**symbolic logic**

or **mathematical logic,**

formalized system of deductive logic, employing abstract symbols for the various aspects of natural language. Symbolic logic draws on the concepts and techniques of mathematics, notably set theory, and in turn has contributed to**.....** Click the link for more information. .

## Set

a young plant raised for subsequent planting in a garden, park, or similar place. Sets of fruit crops are obtained in fruit nurseries; they are usually produced from grafted seedlings (stocks). Sets of berry crops (currant, gooseberry) are one-year-old nongrafted plants. The root suckers of raspberry plants are used as sets. In forestry, sets are young trees that have been raised from seeds or cuttings.

## Set

(also Seth), in ancient Egyptian religion and mythology, a god initially venerated in the city of Ombos and whose cult then apparently spread throughout Upper Egypt and the northwest part of the Nile Delta. Set was considered a god of the desert and of foreign countries. According to Egyptian mythology, he was the brother and murderer of Osiris and was subsequently defeated by Horus, the son of Osiris. He was depicted in the form of an unidentifiable animal.

## set

[set]## set

**1.**The condition reached by a cement paste, mortar, or concrete when it has lost plasticity to an arbitrary degree; usually measured in terms of resistance to penetration or deformation; initial set refers to first stiffening, final set to attainment of significant rigidity.

**2.**The hydration and hardening of a gypsum plaster.

**3.**To convert a liquid resin or an adhesive to a hardened state by chemical or physical action such as condensation, polymerization, oxidation, vulcanization, gelation, hydration, or the evaporation of volatile constituents.

**4.**See

**saw set.**

**5.**In plastering, to apply a finishing coat.

**6.**To drive a nail below the surface of the wood (with the use of a nail set).

**7.**The strain remaining after complete release of the load producing a deformation.

**8.**Collectively, the pieces of scenery that make up a theatrical scene.

**9.**To coat the back surface of a tile so that it will adhere to the surface to which it is applied.

## set

**1.**

*Maths*

*logic*

**a.**a collection of numbers, objects, etc., that is treated as an entity: {3, the moon} is the set the two members of which are the number 3 and the moon

**b.**(in some formulations) a class that can itself be a member of other classes

**2.**any apparatus that receives or transmits television or radio signals

**3.**

*Tennis*

*squash*

*badminton*one of the units of a match, in tennis one in which one player or pair of players must win at least six games

**4.**

**a.**the number of couples required for a formation dance

**b.**a series of figures that make up a formation dance

**5.**

**a.**a band's or performer's concert repertoire on a given occasion

**b.**a continuous performance

## SET

(security)## SET

(electronics)## SET

(standard)## set

(4)For each set there is a predicate (or property) which is true for (possessed by) exactly those objects which are elements of the set. The predicate may be defined by the set or vice versa. Order and repetition of elements within the set are irrelevant so, for example, 1, 2, 3 = 3, 2, 1 = 1, 3, 1, 2, 2.

Some common set of numbers are given the following names:

N = the natural numbers 0, 1, 2, ...

Z = the integers ..., -2, -1, 0, 1, 2, ...

Q = the rational numbers p/q where p, q are in Z and q /= 0.

R = the real numbers

C = the complex numbers.

The empty set is the set with no elements. The intersection of two sets X and Y is the set containing all the elements x such that x is in X and x is in Y. The union of two sets is the set containing all the elements x such that x is in X or x is in Y.

See also set complement.

## Set

**(1)**An internal DOS/Windows command that sets environment variables, which are stored values used by the operating system and many applications. To display the current values, type:

set

SETTING A VALUE

The

**set**command creates an environment variable and places a value into it. Blank spaces matter. The following examples create NEWVAR with a value of "a."

set newvar=acreate newvar with "a"set newvar= acreate newvar with " a"set newvar=delete newvar

**(2)**(SET) (

**S**ecure

**E**lectronic

**T**ransaction) A standard protocol from MasterCard and Visa for securing online credit card payments via the Internet. In this three-way transaction, the user, merchant and bank must use the SET protocols.

Credit card data and a digital certificate (for authentication) is stored in a plug-in to the user's Web browser. The order is received by a SET-enabled merchant server that passes encrypted payment information to the bank. Approval is electronically sent to the merchant.