set

Sets and their relationships are often represented by Venn diagrams. The sets are drawn as circles – the area of overlap between the circles shows elements that are common to each set, and thus represent a third set. (Top) A Venn diagram of two intersecting sets and (bottom) a Venn diagram showing the set of whole numbers from 1 to 20 and the subsets P and O of prime and odd numbers, respectively. The intersection of P and O contains all the prime numbers that are also odd.

In mathematics, any collection of defined things (elements), provided the elements are distinct and that there is a rule to decide whether an element is a member of a set. It is usually denoted by a capital letter and indicated by curly brackets {}.

For example, L may represent the set that consists of all the letters of the alphabet. The symbol ∈ stands for ‘is a member of’; thus p ∈ L means that p belongs to the set consisting of all letters, and 4 ∉ L means that 4 does not belong to the set consisting of all letters.

There are various types of sets. A finite set has a limited number of members, such as the letters of the alphabet; an infinite set has an unlimited number of members, such as all whole numbers; an empty or null set has no members, such as the number of people who have swum across the Atlantic Ocean, written as {} or ø; a single-element set has only one member, such as days of the week beginning with M, written as {Monday}. Equal sets have the same members; for example, if W = {days of the week} and S = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}, it can be said that W = S. Sets with the same number of members are equivalent sets. Sets with some members in common are intersecting sets; for example, if R = {red playing cards} and F = {face cards}, then R and F share the members that are red face cards. Sets with no members in common are disjoint sets. Sets contained within others are subsets; for example, V = {vowels} is a subset of L = {letters of the alphabet}.

Sets and their interrelationships are often illustrated by a Venn diagram.

Set

In Egyptian mythology, the god of night, the desert, and of all evils. Portrayed as a grotesque animal with long ears and a tail, Set was the murderer of his brother Osiris, later ruler of the underworld.

Osiris was first trapped in a chest and thrown into the Nile, and then cut into 14 pieces and scattered throughout Egypt. In revenge for his father's death, Horus fought Set in hand-to-hand combat and emasculated him; Set tore out his nephew's eye. The gods intervened to stop the fight, healed their wounds, and passed judgement in favour of Horus; Set was ordered to return the eye, which was later given to Osiris.

He was worshipped by the nomadic Hyksos peoples.

SET

Form of public key infrastructure developed by the credit card companies Visa and Mastercard. SET provides confidentiality and integrity of information, and authentication of customer and merchant, but is expensive and difficult to implement.

set

In drama, the scenery and props (properties, the movable objects used by the actors or decorating the set).

set

In music, the old English name for a suite. Also a series, normally of pitches but also of rhythms or other musical parameters, used in the composition of a piece. See also serialism.