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A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
Universe set and complement notation. ... and hence together with the distributive and complement laws above, show that it is a Boolean algebra. ...
The notation / is also used, and is less ambiguous. Denotes the set of rational numbers (fractions of two integers). It is often denoted also by . Denotes the set of p-adic numbers, where p is a prime number.
Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...
Set theory begins with a fundamental binary relation between an object o and a set A. If o is a member (or element) of A, the notation o ∈ A is used. A set is described by listing elements separated by commas, or by a characterizing property of its elements, within braces { }. [8]
Notation and terminology. The binary relation "is an element of", also called set membership, is denoted by the symbol "∈". Writing means ...
In set-builder notation, ... together with the operations given by union, intersection, and complementation, is a Boolean algebra. In this Boolean algebra, ...