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In mathematics, a set is a collection of different things; 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 sets.
- Mathematical Object
Schlegel wireframe 8-cell. A mathematical object is an...
- Element (Mathematics)
In mathematics, an element (or member) of a set is any one...
- Infinite Set
The set of all rational numbers is a countably infinite set...
- Mathematical Object
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole.
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
A set is an idea from mathematics. A set has members (also called elements ). A set is defined by its members, so any two sets with the same members are the same (e.g., if set and set have the same members, then ). Example of a set of polygons. A set cannot have the same member more than once.
The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. Before this period, sets were not considered to be mathematical objects, and logic, although used for mathematical proofs, belonged to philosophy and was not specifically studied by mathematicians.
Relative to measurability. Borel set. Baire set. Measurable set, Non-measurable set. Universally measurable set. Relative to a measure. Negligible set. Null set. Haar null set. In a linear space. Convex set. Balanced set, Absolutely convex set. Relative to the real/complex numbers. Fractal set.
A set is a collection of objects (without repetitions). To describe a set, either list all its elements explicitly, or use a descriptive method. Intervals are sets of real numbers. The elements in a set can be any type of object, including sets. We can even have a set containing dissimilar elements.
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