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In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. [1] In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set . [ 2 ]
MathType is a graphical editor for mathematical equations, allowing entry with the mouse or keyboard in a full graphical WYSIWYG environment. [2] This contrasts to document markup languages such as LaTeX where equations are entered as markup in a text editor and then processed into a typeset document as a separate step.
A mathematical markup language is a computer notation for representing mathematical formulae, based on mathematical notation.Specialized markup languages are necessary because computers normally deal with linear text and more limited character sets (although increasing support for Unicode is obsoleting very simple uses).
Cantor's theorem and its proof are closely related to two paradoxes of set theory. Cantor's paradox is the name given to a contradiction following from Cantor's theorem together with the assumption that there is a set containing all sets, the universal set. In order to distinguish this paradox from the next one discussed below, it is important ...
SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.
In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S ...
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The power set axiom does not specify what subsets of a set exist, only that there is a set containing all those that do. [2] Not all conceivable subsets are guaranteed to exist. In particular, the power set of an infinite set would contain only "constructible sets" if the universe is the constructible universe but in other models of ZF set ...