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The relationship between universe and complement. In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation.
In mathematics, a space is a set (sometimes known as a universe) endowed with a structure defining the relationships among the elements of the set. A subspace is a subset of the parent space which retains the same structure.
In physics and cosmology, the mathematical universe hypothesis (MUH), also known as the ultimate ensemble theory, is a speculative "theory of everything" (TOE) proposed by cosmologist Max Tegmark. [ 1 ] [ 2 ] According to the hypothesis, the universe is a mathematical object in and of itself.
The culmination that Tegmark seeks to lead us to is the "Level IV multiverse". This level contends that the Universe is not just well described by mathematics, but, in fact, is mathematics. All possible mathematical structures have a physical existence, and collectively, give a multiverse that subsumes all others.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
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The change in terminology is sometimes called "conglomerate convention". [7]: 6 The first step, made by Mac Lane, [1]: 195 [2]: 23 is to apply the term "class" only to subsets of . Mac Lane does not redefine existing set-theoretic terms; rather, he works in a set theory without classes (ZFC, not NBG/MK), calls members of "small sets", and states that the small sets and the classes satisfy the ...