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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 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.
Frontispiece of Operum Mathematicorum Pars Prima (1657) by John Wallis, the first volume of Opera Mathematica including a chapter entitled Mathesis Universalis.. Mathesis universalis (from Greek: μάθησις, mathesis "science or learning", and Latin: universalis "universal") is a hypothetical universal science modelled on mathematics envisaged by Descartes and Leibniz, among a number of ...
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.
The domain of a structure is an arbitrary set; it is also called the underlying set of the structure, its carrier (especially in universal algebra), its universe (especially in model theory, cf. universe), or its domain of discourse. In classical first-order logic, the definition of a structure prohibits the empty domain. [citation needed] [5]
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.
The universe is often defined as "the totality of existence", or everything that exists, everything that has existed, and everything that will exist. [24] In fact, some philosophers and scientists support the inclusion of ideas and abstract concepts—such as mathematics and logic—in the definition of the universe.
Different mathematical models of the universe's global geometry can be constructed, all consistent with current observations and general relativity. Hence, it is unclear whether the observable universe matches the entire universe or is significantly smaller, though it is generally accepted that the universe is larger than the observable universe.